{"id":35179,"date":"2023-10-22T21:04:00","date_gmt":"2023-10-22T21:04:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=35179"},"modified":"2023-10-27T17:45:44","modified_gmt":"2023-10-27T17:45:44","slug":"convert-decimal-to-binary-formula-table-facts-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-binary","title":{"rendered":"Convert Decimal To Binary &#8211; Formula, Table, Facts, Examples, FAQs"},"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-8cf25ae5-714a-4cc2-8eff-587b89bfe6e0\" 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-binary#0-what-is-decimal-to-binary-conversion>What Is Decimal to Binary Conversion?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-binary#3-how-to-convert-decimal-numbers-into-binary-numbers>How to Convert Decimal Numbers into Binary Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-binary#5-decimal-to-binary-conversion-table>Decimal to Binary Conversion Table<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-binary#8-solved-examples-on-decimal-to-binary-conversion>Solved Examples on Decimal to Binary Conversion<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-binary#9-practice-problems-on-decimal-to-binary-conversion>Practice Problems on Decimal to Binary Conversion<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-binary#10-frequently-asked-questions-about-decimal-to-binary-conversion>Frequently Asked Questions about Decimal to Binary Conversion<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-decimal-to-binary-conversion\">What Is Decimal to Binary Conversion?<\/h2>\n\n\n\n<p><strong>In the decimal to binary conversion, we convert a given base-10 number into an equivalent base-2 number.&nbsp;<\/strong><\/p>\n\n\n\n<p>For example, the binary equivalent of 5 is (101)<sub>2<\/sub>.&nbsp;<\/p>\n\n\n\n<p>Writing any decimal number in binary simply means finding a number equivalent to it in the binary number system.<\/p>\n\n\n\n<p>Note that there is no decimal to binary formula for direct conversion. Decimal to binary conversion is a process done by dividing the decimal number to 2. Note down all the remainders. Continuous division is carried out until the quotient reaches 0. Writing all the remainders in reverse order we get the equivalent binary number.&nbsp;<\/p>\n\n\n\n<p><strong>Example:<\/strong> 21<sub>10<\/sub> = 10101<sub>2<\/sub><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"575\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-to-binary-conversion-example.png\" alt=\"Decimal to binary conversion example\" class=\"wp-image-35209\" title=\"Decimal to binary conversion example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-to-binary-conversion-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-to-binary-conversion-example-300x278.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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\" id=\"1-what-is-decimal-number-system\">What Is Decimal Number System?<\/h2>\n\n\n\n<p>The decimal number system, also known as the Hindu-Arabic number system, is the base-10 number system. It uses the 10 digits or symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.<\/p>\n\n\n\n<p>It is the most commonly used <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-system\">number system<\/a>. Thus, if the base is not mentioned, the number is considered to be a decimal number.&nbsp;<\/p>\n\n\n\n<p>Each digit in the decimal system has a place value depending upon its position and the place value of every digit is ten times more significant than the previous digit. In the decimal system there are place values as ones, tens, hundreds, thousands, etc. (increasing power of 10).<\/p>\n\n\n\n<p><strong>Example 1:<\/strong> 42 is a decimal number, then place value of 2 is one, and its value is 2 \u00d7 1 = 2 and place value of 4 is ten&nbsp; and its value is&nbsp; 4 \u00d7 10 = 40 .&nbsp;<\/p>\n\n\n\n<p>&nbsp;Let us look some more example for a better understanding,&nbsp;<\/p>\n\n\n\n<p><strong>Example 2: <\/strong>15 = (15)<sub>10<\/sub> = 1 \u00d7 10 + 5&nbsp; \u00d7 1&nbsp;<\/p>\n\n\n\n<p><strong>Example 3: <\/strong>245 = (245)<sub>10<\/sub> = 2 \u00d7 10\u00b2 + 4 \u00d7 10 + 5 \u00d7 1<\/p>\n\n\n\n<p><strong>Example 4: <\/strong>2000 = (2000)<sub>10<\/sub> = 2 \u00d7 10\u00b3 + 0 \u00d7 10\u00b2 + 0 \u00d7 10 + 0 \u00d7 1<\/p>\n\n\n\n<p><strong>Example 5: <\/strong>35.55 = (35.55)<sub>10<\/sub> = 3 \u00d7 10<sup>2<\/sup> + 5 \u00d7 10<sup>1<\/sup> + 5 \u00d7 10<sup>-1<\/sup>+ 5 \u00d7 10<sup>-2<\/sup><\/p>\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 href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-without-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-without-regrouping-missing-numbers.jpeg\" alt=\"Add a Whole and a Decimal Number without 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 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src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-horizontal-timed-practice.jpeg\" alt=\"Add a Whole and a Decimal Number: Horizontal Timed 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            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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\" id=\"2-what-is-binary-number-system\">What Is Binary Number System?<\/h2>\n\n\n\n<p><strong>The binary number system is a base-2 number system in which numbers are represented using only two digits: 0 and 1.<\/strong><\/p>\n\n\n\n<p>Each <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/digit\">digit<\/a> of the binary number system is called a bit. Bit can either be 0 or 1.<\/p>\n\n\n\n<p><strong>Example:<\/strong> 1101 is a four-bit binary number.&nbsp;<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;100001 is a six-bit binary number.<\/p>\n\n\n\n<p>The Most Significant Bit (MSB) is the bit on the far left end of a binary number, while the Least Significant Bit (LSB) is the bit on the far right end (LSB).<\/p>\n\n\n\n<p>In the binary<strong> <\/strong>system, the place values go like ones, twos, fours, etc (increasing power of 2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"458\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/binary-place-values.png\" alt=\"Binary place values\" class=\"wp-image-35211\" title=\"Binary place values\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/binary-place-values.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/binary-place-values-300x222.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-convert-decimal-numbers-into-binary-numbers\">How to Convert Decimal Numbers into Binary Numbers<\/h2>\n\n\n\n<p>To convert <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/decimals\/decimal\">decimal<\/a> numbers to binary, we divide the given decimal number repeatedly by 2 and the remainder are noted down till we get 0 as the final quotient.&nbsp;<\/p>\n\n\n\n<p>Here are the steps for converting decimal numbers into binary:<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Divide the given decimal number by 2 and note down the remainder and quotient.<\/p>\n\n\n\n<p><strong>Step 2<\/strong>: Now, divide the quotient obtained in step 1 by 2, and note down the remainder again.<\/p>\n\n\n\n<p><strong>Step 3:<\/strong> Repeat the above steps until you get 0 as the quotient.<\/p>\n\n\n\n<p><strong>Step 4:<\/strong> Now, write the remainders in the reverse order (from the last to the first).<\/p>\n\n\n\n<p><strong>T<\/strong>he Least Significant Bit (LSB) of the binary number is at the top and the Most Significant Bit (MSB) is at the bottom.<\/p>\n\n\n\n<p><strong>Example:<\/strong> Convert 14<sub>10<\/sub> into binary.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"525\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converting-the-decimal-number-14-to-binary.png\" alt=\"Converting the decimal number 14 to binary\" class=\"wp-image-35212\" title=\"Converting the decimal number 14 to binary\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converting-the-decimal-number-14-to-binary.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converting-the-decimal-number-14-to-binary-300x254.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-how-to-convert-decimal-fraction-into-binary\">How to Convert Decimal Fraction into Binary<\/h2>\n\n\n\n<p>To find the binary equivalent of the decimal fraction, we find the binary equivalent of the integral part and the fractional part separately and add them together to find the answer.<\/p>\n\n\n\n<p>To convert the fractional part into binary, multiply the fractional part of the decimal number repeatedly by 2 and note down the integral part and fractional part of the result. Repeat this process until the fractional part becomes 0.<\/p>\n\n\n\n<p>The answer will be the integral parts obtained in each multiplication (in the right sequence).<\/p>\n\n\n\n<p>Note that if the fractional part is not becoming 0 and if the process goes on, the fractional number will have an infinite length. In such cases, we stop the process when we get the required number of bits.<\/p>\n\n\n\n<p><strong>Example 1:<\/strong> Find the binary fraction equivalent of 0.125<sub>10<\/sub><\/p>\n\n\n\n<p>0.125 \u00d7 2 = 0 + 0.250&nbsp;<\/p>\n\n\n\n<p>0.250 \u00d7 2 = 0 + 0.500&nbsp;&nbsp;<\/p>\n\n\n\n<p>0.500 \u00d7 2 = 1 + 0.000&nbsp;&nbsp;<\/p>\n\n\n\n<p>Thus the binary equivalent of 0.125\u2081\u2080 is 0.001.<\/p>\n\n\n\n<p><strong>Example 2:<\/strong> 0.6875<sub>10<\/sub> = 1011<sub>2<\/sub><\/p>\n\n\n\n<p>0.6875 \u00d7 2 = 1 + 0.375<\/p>\n\n\n\n<p>0.3750 \u00d7 2 = 0 + 0.75<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;0.75 \u00d7 2 = 1 + 0.5<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;0.50 \u00d7 2 = 1 + 0<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-decimal-to-binary-conversion-table\">Decimal to Binary Conversion Table<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Decimal Number<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Binary Number<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><td class=\"has-text-align-left\" data-align=\"left\">10<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">3<\/td><td class=\"has-text-align-left\" data-align=\"left\">11<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">4<\/td><td class=\"has-text-align-left\" data-align=\"left\">100<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">5<\/td><td class=\"has-text-align-left\" data-align=\"left\">101<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">6<\/td><td class=\"has-text-align-left\" data-align=\"left\">110<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">7<\/td><td class=\"has-text-align-left\" data-align=\"left\">111<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">8<\/td><td class=\"has-text-align-left\" data-align=\"left\">1000<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">9<\/td><td class=\"has-text-align-left\" data-align=\"left\">1001<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">0.1<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.00011<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">0.2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.00110<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">0.3<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.01001<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">0.5<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.1<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">0.6<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.10011<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">0.7<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.10110<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">0.8<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.11001<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">0.9<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.11100<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about decimal to binary conversion along with the steps for the conversion. We also learned how to convert <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/decimals\/decimal-fraction\">decimal fractions<\/a> into binary. Let\u2019s solve a few examples based on the decimal to binary conversion.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-facts-about-decimal-to-binary-conversion\">Facts about Decimal to Binary Conversion<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Binary number system has base 2. Binary digits are called &#8220;bits.&#8221;<\/li>\n\n\n\n<li>In binary, each digit&#8217;s position represents a power of 2.<\/li>\n\n\n\n<li>The decimal number system has base 10.<\/li>\n\n\n\n<li>In computer language, one binary digit is called a <strong>bit<\/strong>, two digits are called a <strong>crumb<\/strong>, four digits are called a <strong>nibble<\/strong>, and eight digits are called a <strong>byte<\/strong>.<\/li>\n\n\n\n<li>Binary numbers may have leading zeros, which do not contribute to the value of the number. For example, 00111 is equivalent to 111 in binary.<\/li>\n\n\n\n<li>Converting from binary to decimal involves multiplying each binary digit by the corresponding power of 2 and adding the products to get the decimal value.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-solved-examples-on-decimal-to-binary-conversion\">Solved Examples on Decimal to Binary Conversion<\/h2>\n\n\n\n<p><strong>Example 1: Convert decimal to binary: 100<\/strong><strong><sub>10<\/sub><\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>Let Q represent the Quotient and R represent the Remainder.<\/p>\n\n\n\n<p>100 \u00f7 2 gives Q = 50 and R = 0<\/p>\n\n\n\n<p>50 \u00f7 2 gives Q = 25 and R = 0<\/p>\n\n\n\n<p>25 \u00f7 2 gives Q = 12 and R = 1<\/p>\n\n\n\n<p>12 \u00f7 2 gives Q = 6 and R = 0<\/p>\n\n\n\n<p>6 \u00f7 2 gives Q = 3 and R = 0<\/p>\n\n\n\n<p>3 \u00f7 2 gives Q = 1 and R = 1<\/p>\n\n\n\n<p>1 \u00f7 2 gives Q = 0 and R = 1<\/p>\n\n\n\n<p>Write down the remainders from last to the first to find the binary conversion of the given decimal number.<\/p>\n\n\n\n<p>100\u2081\u2080 = 1100100\u2082<\/p>\n\n\n\n<p><strong>Example 2: Convert the Decimal Number 144 into a Binary Number.<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong><strong>:&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Division by 2<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Quotient<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Remainder<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">144 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">72<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">72 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">36<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">36 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">18<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">18 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">9<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">9 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">4<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">4 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">2 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">1 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Hence, 144\u2081\u2080 = 10010000\u2082<\/p>\n\n\n\n<p><strong>Example 3: Convert 13<\/strong><strong><sub>10<\/sub><\/strong><strong> to base 2 number system.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Division by 2<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Quotient<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Remainder<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">13 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">6<\/td><td class=\"has-text-align-left\" data-align=\"left\">1&nbsp;<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">6 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">3<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">3 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">1 \u00f7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">1&nbsp;<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Hence, 131<sub>10<\/sub> = 1101\u2082<\/p>\n\n\n\n<p><strong>Example 4: Convert 174.25\u2081\u2080 to base 2 number system.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Here, we have to convert decimal fraction to binary.<\/p>\n\n\n\n<p>First, we will find the binary equivalent of 174.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Division by 2<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Quotient<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Remainder<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">174 <strong>\u00f7 <\/strong>2<\/td><td class=\"has-text-align-left\" data-align=\"left\">87<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">87 <strong>\u00f7 <\/strong>2<\/td><td class=\"has-text-align-left\" data-align=\"left\">43<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">43 <strong>\u00f7 <\/strong>2<\/td><td class=\"has-text-align-left\" data-align=\"left\">21<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">21 <strong>\u00f7 <\/strong>2<\/td><td class=\"has-text-align-left\" data-align=\"left\">10<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">10 <strong>\u00f7 <\/strong>2<\/td><td class=\"has-text-align-left\" data-align=\"left\">5<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">5 <strong>\u00f7 <\/strong>2<\/td><td class=\"has-text-align-left\" data-align=\"left\">2<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">2 <strong>\u00f7 <\/strong>2<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">1 <strong>\u00f7 <\/strong>2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>So, the binary equivalent of 174 is 10101110<sub>2<\/sub>.<\/p>\n\n\n\n<p>Next, we find the binary equivalent of 0.25<sub>10<\/sub>.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Multiply by 2<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Result<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">0.25 \u00d7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">0 + 0.50<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">0.5&nbsp; \u00d7 2<\/td><td class=\"has-text-align-left\" data-align=\"left\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1 + 0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Thus, the binary equivalent of&nbsp; 0.25\u2081\u2080 is 0.01<\/p>\n\n\n\n<p>The binary equivalent of 174.25\u2081\u2080 is 10101110 + .0.01 = 10101110.01<\/p>\n\n\n\n<p><strong>Example 5: Convert 10.2<\/strong><strong><sub>10<\/sub><\/strong><strong> to base 2 number system.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p>First we will find the binary equivalent of the integral part of the number that is 10.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td>10 <strong>\u00f7 <\/strong>2<\/td><td>5<\/td><td>0<\/td><\/tr><tr><td>5 <strong>\u00f7 <\/strong>2<\/td><td>2<\/td><td>1<\/td><\/tr><tr><td>2 <strong>\u00f7 <\/strong>2<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>1 <strong>\u00f7 <\/strong>2<\/td><td>0<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Thus, 10<sub>10<\/sub> = 1010<sub>2<\/sub><\/p>\n\n\n\n<p>Now, let\u2019s find the binary equivalent of 0.2.<\/p>\n\n\n\n<p>0.2 \u00d7 2 = 0 + 0.4&nbsp;<\/p>\n\n\n\n<p>0.4 \u00d7 2 = 0 + 0.8&nbsp;<\/p>\n\n\n\n<p>0.8 \u00d7 2 = 1 + 0.6&nbsp;<\/p>\n\n\n\n<p>0.6 \u00d7 2 = 1 + 0.2&nbsp;<\/p>\n\n\n\n<p>Write the integer values obtained in each multiplication to find the answer.<\/p>\n\n\n\n<p>Thus 0.2\u2081\u2080 = 0.0011\u2082<\/p>\n\n\n\n<p>In conclusion, the binary equivalent of 10.2 is the sum of 10102\u2082 and 0.0011\u2082.<\/p>\n\n\n\n<p>10.2\u2081\u2080 =&nbsp; 1010\u2082 + &nbsp;0.0011\u2082 = 1010.0011\u2082.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-practice-problems-on-decimal-to-binary-conversion\">Practice Problems on Decimal to Binary Conversion<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Convert Decimal To Binary - Formula, Table, Facts, Examples, FAQs<\/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\">The binary equivalent of 5 is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">100\u2082<\/div><div class=\"spq_answer_block\" data-value=\"1\">101\u2082<\/div><div class=\"spq_answer_block\" data-value=\"2\">110\u2082<\/div><div class=\"spq_answer_block\" data-value=\"3\">111\u2082<\/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: 101\u2082<br\/>5 \u00f7 2 = 2 R 1<br>\r\n2 \u00f7 2 = 1 R 0<br>\r\n1 \u00f7 2 = 0 R 1<br>\r\nWrite the remainders in the reverse order to find the answer.<br>\r\nThus, the binary equivalent of 5 is 101.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the binary equivalent of 55?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">100111\u2082<\/div><div class=\"spq_answer_block\" data-value=\"1\">110001\u2082<\/div><div class=\"spq_answer_block\" data-value=\"2\">100011\u2082<\/div><div class=\"spq_answer_block\" data-value=\"3\">110111\u2082<\/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: 110111\u2082<br\/>55 \u00f7 2 = 27 with remainder 1<br>\r\n27 \u00f7 2 = 13 with remainder 1<br>\r\n13 \u00f7 2 = 6 with remainder 1<br>\r\n6 \u00f7 2 = 3 with remainder 0<br>\r\n3 \u00f7 2 = 1 with remainder 1<br>\r\n1 \u00f7 2 = 0 with remainder 1<br>\r\nWriting the remainders in the reverse order, we get<br>\r\n5510 =  110111\u2082<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the binary equivalent of 0.75?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">0.11<\/div><div class=\"spq_answer_block\" data-value=\"1\">0.101<\/div><div class=\"spq_answer_block\" data-value=\"2\">1001011<\/div><div class=\"spq_answer_block\" data-value=\"3\">110111<\/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: 0.11<br\/>Conversion of decimal fraction 0.75 into binary is:<br>\r\n0.75 \u00d7 2 = 1 + 0.5<br>\r\n0.5 \u00d7 2 = 1 + 0<br>\r\nHence, the decimal number 0.75 in binary is 0.11.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What is the binary equivalent of $1.1_{10}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1.00011\u2082<\/div><div class=\"spq_answer_block\" data-value=\"1\">1.10101\u2082<\/div><div class=\"spq_answer_block\" data-value=\"2\">1.001\u2082<\/div><div class=\"spq_answer_block\" data-value=\"3\">0.0111\u2082<\/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: 1.00011\u2082<br\/>Integral part: 1 \u00f7 2 = 0 R 1<br>\r\nThus, the binary equivalent of 1 is 1. <br>\r\nFractional part: 0.1 into binary is:<br>\r\n0.1 \u00d7 2 =  0 + 0.2 <br>\r\n0.2 \u00d7 2 = 0 + 0.4 <br>\r\n0.4 \u00d7 2 = 0 + 0.8<br>\r\n0.8 \u00d7 2 = 1 + 0.6  <br>\r\n0.6 \u00d7 2 = 1 + 0.2  <br>\r\nWe can stop the process here since 0.2 is repeated.<br>\r\nThe binary equivalent of 0.2 is 0.00011<br>\r\nHence, 1.1\u2081\u2080 = 1 +  0.00011 = 1.00011\u2082<\/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                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Convert Decimal To Binary - Formula, Table, Facts, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Convert Decimal To Binary\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The binary equivalent of 5 is\",\n                    \"text\": \"The binary equivalent of 5 is\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"5 \u00f7 2 = 2 R 1<br>\r\n2 \u00f7 2 = 1 R 0<br>\r\n1 \u00f7 2 = 0 R 1<br>\r\nWrite the remainders in the reverse order to find the answer.<br>\r\nThus, the binary equivalent of 5 is 101.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"100\u2082\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 \u00f7 2 = 2 R 1<br>\r\n2 \u00f7 2 = 1 R 0<br>\r\n1 \u00f7 2 = 0 R 1<br>\r\nWrite the remainders in the reverse order to find the answer.<br>\r\nThus, the binary equivalent of 5 is 101.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"110\u2082\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 \u00f7 2 = 2 R 1<br>\r\n2 \u00f7 2 = 1 R 0<br>\r\n1 \u00f7 2 = 0 R 1<br>\r\nWrite the remainders in the reverse order to find the answer.<br>\r\nThus, the binary equivalent of 5 is 101.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"111\u2082\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 \u00f7 2 = 2 R 1<br>\r\n2 \u00f7 2 = 1 R 0<br>\r\n1 \u00f7 2 = 0 R 1<br>\r\nWrite the remainders in the reverse order to find the answer.<br>\r\nThus, the binary equivalent of 5 is 101.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"101\u2082\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"5 \u00f7 2 = 2 R 1<br>\r\n2 \u00f7 2 = 1 R 0<br>\r\n1 \u00f7 2 = 0 R 1<br>\r\nWrite the remainders in the reverse order to find the answer.<br>\r\nThus, the binary equivalent of 5 is 101.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"5 \u00f7 2 = 2 R 1<br>\r\n2 \u00f7 2 = 1 R 0<br>\r\n1 \u00f7 2 = 0 R 1<br>\r\nWrite the remainders in the reverse order to find the answer.<br>\r\nThus, the binary equivalent of 5 is 101.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the binary equivalent of 55?\",\n                    \"text\": \"What is the binary equivalent of 55?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"55 \u00f7 2 = 27 with remainder 1<br>\r\n27 \u00f7 2 = 13 with remainder 1<br>\r\n13 \u00f7 2 = 6 with remainder 1<br>\r\n6 \u00f7 2 = 3 with remainder 0<br>\r\n3 \u00f7 2 = 1 with remainder 1<br>\r\n1 \u00f7 2 = 0 with remainder 1<br>\r\nWriting the remainders in the reverse order, we get<br>\r\n5510 =  110111\u2082\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"100111\u2082\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"55 \u00f7 2 = 27 with remainder 1<br>\r\n27 \u00f7 2 = 13 with remainder 1<br>\r\n13 \u00f7 2 = 6 with remainder 1<br>\r\n6 \u00f7 2 = 3 with remainder 0<br>\r\n3 \u00f7 2 = 1 with remainder 1<br>\r\n1 \u00f7 2 = 0 with remainder 1<br>\r\nWriting the remainders in the reverse order, we get<br>\r\n5510 =  110111\u2082\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"110001\u2082\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"55 \u00f7 2 = 27 with remainder 1<br>\r\n27 \u00f7 2 = 13 with remainder 1<br>\r\n13 \u00f7 2 = 6 with remainder 1<br>\r\n6 \u00f7 2 = 3 with remainder 0<br>\r\n3 \u00f7 2 = 1 with remainder 1<br>\r\n1 \u00f7 2 = 0 with remainder 1<br>\r\nWriting the remainders in the reverse order, we get<br>\r\n5510 =  110111\u2082\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"100011\u2082\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"55 \u00f7 2 = 27 with remainder 1<br>\r\n27 \u00f7 2 = 13 with remainder 1<br>\r\n13 \u00f7 2 = 6 with remainder 1<br>\r\n6 \u00f7 2 = 3 with remainder 0<br>\r\n3 \u00f7 2 = 1 with remainder 1<br>\r\n1 \u00f7 2 = 0 with remainder 1<br>\r\nWriting the remainders in the reverse order, we get<br>\r\n5510 =  110111\u2082\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"110111\u2082\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"55 \u00f7 2 = 27 with remainder 1<br>\r\n27 \u00f7 2 = 13 with remainder 1<br>\r\n13 \u00f7 2 = 6 with remainder 1<br>\r\n6 \u00f7 2 = 3 with remainder 0<br>\r\n3 \u00f7 2 = 1 with remainder 1<br>\r\n1 \u00f7 2 = 0 with remainder 1<br>\r\nWriting the remainders in the reverse order, we get<br>\r\n5510 =  110111\u2082\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"55 \u00f7 2 = 27 with remainder 1<br>\r\n27 \u00f7 2 = 13 with remainder 1<br>\r\n13 \u00f7 2 = 6 with remainder 1<br>\r\n6 \u00f7 2 = 3 with remainder 0<br>\r\n3 \u00f7 2 = 1 with remainder 1<br>\r\n1 \u00f7 2 = 0 with remainder 1<br>\r\nWriting the remainders in the reverse order, we get<br>\r\n5510 =  110111\u2082\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the binary equivalent of 0.75?\",\n                    \"text\": \"What is the binary equivalent of 0.75?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Conversion of decimal fraction 0.75 into binary is:<br>\r\n0.75 \u00d7 2 = 1 + 0.5<br>\r\n0.5 \u00d7 2 = 1 + 0<br>\r\nHence, the decimal number 0.75 in binary is 0.11.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.101\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Conversion of decimal fraction 0.75 into binary is:<br>\r\n0.75 \u00d7 2 = 1 + 0.5<br>\r\n0.5 \u00d7 2 = 1 + 0<br>\r\nHence, the decimal number 0.75 in binary is 0.11.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1001011\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Conversion of decimal fraction 0.75 into binary is:<br>\r\n0.75 \u00d7 2 = 1 + 0.5<br>\r\n0.5 \u00d7 2 = 1 + 0<br>\r\nHence, the decimal number 0.75 in binary is 0.11.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"110111\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Conversion of decimal fraction 0.75 into binary is:<br>\r\n0.75 \u00d7 2 = 1 + 0.5<br>\r\n0.5 \u00d7 2 = 1 + 0<br>\r\nHence, the decimal number 0.75 in binary is 0.11.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"0.11\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Conversion of decimal fraction 0.75 into binary is:<br>\r\n0.75 \u00d7 2 = 1 + 0.5<br>\r\n0.5 \u00d7 2 = 1 + 0<br>\r\nHence, the decimal number 0.75 in binary is 0.11.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Conversion of decimal fraction 0.75 into binary is:<br>\r\n0.75 \u00d7 2 = 1 + 0.5<br>\r\n0.5 \u00d7 2 = 1 + 0<br>\r\nHence, the decimal number 0.75 in binary is 0.11.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the binary equivalent of $$1.1_{10}$$?\",\n                    \"text\": \"What is the binary equivalent of $$1.1_{10}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Integral part: 1 \u00f7 2 = 0 R 1<br>\r\nThus, the binary equivalent of 1 is 1. <br>\r\nFractional part: 0.1 into binary is:<br>\r\n0.1 \u00d7 2 =  0 + 0.2 <br>\r\n0.2 \u00d7 2 = 0 + 0.4 <br>\r\n0.4 \u00d7 2 = 0 + 0.8<br>\r\n0.8 \u00d7 2 = 1 + 0.6  <br>\r\n0.6 \u00d7 2 = 1 + 0.2  <br>\r\nWe can stop the process here since 0.2 is repeated.<br>\r\nThe binary equivalent of 0.2 is 0.00011<br>\r\nHence, 1.1\u2081\u2080 = 1 +  0.00011 = 1.00011\u2082\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1.10101\u2082\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Integral part: 1 \u00f7 2 = 0 R 1<br>\r\nThus, the binary equivalent of 1 is 1. <br>\r\nFractional part: 0.1 into binary is:<br>\r\n0.1 \u00d7 2 =  0 + 0.2 <br>\r\n0.2 \u00d7 2 = 0 + 0.4 <br>\r\n0.4 \u00d7 2 = 0 + 0.8<br>\r\n0.8 \u00d7 2 = 1 + 0.6  <br>\r\n0.6 \u00d7 2 = 1 + 0.2  <br>\r\nWe can stop the process here since 0.2 is repeated.<br>\r\nThe binary equivalent of 0.2 is 0.00011<br>\r\nHence, 1.1\u2081\u2080 = 1 +  0.00011 = 1.00011\u2082\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1.001\u2082\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Integral part: 1 \u00f7 2 = 0 R 1<br>\r\nThus, the binary equivalent of 1 is 1. <br>\r\nFractional part: 0.1 into binary is:<br>\r\n0.1 \u00d7 2 =  0 + 0.2 <br>\r\n0.2 \u00d7 2 = 0 + 0.4 <br>\r\n0.4 \u00d7 2 = 0 + 0.8<br>\r\n0.8 \u00d7 2 = 1 + 0.6  <br>\r\n0.6 \u00d7 2 = 1 + 0.2  <br>\r\nWe can stop the process here since 0.2 is repeated.<br>\r\nThe binary equivalent of 0.2 is 0.00011<br>\r\nHence, 1.1\u2081\u2080 = 1 +  0.00011 = 1.00011\u2082\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.0111\u2082\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Integral part: 1 \u00f7 2 = 0 R 1<br>\r\nThus, the binary equivalent of 1 is 1. <br>\r\nFractional part: 0.1 into binary is:<br>\r\n0.1 \u00d7 2 =  0 + 0.2 <br>\r\n0.2 \u00d7 2 = 0 + 0.4 <br>\r\n0.4 \u00d7 2 = 0 + 0.8<br>\r\n0.8 \u00d7 2 = 1 + 0.6  <br>\r\n0.6 \u00d7 2 = 1 + 0.2  <br>\r\nWe can stop the process here since 0.2 is repeated.<br>\r\nThe binary equivalent of 0.2 is 0.00011<br>\r\nHence, 1.1\u2081\u2080 = 1 +  0.00011 = 1.00011\u2082\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1.00011\u2082\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Integral part: 1 \u00f7 2 = 0 R 1<br>\r\nThus, the binary equivalent of 1 is 1. <br>\r\nFractional part: 0.1 into binary is:<br>\r\n0.1 \u00d7 2 =  0 + 0.2 <br>\r\n0.2 \u00d7 2 = 0 + 0.4 <br>\r\n0.4 \u00d7 2 = 0 + 0.8<br>\r\n0.8 \u00d7 2 = 1 + 0.6  <br>\r\n0.6 \u00d7 2 = 1 + 0.2  <br>\r\nWe can stop the process here since 0.2 is repeated.<br>\r\nThe binary equivalent of 0.2 is 0.00011<br>\r\nHence, 1.1\u2081\u2080 = 1 +  0.00011 = 1.00011\u2082\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Integral part: 1 \u00f7 2 = 0 R 1<br>\r\nThus, the binary equivalent of 1 is 1. <br>\r\nFractional part: 0.1 into binary is:<br>\r\n0.1 \u00d7 2 =  0 + 0.2 <br>\r\n0.2 \u00d7 2 = 0 + 0.4 <br>\r\n0.4 \u00d7 2 = 0 + 0.8<br>\r\n0.8 \u00d7 2 = 1 + 0.6  <br>\r\n0.6 \u00d7 2 = 1 + 0.2  <br>\r\nWe can stop the process here since 0.2 is repeated.<br>\r\nThe binary equivalent of 0.2 is 0.00011<br>\r\nHence, 1.1\u2081\u2080 = 1 +  0.00011 = 1.00011\u2082\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-frequently-asked-questions-about-decimal-to-binary-conversion\">Frequently Asked Questions about Decimal to Binary Conversion<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\" 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-0-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\"><strong>How many unique symbols are used in the Binary 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-0-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\">\n\n<p>There are only two symbols used in the binary number system 0 and 1.<\/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-1-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\"><strong>How many unique symbols are used in the Decimal 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-1-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\">\n\n<p>There are ten symbols used in the decimal number system:<br>0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.<\/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-2-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\"><strong>How can we define the base of a 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-2-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\">\n\n<p>Base of a number system depends upon the number of symbols (or digits) we used to denote the numbers of that system,<\/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-3-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\"><strong>What is the value of decimal number 10 in binary?<\/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-3-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\">\n\n<p>Decimal number 10 is equivalent to 1010 in binary.<\/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-4-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\"><strong>What is a byte?<\/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-4-7fcbcda3-6586-4ee6-9dfd-8d9db9e8955d\">\n\n<p>Byte, is the basic unit of information in computer storage and processing. A byte consists of 8 adjacent binary digits (bits).<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Decimal to Binary Conversion? In the decimal to binary conversion, we convert a given base-10 number into an equivalent base-2 number.&nbsp; For example, the binary equivalent of 5 is (101)2.&nbsp; Writing any decimal number in binary simply means finding a number equivalent to it in the binary number system. Note that there is &#8230; <a title=\"Convert Decimal To Binary &#8211; Formula, Table, Facts, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/decimal-to-binary\" aria-label=\"More on Convert Decimal To Binary &#8211; Formula, Table, Facts, Examples, FAQs\">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-35179","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\/35179","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=35179"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35179\/revisions"}],"predecessor-version":[{"id":35217,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35179\/revisions\/35217"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=35179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=35179"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=35179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}