{"id":1488,"date":"2022-04-19T12:34:41","date_gmt":"2022-04-19T12:34:41","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1488"},"modified":"2023-03-13T04:11:59","modified_gmt":"2023-03-13T04:11:59","slug":"base-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/base","title":{"rendered":"Base in Math &#8211; Definition, Types, Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><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-17d9583e-92b7-432e-ac23-5d07d1e8c03e\" 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\/geometry\/base#0-what-is-base-in-math>What Is Base in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/base#2-how-to-show-the-base>How to Show the Base?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/base#11-examples-of-other-number-systems-and-their-bases>Examples of Other Number Systems and Their Bases<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/base#14-solved-examples-on-base-in-math>Solved Examples on Base in Math<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/base#15-practice-problems-on-base-in-math>Practice Problems on Base in Math<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/base#16-frequently-asked-questions-on-base-in-math>Frequently Asked Questions on Base in Math<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"0-what-is-base-in-math\">What Is Base in Math?<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">The number system we use daily is the base-ten number system. It means that it uses ten different digits to represent numbers.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"357\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-1.png\" alt=\"Base ten number system place values\" class=\"wp-image-26013\" title=\"Base ten number system place values\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-1-300x173.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Base in math refers to the number of digits used to form the numbers<\/strong>. We have many number systems that use different bases.\u00a0<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Examples of base in math are as follows:<\/strong><\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The binary number system uses only 2 digits, that is, 0 and 1 to represent the numbers.&nbsp;<\/li>\n\n\n\n<li class=\" eplus-wrapper\">The octal number system uses 8 digits, that is, 0 to 7, to represent the numbers.&nbsp;<\/li>\n\n\n\n<li class=\" eplus-wrapper\">The most common number system that we use in our daily life is the decimal number system that uses the base 10, which uses digits from 0 to 9 for representing numbers.&nbsp;<\/li>\n\n\n\n<li class=\" eplus-wrapper\">We also have a hexadecimal number system that uses 10 digits that is from 0 to 9 and 6 alphabets from A to F to represent the numbers in the number system.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"1-definition-of-a-base-in-math-\">Definition of a Base in Math&nbsp;<\/h3>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Base in math can be defined as the total number of digits or sometimes, the combination of digits and letters that is used to express numbers in a number system<\/strong>.\u00a0<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Another name for the base of a number system is \u201c<strong>radix<\/strong>.\u201d There are many number systems and each one of them has different bases. Numbers in a base start from 0.\u00a0<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Here are a few examples of base numbers in math and the number systems:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"405\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-2.png\" alt=\"Base of different number systems\" class=\"wp-image-26014\" title=\"Base of different number systems\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-2-300x196.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-multiples-of-100-using-base-10-blocks\" 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\/add_sub_pv_add_multiples_100_model_pt.png\" alt=\"Add Multiples of 100 Using Base-10 Blocks 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 Multiples of 100 Using Base-10 Blocks 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-using-base-10-blocks\" 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\/add_sub_pv_add_2d_2d_model_pt.png\" alt=\"Add Using Base-10 blocks 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 Using Base-10 blocks 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\/choose-the-equivalent-value-based-on-place-value\" 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\/place_value_relate_value_diff_places_pt.png\" alt=\"Choose the Equivalent Value Based on Place Value 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\">Choose the Equivalent Value Based on Place Value 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\/compose-numbers-based-on-tens-and-ones\" 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\/place_value_compose_10s_1s_1_pt.png\" alt=\"Compose Numbers based on Tens and Ones 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\">Compose Numbers based on Tens and Ones 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\/count-in-tens-using-base-10-blocks\" 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\/place_value_count_10s_base_10_block_pt.png\" alt=\"Count in Tens using Base 10 Blocks 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\">Count in Tens using Base 10 Blocks 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\/determine-the-tens-and-ones-in-base-10-blocks\" 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\/place_value_how_many_10s_1s_1_100_pt.png\" alt=\"Determine the Tens and Ones in Base 10 Blocks 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\">Determine the Tens and Ones in Base 10 Blocks 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\/find-the-number-using-base-10-blocks\" 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\/place_value_identify_number_3_pt.png\" alt=\"Find the Number using Base 10 Blocks 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\">Find the Number using Base 10 Blocks 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\/how-many-tens-and-how-many-ones-in-base-10-blocks\" 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\/place_value_how_many_10s_1s_1_50_pt.png\" alt=\"How many Tens and How many Ones in Base 10 Blocks 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\">How many Tens and How many Ones in Base 10 Blocks 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\/how-many-tens-and-ones-in-base-10-blocks\" 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\/place_value_how_many_10s_1s_1_pt.png\" alt=\"How many Tens and Ones in Base 10 Blocks 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\">How many Tens and Ones in Base 10 Blocks 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\/identify-the-number-from-base-10-blocks\" 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\/place_value_identify_number_1_pt.png\" alt=\"Identify the Number from Base 10 Blocks 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\">Identify the Number from Base 10 Blocks 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=\"eplus-wrapper wp-block-heading\" id=\"2-how-to-show-the-base\">How to Show the Base?<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">The base of any number is represented by adding a subscript to the number. It is written beside the given number in a smaller size.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">To express a number in a particular base, we consider the following.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The number<\/li>\n\n\n\n<li class=\" eplus-wrapper\">The base<\/li>\n\n\n\n<li class=\" eplus-wrapper\">The position of the number and the base<\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\">Decimal number 563 can be expressed as $563_{10}$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$563_{10} = (5 \\times 10^{2}) + (6 \\times 10^{1}) + (3 \\times 10^{0})$<\/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-multiples-of-10-using-base-10-blocks\" 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-multiples-of-10-using-base-10-blocks.jpeg\" alt=\"Add Multiples of 10 using Base 10 Blocks 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\/compare-using-base-10-blocks\" 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\/compare-using-base-10-blocks.jpeg\" alt=\"Compare Using Base-10 Blocks 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\/identify-the-number-shown-by-base-ten-blocks\" 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\/identify-the-number-shown-by-base-ten-blocks.jpeg\" alt=\"Identify the Number Shown by Base Ten Blocks 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\/identify-the-number-shown-using-base-10-blocks\" 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\/identify-the-number-shown-using-base-10-blocks.jpeg\" alt=\"Identify the Number Shown Using Base 10 Blocks 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\/make-a-number-using-base-ten-blocks\" 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\/make-a-number-using-base-ten-blocks.jpeg\" alt=\"Make a Number Using Base Ten Blocks 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\/represent-the-number-using-base-10-blocks\" 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\/represent-the-number-using-base-10-blocks.jpeg\" 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"eplus-wrapper wp-block-heading\" id=\"3-binary-number-system-base-2\">Binary Number System (Base-2)<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Base-2 number system or binary number system uses only 2 digits, 0 and 1<\/strong>. This system of base is popularly used in computers to store and process data. The digits 0 and 1 are called binary digits or BITS, in the abbreviated form. A subscript 2 is used to identify a base-2 number.\u00a0<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Let\u2019s see how to convert bases in math. We will convert a binary number into its decimal form.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-3.png\" alt=\"Binary to decimal conversion example\" class=\"wp-image-26016\" title=\"Binary to decimal conversion example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-3-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Let\u2019s see another example.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$101_{2} = (1 \\times 2^{0}) + (0 \\times 2^{1}) + (1 \\times 2^{2})$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$= 1 + 2 + 4$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$= 7$<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"4-decimal-numbers-and-their-corresponding-binary-equivalents\">Decimal Numbers and Their Corresponding Binary Equivalents<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">Now, we will see how to convert a decimal number to its corresponding binary number.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Example 1: Let\u2019s find the corresponding binary number of the decimal number 10.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\\frac{10}{2} = 5,\\; remainder\\; = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\\frac{5}{2} = 2,\\; remainder\\; = 1$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\\frac{2}{2} = 1,\\; remainder\\; = 0$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\\frac{1}{2} = 0,\\; remainder\\; = 1$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">We divide the decimal number by 2 until we get 0 and keep track of the remainder, then we write the remainder from last to first, i.e., bottom to top as: 1010<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Hence $10_{10} = 1010_{2}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Example 2: We can also write this using the division method as follows.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"329\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-4.png\" alt=\"Decimal to binary conversion example\" class=\"wp-image-26017\" title=\"Decimal to binary conversion example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-4-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Let us look at a table to better understand the conversions:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"650\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-5.png\" alt=\"First ten decimal numbers and their binary equivalents\" class=\"wp-image-26018\" title=\"First ten decimal numbers and their binary equivalents\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-5-286x300.png 286w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"5-octal-number-system-base-8-\"><strong>Octal Number System (Base-8)<\/strong><\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Base-8 number system uses the 8 digits (0 to 7)<\/strong>. The subscript 8 is used to represent a base-8 number. Let us take an example of a number in the octal number system, and convert into its decimal equivalent.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$401_{8} = (1 \\times 8^{0}) + (0 \\times 8^{1}) + (4 \\times 8^{2})$&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 1 + 0 + 256$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp; &nbsp; &nbsp; &nbsp; $=257$<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"6-decimal-numbers-and-their-corresponding-octal-equivalents\">Decimal Numbers and Their Corresponding Octal Equivalents<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">Now, we will see how to convert a decimal number to its corresponding octal number.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example 1: <\/strong>Let us consider the decimal number 13. The corresponding octal number will be calculated as<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\\frac{13}{8} = 1,\\; remainder\\; = 5$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\\frac{1}{8} = 0,\\; remainder\\; = 1$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">We divide the decimal number by 8 until we get 0 and keep track of the remainder, then we write the remainder from last to first, i.e., bottom to top as: 15<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Hence, the octal number 13 is equal to 15 in the octal number system.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Example 2: Let\u2019s find the octal equivalent of the decimal number 100. Here, we follow the same method but represent the division in a tabular form.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-6.png\" alt=\"Decimal number to octal number conversion\" class=\"wp-image-26019\" title=\"Decimal number to octal number conversion\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-6.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-6-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Let us look at a table to better understand the conversions:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"916\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-7.png\" alt=\"Decimal numbers and their octal equivalents\" class=\"wp-image-26020\" title=\"Decimal numbers and their octal equivalents\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-7.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-7-203x300.png 203w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"7-decimal-number-system-base-10\">Decimal Number System (Base-10)<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>The base-10 number system uses the digits from 0 to 9. It is called base-10 or the decimal number system<\/strong> since there are only ten digits involved in representing any number. It is one of the most commonly used number systems around the world. We use this number system in our everyday life. Let us understand how we count in the base-10 number system. The subscript 10 is used to represent a base-10 number.\u00a0<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Let us take an example.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$743_{10} = (3 \\times 10^{0}) + (4 \\times 10^{1}) + (7 \\times 10^{2})$. We often do not write 10 as the subscript to represent the decimal number system. So, if you see any number without any subscript written, you should understand that it is a base-10 number.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"8-numbers-in-decimal-number-system\">Numbers in Decimal Number System<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">The numbers in the decimal system follow a certain pattern as we observe the sets of ten numbers. If you place the digit 1 in the beginning of the first ten numbers, you get the set of the second ten numbers. Check it out. and so on.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"442\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-8.png\" alt=\"Numbers in Decimal Number System\" class=\"wp-image-26021\" title=\"Numbers in Decimal Number System\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-8.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-8-300x214.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"9-hexadecimal-number-system-base-16\">Hexadecimal Number System (Base-16)<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>The base-16 number system uses numbers as well as alphabets to represent numbers. Numbers from 0 to 9 and alphabets from A to F are used<\/strong>.\u00a0<\/p>\n\n\n\n<p class=\" eplus-wrapper\">The 10 digits and 6 alphabets used are as follows:&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$0,\\; 1,\\; 2,\\; 3,\\; 4,\\; 5,\\; 6,\\; 7,\\; 8,\\; 9,\\; A,\\; B,\\; C,\\; D,\\; E,\\; F$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">The base-16 system is commonly used in digital systems and computers for storage purposes.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Let us convert one hexadecimal number into the decimal number.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$3AE_{16} = (14 \\times 16^{0}) + (10 \\times 16^{1}) + (3 \\times 16^{2})$<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"10-decimal-numbers-and-corresponding-hexadecimal-equivalents-chart\">Decimal Numbers and Corresponding Hexadecimal Equivalents Chart<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">A hexadecimal number is represented as shown in the table given below. Each digit is multiplied by the power of 16 based on its position (the position starts from right to left) and the products are added.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"880\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-9.png\" alt=\"Decimal numbers and their hexadecimal equivalents and so on.\" class=\"wp-image-26022\" title=\"Decimal numbers and their hexadecimal equivalents and so on.\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-9.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-9-211x300.png 211w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Let\u2019s see how we can convert a decimal number into its hexadecimal equivalent.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"307\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-10.png\" alt=\"Decimal to hexadecimal example\" class=\"wp-image-26023\" title=\"Decimal to hexadecimal example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-10.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-10-300x149.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"11-examples-of-other-number-systems-and-their-bases\">Examples of Other Number Systems and Their Bases<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">Now that we have learned about some commonly used base systems, let us see what other base systems there are:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"414\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-11.png\" alt=\"Base names based on the base numbers\" class=\"wp-image-26024\" title=\"Base names based on the base numbers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-11.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-11-300x200.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"12-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">In this article, we learned about the base numbers, number systems, and how the base system in math works. Let\u2019s solve a few examples and practice problems!<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"13-facts-about-base-in-math\">Facts about Base in Math<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The Number Base is also called the Radix. For example, for the decimal system the radix is ten.<\/li>\n\n\n\n<li class=\" eplus-wrapper\">In Roman Numerals, 7 symbols are used to express their number system. Also, there is no symbol for 0!&nbsp;<\/li>\n<\/ul>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"14-solved-examples-on-base-in-math\">Solved Examples on Base in Math<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>1. Convert the following base-10 numbers to their base-2 equivalents.<\/strong><\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\"><strong>20<\/strong><\/li>\n\n\n\n<li class=\" eplus-wrapper\"><strong>123<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">We know that to convert a base-10 number to a base-2 number, we have to divide it repeatedly by 2 until we get zero and then write the remainder from last to first.<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"170\" height=\"173\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-solved-1.png\" alt=\"\" class=\"wp-image-26025\" title=\"Base-10 to base-2 conversion\"\/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">So, $20_{10} = 10100_{2}$<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Let\u2019s find the binary equivalent of $123_{10}$.<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"190\" height=\"290\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-practice-problem.png\" alt=\"Decimal to binary conversion\" class=\"wp-image-26027\" title=\"Decimal to binary conversion\"\/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">So, $123_{10} = 1111011_{2}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>2. Convert the hexadecimal number 7AB<\/strong><strong><sub>16<\/sub><\/strong><strong> to base-10 decimal number.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">The following are steps to convert a hexadecimal number to a decimal number:<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Step 1: Find the decimal equivalent of the hexadecimal alphabet from the table given.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Step 2: Multiply each digit with the power of 16 raised to its positional value taken from right to left. The right-most digit has positional value 0, the second most right has 1 and so on.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Step 3: Now add all the products.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$7AB_{16} = (11 \\times 16^{0}) + (10 \\times 16^{1}) + (7 \\times 16^{2})$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$=11 + 160 + 1792$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$=1963_{10}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Therefore, $7AB_{16} = 1963_{10}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>3. Convert <\/strong>$162_{8}$<strong><sub> <\/sub>from base-8 (octal), then to base-16 (hexadecimal) number system.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">To solve this, we will first convert the number from base-8 (octal number system) to base-10 (decimal number system) and then convert it from base-10 to base-16.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Step 1: Convert $163_{8}$ to base-10.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$162_{8} = (2 \\times 8^{0}) + (6 \\times 8^{1}) + (1 \\times 8^{2})$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$= 2 + 48 + 64$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$= 114_{10}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Step 2: Now, let us convert $114_{10}$ to base-16 (hexadecimal). We do this by dividing 114 repeatedly by 16 until we get a quotient lesser than 16. This is depicted below.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\\frac{114}{16}= 7,\\; remainder\\; = 2$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\\frac{7}{16} = 0,\\; remainder\\; = 7$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Now we take the remainders from last to first, i.e., 7 then 3<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Therefore, $162_{8} = 72_{16}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>4. Add base-8 numbers <\/strong>$25_{8}$<strong> and <\/strong>$32_{8}$<strong> and give the result.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">First we convert both base-8 numbers to base-10 decimal number system<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$25_{8} = (5 \\times 8^{0}) + (2 \\times 8^{1}) = 5 + 16 = 21_{10}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Similarly,$ 32_{8} = (2 \\times 8^{0}) + (3 \\times 8^{1}) = 2 + 24 = 261_{0}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Adding both base-10 numbers: $21 + 26 = 47$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Now, we convert $47_{10}$ to base-8 number<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\\frac{47}{8} = 5,\\; remainder\\; = 7$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$\\frac{7}{8} = 0,\\; remainder\\; = 7$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Hence the sum of the two octal numbers $25_{8}$ and $32_{8}$&nbsp;is $77_{8}$<sub>.<\/sub><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>5. Subtract base-8 numbers <\/strong>$25_{8}$<strong> and <\/strong>$32_{8}$<strong> and give the result.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">First we convert both base-8 numbers to base-10 decimal number system<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$25_{8} = (5 \\times 8^{0}) + (2 \\times 8^{1}) = 5 + 16 = 21_{10}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Similarly, $32_{8} = (2 \\times 8^{0}) + (3 \\times 8^{1}) = 2 + 24 = 26_{10}$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Subtracting both base-10 numbers we get $26 \\;-\\; 21 = 5$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">In the octal number system, 5 is the same as 5 in the decimal number system. Hence, the difference between the two octal numbers $25_{8}$ and $32_{8}$&nbsp;is $5_{8}$.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"15-practice-problems-on-base-in-math\">Practice Problems on Base in Math<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Base in Math - Definition With Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the binary equivalent of 24?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">11000<\/div><div class=\"spq_answer_block\" data-value=\"1\">10110<\/div><div class=\"spq_answer_block\" data-value=\"2\">10101<\/div><div class=\"spq_answer_block\" data-value=\"3\">11100<\/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: 11000<br\/>To convert a decimal number to its equivalent binary, we divide the decimal number by 2 until we get 0 as a quotient and then write the remainder from the last to first, that is, from bottom to top.\r\nTherefore, $24_{10} = 11000_{2}$<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-solved-2-1.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the decimal equivalent of the base-8 number $45_{8}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$20_{8}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$37_{8}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$35_{8}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$34_{8}$<\/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: $37_{8}$<br\/>$45_{8} = (5 \\times 8^{0}) + (4 \\times 8^{1}) = 5 + 32 = 37_{10}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following alphabet is not used in the hexadecimal number system?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">B<\/div><div class=\"spq_answer_block\" data-value=\"1\">C<\/div><div class=\"spq_answer_block\" data-value=\"2\">G<\/div><div class=\"spq_answer_block\" data-value=\"3\">E<\/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: G<br\/>The alphabet G is not used in the hexadecimal number system.<\/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\">What is the value of the hexadecimal number $6BC_{16}$ in base-10 decimal number?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1722<\/div><div class=\"spq_answer_block\" data-value=\"1\">1723<\/div><div class=\"spq_answer_block\" data-value=\"2\">1724<\/div><div class=\"spq_answer_block\" data-value=\"3\">1725<\/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: 1724<br\/>$6BC_{16} = (12 \\times 16^{0}) + (11 \\times 16^{1}) + (6 \\times 16^{2})$<br>\r\n\t$= 12 + 176 + 1536$<br>\r\n\t$= 1724_{10}$<br>\r\nTherefore, $6BC_{16} = 1724_{10}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">What is the base of the ternary base system?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2<\/div><div class=\"spq_answer_block\" data-value=\"1\">4<\/div><div class=\"spq_answer_block\" data-value=\"2\">5<\/div><div class=\"spq_answer_block\" data-value=\"3\">3<\/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: 3<br\/>The base of the ternary base system is 3. It uses the digits 0, 1, and 2.<\/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\": \"Base in Math - Definition With Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Base in Math\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the binary equivalent of 24?\",\n                    \"text\": \"What is the binary equivalent of 24?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"To convert a decimal number to its equivalent binary, we divide the decimal number by 2 until we get 0 as a quotient and then write the remainder from the last to first, that is, from bottom to top.\r\nTherefore, $$24_{10} = 11000_{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10110\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To convert a decimal number to its equivalent binary, we divide the decimal number by 2 until we get 0 as a quotient and then write the remainder from the last to first, that is, from bottom to top.\r\nTherefore, $$24_{10} = 11000_{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10101\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To convert a decimal number to its equivalent binary, we divide the decimal number by 2 until we get 0 as a quotient and then write the remainder from the last to first, that is, from bottom to top.\r\nTherefore, $$24_{10} = 11000_{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"11100\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To convert a decimal number to its equivalent binary, we divide the decimal number by 2 until we get 0 as a quotient and then write the remainder from the last to first, that is, from bottom to top.\r\nTherefore, $$24_{10} = 11000_{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"11000\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"To convert a decimal number to its equivalent binary, we divide the decimal number by 2 until we get 0 as a quotient and then write the remainder from the last to first, that is, from bottom to top.\r\nTherefore, $$24_{10} = 11000_{2}$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-solved-2-1.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"To convert a decimal number to its equivalent binary, we divide the decimal number by 2 until we get 0 as a quotient and then write the remainder from the last to first, that is, from bottom to top.\r\nTherefore, $$24_{10} = 11000_{2}$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/base-solved-2-1.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the decimal equivalent of the base-8 number $$45_{8}$$?\",\n                    \"text\": \"What is the decimal equivalent of the base-8 number $$45_{8}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$45_{8} = (5 \\\\times 8^{0}) + (4 \\\\times 8^{1}) = 5 + 32 = 37_{10}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$20_{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$45_{8} = (5 \\\\times 8^{0}) + (4 \\\\times 8^{1}) = 5 + 32 = 37_{10}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$35_{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$45_{8} = (5 \\\\times 8^{0}) + (4 \\\\times 8^{1}) = 5 + 32 = 37_{10}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$34_{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$45_{8} = (5 \\\\times 8^{0}) + (4 \\\\times 8^{1}) = 5 + 32 = 37_{10}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$37_{8}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$45_{8} = (5 \\\\times 8^{0}) + (4 \\\\times 8^{1}) = 5 + 32 = 37_{10}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$45_{8} = (5 \\\\times 8^{0}) + (4 \\\\times 8^{1}) = 5 + 32 = 37_{10}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following alphabet is not used in the hexadecimal number system?\",\n                    \"text\": \"Which of the following alphabet is not used in the hexadecimal number system?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The alphabet G is not used in the hexadecimal number system.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"B\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The alphabet G is not used in the hexadecimal number system.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"C\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The alphabet G is not used in the hexadecimal number system.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"E\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The alphabet G is not used in the hexadecimal number system.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"G\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The alphabet G is not used in the hexadecimal number system.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The alphabet G is not used in the hexadecimal number system.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of the hexadecimal number $$6BC_{16}$$ in base-10 decimal number?\",\n                    \"text\": \"What is the value of the hexadecimal number $$6BC_{16}$$ in base-10 decimal number?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$6BC_{16} = (12 \\\\times 16^{0}) + (11 \\\\times 16^{1}) + (6 \\\\times 16^{2})$$<br>\r\n\t$$= 12 + 176 + 1536$$<br>\r\n\t$$= 1724_{10}$$<br>\r\nTherefore, $$6BC_{16} = 1724_{10}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1722\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$6BC_{16} = (12 \\\\times 16^{0}) + (11 \\\\times 16^{1}) + (6 \\\\times 16^{2})$$<br>\r\n\t$$= 12 + 176 + 1536$$<br>\r\n\t$$= 1724_{10}$$<br>\r\nTherefore, $$6BC_{16} = 1724_{10}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1723\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$6BC_{16} = (12 \\\\times 16^{0}) + (11 \\\\times 16^{1}) + (6 \\\\times 16^{2})$$<br>\r\n\t$$= 12 + 176 + 1536$$<br>\r\n\t$$= 1724_{10}$$<br>\r\nTherefore, $$6BC_{16} = 1724_{10}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1725\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$6BC_{16} = (12 \\\\times 16^{0}) + (11 \\\\times 16^{1}) + (6 \\\\times 16^{2})$$<br>\r\n\t$$= 12 + 176 + 1536$$<br>\r\n\t$$= 1724_{10}$$<br>\r\nTherefore, $$6BC_{16} = 1724_{10}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1724\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$6BC_{16} = (12 \\\\times 16^{0}) + (11 \\\\times 16^{1}) + (6 \\\\times 16^{2})$$<br>\r\n\t$$= 12 + 176 + 1536$$<br>\r\n\t$$= 1724_{10}$$<br>\r\nTherefore, $$6BC_{16} = 1724_{10}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$6BC_{16} = (12 \\\\times 16^{0}) + (11 \\\\times 16^{1}) + (6 \\\\times 16^{2})$$<br>\r\n\t$$= 12 + 176 + 1536$$<br>\r\n\t$$= 1724_{10}$$<br>\r\nTherefore, $$6BC_{16} = 1724_{10}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the base of the ternary base system?\",\n                    \"text\": \"What is the base of the ternary base system?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The base of the ternary base system is 3. It uses the digits 0, 1, and 2.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The base of the ternary base system is 3. It uses the digits 0, 1, and 2.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The base of the ternary base system is 3. It uses the digits 0, 1, and 2.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The base of the ternary base system is 3. It uses the digits 0, 1, and 2.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"3\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The base of the ternary base system is 3. It uses the digits 0, 1, and 2.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The base of the ternary base system is 3. It uses the digits 0, 1, and 2.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"16-frequently-asked-questions-on-base-in-math\">Frequently Asked Questions on Base in Math<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-a8530bc2-cb60-407b-9671-364784185552\" 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-a8530bc2-cb60-407b-9671-364784185552\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a8530bc2-cb60-407b-9671-364784185552\"><strong>What is 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-0-a8530bc2-cb60-407b-9671-364784185552\">\n\n<p class=\" eplus-wrapper\">A set of digits or numbers that are used to express or write numbers is called a number 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-1-a8530bc2-cb60-407b-9671-364784185552\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a8530bc2-cb60-407b-9671-364784185552\"><strong>What is the most common number system in the world?<\/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-a8530bc2-cb60-407b-9671-364784185552\">\n\n<p class=\" eplus-wrapper\">The decimal number system, or base-10 number system, is the most commonly used number system in the world.<\/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-a8530bc2-cb60-407b-9671-364784185552\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a8530bc2-cb60-407b-9671-364784185552\"><strong>What are natural numbers?<\/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-a8530bc2-cb60-407b-9671-364784185552\">\n\n<p class=\" eplus-wrapper\">Positive whole numbers, excluding 0, i.e, 1, 2, 3, 4\u2026, are called natural numbers.<\/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-a8530bc2-cb60-407b-9671-364784185552\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a8530bc2-cb60-407b-9671-364784185552\"><strong>What is the base of solids?<\/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-a8530bc2-cb60-407b-9671-364784185552\">\n\n<p class=\" eplus-wrapper\">The bottom face of any solid is called its base.<\/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-a8530bc2-cb60-407b-9671-364784185552\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a8530bc2-cb60-407b-9671-364784185552\"><strong>What is the base of an exponent?<\/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-a8530bc2-cb60-407b-9671-364784185552\">\n\n<p class=\" eplus-wrapper\">The base is a number that is raised to a certain power. It tells us what number is being multiplied. Example: In $5^{2}$, the number 5 is the base.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What Is Base in Math? The number system we use daily is the base-ten number system. It means that it uses ten different digits to represent numbers. Base in math refers to the number of digits used to form the numbers. We have many number systems that use different bases.\u00a0 Examples of base in math &#8230; <a title=\"Base in Math &#8211; Definition, Types, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/base\" aria-label=\"More on Base in Math &#8211; Definition, Types, Examples\">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-1488","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\/1488","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=1488"}],"version-history":[{"count":18,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1488\/revisions"}],"predecessor-version":[{"id":26247,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1488\/revisions\/26247"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1488"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1488"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1488"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}