{"id":26116,"date":"2023-03-09T12:24:27","date_gmt":"2023-03-09T12:24:27","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26116"},"modified":"2024-02-05T15:31:34","modified_gmt":"2024-02-05T15:31:34","slug":"decimal-to-octal-steps-methods-conversion-table","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-octal-conversion","title":{"rendered":"Decimal to Octal: Steps, Methods, Conversion Table"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-db478fc8-f438-4df9-a5fc-81a20ed46cd1\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-octal-conversion#0-what-is-decimal-to-octal-conversion-in-math>What Is Decimal to Octal Conversion in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-octal-conversion#2-how-to-convert-decimal-to-octal>How to Convert Decimal to Octal<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-octal-conversion#6-decimal-to-octal-conversion-table>Decimal to Octal Conversion Table<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-octal-conversion#10-solved-examples-on-decimal-to-octal-conversion>Solved Examples on Decimal to Octal Conversion<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-octal-conversion#11-practice-problems-on-decimal-to-octal-conversion>Practice Problems on Decimal to Octal Conversion<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-octal-conversion#12-frequently-asked-questions-on-decimal-to-octal-conversion>Frequently Asked Questions on Decimal to Octal Conversion<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-decimal-to-octal-conversion-in-math\">What Is Decimal to Octal Conversion in Math?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The <strong>decimal number system consists of 10 digits \u2014 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9<\/strong>. It is the most commonly used number system. The octal number system is the base-8 number system and uses the digits 0 to 7.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">A number in the octal number system has base 8. A <strong>number in the decimal number number system has base 10<\/strong>. Here, we will learn the conversion of a decimal number system to an octal number system. In the decimal to octal conversion, a number in the decimal system is converted into its equivalent octal number.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To convert a decimal number to a binary number, we divide it by 2 (since base is 2), and write remainders in the reverse order. So, how do you convert a decimal number to an octal base? To convert decimal to octal, we divide the number by 8 until we get 0 as the quotient, and then write remainders in the reverse order.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s get to know the steps to convert decimal to octal.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimal-fractions-using-equivalence\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_convert_to_equi_frac_to_add_pt.png\" alt=\"Add Decimal Fractions Using Equivalence Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Decimal Fractions Using Equivalence Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimals-greater-than-1-using-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_add_sub_add_dec_greater_than_1_models_pt.png\" alt=\"Add Decimals (Greater than 1) Using Model Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Decimals (Greater than 1) Using Model Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimals-less-than-1-using-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_add_sub_add_dec_less_than_1_models_pt.png\" alt=\"Add Decimals (Less than 1) Using Model Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Decimals (Less than 1) Using Model Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimals-with-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_add_sub_add_dec_with_regrouping_pt.png\" alt=\"Add Decimals with Regrouping Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Decimals with Regrouping Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimals-without-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_add_sub_add_dec_without_regrouping_pt.png\" alt=\"Add Decimals without Regrouping Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Decimals without Regrouping Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/arrange-the-decimal-numbers-from-smallest-to-greatest\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_order_dec_2_pt.png\" alt=\"Arrange the Decimal Numbers From Smallest to Greatest Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Arrange the Decimal Numbers From Smallest to Greatest Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/arrange-the-decimal-numbers-in-an-order\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_order_dec_1_pt.png\" alt=\"Arrange the Decimal Numbers in an Order Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Arrange the Decimal Numbers in an Order Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/build-decimal-numbers-up-to-hundredths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_stranded_10_gm.png\" alt=\"Build Decimal Numbers up to Hundredths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Build Decimal Numbers up to Hundredths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/change-decimal-numbers-into-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_convert_dec_to_frac_tenths_pt.png\" alt=\"Change Decimal Numbers into Fractions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Change Decimal Numbers into Fractions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/change-decimals-from-word-form-to-fraction-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_convert_words_to_frac_tenths_pt.png\" alt=\"Change Decimals from Word Form to Fraction Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Change Decimals from Word Form to Fraction Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-steps-to-convert-decimal-to-octal\">Steps to Convert Decimal to Octal<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The steps to convert a decimal number to its equivalent octal number are as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1:<\/strong> Note down the given decimal number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2<\/strong>: If the specified decimal number is less than 8, its octal equivalent is the same number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$0_{10} = 0_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1_{10} = 1_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2_{10} = 2_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$3_{10} = 3_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$4_{10} = 4_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$5_{10}= 5_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$6_{10}= 6_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$7_{10}= 7_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3:<\/strong> If the number is greater than 7, divide it by 8.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4:<\/strong> Note the remainder we obtain after division.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 5:<\/strong> Steps 3 and 4 should be repeated until the quotient is less than 8.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 6:<\/strong> Now, write the remainders in reverse order (bottom to top). The outcome is the octal number that corresponds to the given decimal number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s understand the steps with an example.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"537\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-to-octal-conversion-example.png\" alt=\"Decimal to octal conversion example\" class=\"wp-image-34625\" title=\"Decimal to octal conversion example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-to-octal-conversion-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-to-octal-conversion-example-300x260.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-horizontal-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-horizontal-addition.jpeg\" alt=\"Add a Whole and a Decimal Number with Regrouping: Horizontal Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-missing-digits\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-missing-digits.jpeg\" alt=\"Add a Whole and a Decimal Number with Regrouping: Missing Digits Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-missing-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-missing-numbers.jpeg\" alt=\"Add a Whole and a Decimal Number with Regrouping: Missing Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-vertical-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-vertical-addition.jpeg\" alt=\"Add a Whole and a Decimal Number with Regrouping: Vertical Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-without-regrouping-horizontal-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-without-regrouping-horizontal-addition.jpeg\" alt=\"Add a Whole and a Decimal Number without Regrouping: Horizontal Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-without-regrouping-missing-digits\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-without-regrouping-missing-digits.jpeg\" alt=\"Add a Whole and a Decimal Number without Regrouping: Missing Digits Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a 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Practice\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-how-to-convert-decimal-to-octal\">How to Convert Decimal to Octal<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">An <strong>octal number is a number with base 8<\/strong>, to convert decimal to octal, we start dividing the number by 8 until we get 0 as the quotient and write the acquired remainder in reverse to derive at the equivalent octal number.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us learn the methods of conversion of decimals to octals.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-decimal-to-octal-conversion-methods\">Decimal to Octal Conversion Methods<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">There are two methods of converting decimals to octals:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">1. Convert Decimal to Binary to Octal<\/p>\n\n\n\n<p class=\"eplus-wrapper\">2. Convert Decimal to Octal<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-method-1-convert-decimal-to-binary-to-octal\">Method 1: Convert Decimal to Binary to Octal<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">In this method, we first find the binary equivalent of the given number. Once the binary number is obtained, we convert it into an octal number. Let us understand this method using an example.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: Convert&nbsp; <\/strong>$4_{10}$<strong> to octal.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1: Decimal to Binary<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, we have to convert <strong>&nbsp;<\/strong>$4_{10}$ to binary first. For that, we will divide the given number by 2 as the base of binary numbers is 2.<\/p>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Division by 2<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Quotient<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Remainder<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">$4 \\div 2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$2 \\div 2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$1 \\div 2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>1<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Writing the numbers downwards to upwards, we get $100_{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, 4 is $100_{2}$ in the binary system.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">You can also write this process simply, using the column division as shown below and save your efforts of writing out a big table!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"433\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converting-the-number-4-to-binary-which-is-100.png\" alt=\"Converting the number 4 to binary, which is 100\" class=\"wp-image-34626\" title=\"Converting the number 4 to binary, which is 100\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converting-the-number-4-to-binary-which-is-100.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converting-the-number-4-to-binary-which-is-100-300x210.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2: Binary to Octal<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, let us convert $100_{2}$ to the octal system.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Here\u2019s the important part!<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><em>Group all the 1s and 0s in the binary number in sets of three, starting from the far right. Add zeros to the left of the last digit if you don&#8217;t have enough digits to make a set of three. Identify the octal equivalent of the binary numbers in each group. For that, take a look at the binary to octal conversion table.<\/em>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Binary to Octal Conversion Table:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>BinaryNumber<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>OctalNumber<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">000<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">001<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">010<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">011<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">100<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">101<\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">110<\/td><td class=\"has-text-align-center\" data-align=\"center\">6<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">111<\/td><td class=\"has-text-align-center\" data-align=\"center\">7<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><em>Alt tag: Binary to octal conversion table<\/em><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, for the binary number 100, we have only one group.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can see that $100_{2}$ is $4_{8}$ in octal.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-method-2-convert-decimal-to-octal\">Method 2: Convert Decimal to Octal<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">In this method, the decimal number is divided by 8, each time a reminder is obtained from the previous digit. Once the quotient is less than 8, we obtain the octal number by writing the remainder in reverse order. If the given decimal number is less than 8 the octal number is the same.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us understand this with the help of an example.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: Convert <\/strong>$416_{10}$<strong> to octal.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Divide the given number by 8.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Division by 8<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Quotient<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Remainder<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">$416 \\div 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">52<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$52 \\div 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">6<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>4<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$6 \\div 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>6<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Since the quotient is zero now, we stop the division.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, by taking the remainders in reverse order, we get the equivalent octal number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, $(416)_{10} = (640)_{8}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Note that we can also represent this division as shown below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"359\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converting-the-decimal-number-416-to-octal.png\" alt=\"Converting the decimal number 416 to octal\" class=\"wp-image-34627\" title=\"Converting the decimal number 416 to octal\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converting-the-decimal-number-416-to-octal.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converting-the-decimal-number-416-to-octal-300x174.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Write remainders in reverse order to get the octal number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$416_{10} = 640_{8}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-decimal-to-octal-conversion-table\">Decimal to Octal Conversion Table<\/h2>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Decimal<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Equivalent Octal Number<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Decimal<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Equivalent Octal Number<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>0<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>9<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">11<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>1<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>10<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">12<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>2<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>11<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">13<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>3<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>12<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">14<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>4<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>13<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">15<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>5<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>14<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">16<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>6<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">6<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>15<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">17<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>7<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">7<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>16<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">20<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>8<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>17<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">21<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><em>Alt tag: Decimal to octal conversion table<\/em><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-decimal-to-octal-conversion-with-decimal-point\">Decimal to Octal Conversion with Decimal Point<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Decimals have a whole number part and a fractional part separated by a decimal point. To convert a decimal number into octal, we first convert the whole number part into octal form and then convert the fractional part into octal form. And finally we combine the two results to get the final answer.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: Convert 7.16 into octal form.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1: Separate the decimal number<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Separate the decimal number into two parts: the whole number and the fractional part.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, $7.16 = 7 + 0.16$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2: Convert the whole number part into octal.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $(7)_{10} =&nbsp; (7)_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3: Convert the fractional part 0.16 into octal. Multiply the fractional part by 8. Again divide the product into two parts. Multiply the fractional part by 8 until the fractional part is equal to zero.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Multiply by 8<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Result<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Whole part<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Fractional part<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">$0.16 \\times 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">1.28<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>1<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">0.28<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$0.28 \\times 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">2.24<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>2<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">0.24<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$0.24 \\times 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">1.92<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>1<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">0.92<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$0.92 \\times 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">7.36<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>7<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">0.36<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$0.36 \\times 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">2.88<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>2<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\">0.88<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Take the necessary digits after the decimal point. Now, we have 5 digits as an answer.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Write all the whole number parts from top to bottom that derives the octal number of the fractional number.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, $0.16 = 0.12172$\u2026<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$0.16_{Base\\; 10} = 0.12172&#8230;_{Base\\; 8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$0.16_{10} = 0.12172&#8230;_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4: Add the two octal results.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(7)_{10} =&nbsp; (7)_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(0.16)_{10} = (0.12172..)._{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, $(7.16)_{10} = (7.12172..)_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">or $(7.16)_{10} = (7.12172)_{8}$ (approx. value)<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-facts-about-decimal-to-octal-conversion\">Facts about Decimal to Octal Conversion<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The \u201cdec\u201d in decimal means ten and refers to the fact that each position in a decimal number corresponds to ten times more than the next position. For example, the number 325 means 3 hundreds, 2 tens, and 5 ones.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Humans decided to group in tens because that\u2019s how many fingers we have. It made counting and arithmetic a whole lot easier!<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">In 1801, James Anderson criticized the French for basing the metric system on decimal arithmetic. He suggested base 8, for which he coined the term octal.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The main advantage of using the octal number system is that it uses fewer digits than the decimal and hexadecimal number system. So, it has fewer computations and less computational errors.&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The octal number system is widely used in computer application sectors and digital numbering systems. The octal number is also used in the aviation sector in the form of a code.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we have learnt decimal to octal conversion with steps and methods. Let us solve some decimal to octal examples to grasp the concept better.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-solved-examples-on-decimal-to-octal-conversion\">Solved Examples on Decimal to Octal Conversion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: Convert <\/strong>$52_{10}$<strong> to octal.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Division by 8<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Quotient<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Remainder<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">$52 \\div 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">6<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>4<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$6 \\div 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>6<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Writing remainders in reverse order, we get the equivalent octal number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, $(52)_{10} = (64)_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: Convert <\/strong>$18_{10}$<strong> to octal. (Use the method \u201cdecimal to binary to octal.\u201d)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Decimal to Binary:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">First, let us convert the given decimal number 18 into a binary number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To convert decimal to binary, we have to divide the given decimal number by 2.<\/p>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Division by 2<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Quotient<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Remainder<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">$18 \\div 2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">9<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$9 \\div 2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>1<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$4 \\div 2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$2 \\div 2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$1 \\div 2$<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>1<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the binary equivalent for the given decimal number $18_{10}$ is $10010_{2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Binary to Octal:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, lets convert $10010_{2}$ to octal.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Group all the 1s and 0s in the binary number in sets of three, starting from the far right. Add zeros to the left of the last digit if you don&#8217;t have enough digits to make a set of three.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$10010_{2} = 010 | 010_{2}$ \u2026two groups of 3 digits<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Identify the octal equivalent of the binary numbers in each group using the conversion table.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $010_{2} = 2_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, $010010_{2} = 22_{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the octal value of $10010_{2}$ is $22_{8}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 3: Convert 350.2 into octal form.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Separate the decimal number into two parts: the whole and the fractional. So, $350.2 = 350 + 0.2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">First, we will convert 350 into octal form. We will divide 350 by 8 until you get a quotient of zero.<\/p>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Division by 8<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Quotient<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Remainder<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">$350 \\div 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">43<\/td><td class=\"has-text-align-center\" data-align=\"center\">6<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$43 \\div 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$5 \\div 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Hence, 350 is 536 in octal number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, we will convert the fractional part 0.2 into octal. Let\u2019s take only 5 digits.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Multiplied by 8<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Result<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Whole<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Fractional Part<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>$0.6 \\times 8$<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>1.6<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>1<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0.6<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>$0.6 \\times 8$<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>4.8<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>4<\/strong><\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>0.8<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$0.8 \\times 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">6.4<\/td><td class=\"has-text-align-center\" data-align=\"center\">6<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$0.4 \\times 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">3.2<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$0.2 \\times 8$<\/td><td class=\"has-text-align-center\" data-align=\"center\">1.6<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.6<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">We will write all the integer parts from top to bottom that derives the octal number of the fractional number.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, $0.2 = 0.14631$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, adding the integer and fractional part will give us an octal number.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$536 + 0.14631463 = 536.14631$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the octal number of 350.2 is 536.14631.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-practice-problems-on-decimal-to-octal-conversion\">Practice Problems on Decimal to Octal Conversion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Decimal to Octal: Steps, Methods, Conversion Table<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">How many digits does the decimal number system use?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">8<\/div><div class=\"spq_answer_block\" data-value=\"1\">10<\/div><div class=\"spq_answer_block\" data-value=\"2\">2<\/div><div class=\"spq_answer_block\" data-value=\"3\">16<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 10<br\/>The decimal number system uses digits from 0 to 9 to form other numbers.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">How many digits does the octal number system use to represent all the numbers?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">8<\/div><div class=\"spq_answer_block\" data-value=\"1\">10<\/div><div class=\"spq_answer_block\" data-value=\"2\">2<\/div><div class=\"spq_answer_block\" data-value=\"3\">16<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 8<br\/>The Octal number system uses digits from 0 to 7 to form other numbers.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The equivalent octal number of decimal number 5 is  _________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">10<\/div><div class=\"spq_answer_block\" data-value=\"1\">8<\/div><div class=\"spq_answer_block\" data-value=\"2\">14<\/div><div class=\"spq_answer_block\" data-value=\"3\">5<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 5<br\/>The equivalent octal numbers of decimal numbers from 0 to 7 are the same.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Based on the following division table, we can say that $100_{10} =$<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Practice-Problems-on-Decimal-to-Octal-Conversion-H2-4.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$441_{8}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$4410_{8}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$144_{8}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$44_{8}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $144_{8}$<br\/>We write the remainders obtained in the division in the reverse order.<br>\r\nThus, $100_{10} = 144_{8}$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                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other numbers.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Octal number system uses digits from 0 to 7 to form other numbers.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Octal number system uses digits from 0 to 7 to form other numbers.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"16\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The Octal number system uses digits from 0 to 7 to form other numbers.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The Octal number system uses digits from 0 to 7 to form other numbers.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The Octal number system uses digits from 0 to 7 to form other numbers.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The equivalent octal number of decimal number 5 is  _________.\",\n                    \"text\": \"The equivalent octal number of decimal number 5 is  _________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The equivalent octal numbers of decimal numbers from 0 to 7 are the same.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equivalent octal numbers of decimal numbers from 0 to 7 are the same.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equivalent octal numbers of decimal numbers from 0 to 7 are the same.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"14\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equivalent octal numbers of decimal numbers from 0 to 7 are the same.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The equivalent octal numbers of decimal numbers from 0 to 7 are the same.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The equivalent octal numbers of decimal numbers from 0 to 7 are the same.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Based on the following division table, we can say that $$100_{10} =$$\",\n                    \"text\": \"Based on the following division table, we can say that $$100_{10} =$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Practice-Problems-on-Decimal-to-Octal-Conversion-H2-4.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We write the remainders obtained in the division in the reverse order.<br>\r\nThus, $$100_{10} = 144_{8}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$441_{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We write the remainders obtained in the division in the reverse order.<br>\r\nThus, $$100_{10} = 144_{8}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$4410_{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We write the remainders obtained in the division in the reverse order.<br>\r\nThus, $$100_{10} = 144_{8}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$44_{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We write the remainders obtained in the division in the reverse order.<br>\r\nThus, $$100_{10} = 144_{8}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$144_{8}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We write the remainders obtained in the division in the reverse order.<br>\r\nThus, $$100_{10} = 144_{8}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We write the remainders obtained in the division in the reverse order.<br>\r\nThus, $$100_{10} = 144_{8}$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-frequently-asked-questions-on-decimal-to-octal-conversion\">Frequently Asked Questions on Decimal to Octal Conversion<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-45c9f20d-6348-46c4-9429-2fc6c3515b38\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-45c9f20d-6348-46c4-9429-2fc6c3515b38\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-45c9f20d-6348-46c4-9429-2fc6c3515b38\"><strong>What is an octal number system?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-45c9f20d-6348-46c4-9429-2fc6c3515b38\">\n\n<p class=\"eplus-wrapper\">The octal number system is the number system with base 8. It uses the eight digits 0, 1, 2, 3, 4, 5, 6, and 7.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-45c9f20d-6348-46c4-9429-2fc6c3515b38\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-45c9f20d-6348-46c4-9429-2fc6c3515b38\"><strong>How do you convert octal to decimal?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-45c9f20d-6348-46c4-9429-2fc6c3515b38\">\n\n<p class=\"eplus-wrapper\">The octal to decimal conversion is done by using its base number and place values. Here, we convert octal to decimal or base 8 to decimal (base 10). Find the position of every digit. We should count the position from the right direction of the number. The position count starts from 0. Multiply every digit with 8 to the power of their corresponding position. Finally, calculate the sum of all the multiples.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, let\u2019s convert $(16)_{8}$ to decimal.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(16)_{8} = (1 \\times 8^{1}) + (6 \\times 8^{0}) = 8 + 6 = (14)_{10}$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-45c9f20d-6348-46c4-9429-2fc6c3515b38\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-45c9f20d-6348-46c4-9429-2fc6c3515b38\"><strong>What is the hexadecimal number system ?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-45c9f20d-6348-46c4-9429-2fc6c3515b38\">\n\n<p class=\"eplus-wrapper\">The \u201chexadecimal\u201d&nbsp; numbering system uses the base of 16 system. Their format is quite compact and much easier to understand compared to the long binary strings of 1s and 0s. The hexadecimal numbering system uses 16 (sixteen) different digits with a combination of numbers from 0 through to 15.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-45c9f20d-6348-46c4-9429-2fc6c3515b38\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-45c9f20d-6348-46c4-9429-2fc6c3515b38\"><strong>How can we convert binary to octal?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-45c9f20d-6348-46c4-9429-2fc6c3515b38\">\n\n<p class=\"eplus-wrapper\">Octal numbers are the numbers that can be derived from 3 bits of binary numbers. Group all the 1s and 0s in the binary number in sets of three, starting from the far right. Add zeros to the left of the last digit if you don&#8217;t have enough digits to make a set of three. Identify the octal equivalent of the binary numbers in each group. For that, take a look at the binary to octal conversion table.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example: $011010110_{2} =&nbsp; 011| 010 | 110_{2} = 326_{8}$<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Decimal to Octal Conversion in Math? The decimal number system consists of 10 digits \u2014 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It is the most commonly used number system. The octal number system is the base-8 number system and uses the digits 0 to 7. A number in &#8230; <a title=\"Decimal to Octal: Steps, Methods, Conversion Table\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-octal-conversion\" aria-label=\"More on Decimal to Octal: Steps, Methods, Conversion Table\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-26116","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26116","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=26116"}],"version-history":[{"count":27,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26116\/revisions"}],"predecessor-version":[{"id":39929,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26116\/revisions\/39929"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}