{"id":26469,"date":"2023-03-19T08:59:23","date_gmt":"2023-03-19T08:59:23","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26469"},"modified":"2024-02-05T15:25:41","modified_gmt":"2024-02-05T15:25:41","slug":"terminating-decimals-definition-theorem-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/terminating-decimal","title":{"rendered":"Terminating Decimals &#8211; Definition, Theorem, Examples"},"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-cbdb54bc-d8e5-4b01-b099-c47a0c2bf5dc\" 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\/terminating-decimal#0-what-is-a-terminating-decimal>What Is a Terminating Decimal?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/terminating-decimal#2-how-to-identify-a-terminating-decimal>How to Identify a Terminating Decimal<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/terminating-decimal#4-what-is-a-non-terminating-decimal>What Is a Non-Terminating Decimal?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/terminating-decimal#7-solved-examples-on-terminating-decimals>Solved Examples on Terminating Decimals<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/terminating-decimal#8-practice-problems-on-terminating-decimals>Practice Problems on Terminating Decimals<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/terminating-decimal#9-frequently-asked-questions-on-terminating-decimals>Frequently Asked Questions on Terminating Decimals<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-terminating-decimal\">What Is a Terminating Decimal?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>A terminating decimal is a decimal in which the digits after the decimal point terminate. <\/strong>This means that the digits after the decimal are finite in number. It is a decimal that has an end-digit.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Terminating decimal examples: 17.28, 6.02, \u221222.45435, 0.45, etc.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">A decimal is a number that consists of a whole number and a fractional part. There are two types of decimals categorized on the basis of the number of digits after the decimal point.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Terminating Decimals<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Non-terminating Decimals<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s consider an example of terminating decimals in real life. If you have two chocolates and you ate half of one of the chocolates, then you are left with 1.5 chocolate. This is a terminating decimal since there is only one digit after the decimal point.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"524\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/15-chocolate-as-an-example-of-a-terminating-decimal.webp\" alt=\"1.5 chocolate as an example of a terminating decimal\" class=\"wp-image-36923\" title=\"1.5 chocolate as an example of a terminating decimal\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/15-chocolate-as-an-example-of-a-terminating-decimal.webp 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/15-chocolate-as-an-example-of-a-terminating-decimal-300x254.webp 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-terminating-decimal-definition\">Terminating Decimal Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Terminating decimals can be defined as decimals that have a finite number of digits after the decimal point.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example:<\/strong> 25.37 is a terminating decimal.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"640\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/representing-a-terminating-decimal-number-place-value-blocks.png\" alt=\"Representing a terminating decimal number place value blocks\" class=\"wp-image-36925\" title=\"Representing a terminating decimal number place value blocks\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/representing-a-terminating-decimal-number-place-value-blocks.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/representing-a-terminating-decimal-number-place-value-blocks-291x300.png 291w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Note that all decimals that terminate are rational numbers. In simple words, all terminating decimals are rational numbers. Thus, they can be written in the form of a fraction, as they are rational numbers.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: <\/strong>1.5 can also be written as $\\frac{15}{10}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2:<\/strong> $\\frac{1}{8} = 0.125$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"618\" height=\"459\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/terminating-decimal-example.png\" alt=\"Terminating decimal example\" class=\"wp-image-36926\" title=\"Terminating decimal example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/terminating-decimal-example.png 618w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/terminating-decimal-example-300x223.png 300w\" sizes=\"auto, (max-width: 618px) 100vw, 618px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s see the steps for the long division where we divide 1 by 8 to get the quotient as 0.125. Here, the long division ends after a certain point and we get the remainder 0.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"619\" height=\"617\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/terminating-decimal-in-the-long-division-example.png\" alt=\"Terminating decimal in the long division example\" class=\"wp-image-36927\" title=\"Terminating decimal in the long division example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/terminating-decimal-in-the-long-division-example.png 619w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/terminating-decimal-in-the-long-division-example-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/terminating-decimal-in-the-long-division-example-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/terminating-decimal-in-the-long-division-example-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/terminating-decimal-in-the-long-division-example-120x120.png 120w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/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 eplus-wrapper\" id=\"2-how-to-identify-a-terminating-decimal\">How to Identify a Terminating Decimal<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">You can identify a terminating decimal number using the following conditions:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">It always has a finite number of digits after the decimal point.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">It is a rational number.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">If the simplified form of a rational number has the denominator in the form of $2^m \\times 5^n$, where <em>m<\/em> and <em>n<\/em> are positive integers, then it has a terminating decimal expansion.<\/li>\n<\/ul>\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 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           checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-theorems-on-terminating-decimals\">Theorems on Terminating Decimals<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If a rational number <em>k<\/em> has a terminating decimal expansion, then k can be expressed in the form $\\frac{p}{q}$, such that $q \\neq 0$, where p and q are co-prime and the prime factorization of q is of the form $2^m \\times 5^n$, where <em>m<\/em> and <em>n<\/em> are non-negative integers.<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">Example:$ 0.5 = \\frac{5}{10} = \\frac{1}{2}$<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If <em>k<\/em> $= \\frac{p}{q}$ is a rational number, where q \u2260 0 is a rational number with prime factorization $2^m \\times 5^n$, where <em>m<\/em> and <em>n<\/em> are non-negative integers, then <em>k <\/em>is a terminating decimal number.<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">Example: $\\frac{7}{8}= \\frac{7}{2^3} = 0.875$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-what-is-a-non-terminating-decimal\">What Is a Non-Terminating Decimal?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">These numbers are called non-terminating decimals because the digits after the decimal point do not terminate. This means that the digits after the decimal are infinite in number. These are further divided into two categories:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Recurring Non-terminating Decimal Numbers<\/strong>: In these decimal numbers, the digits after the decimal point are infinite as well as repeating. This means the digits after the decimal place digits follow a specific pattern.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">For example, $4.213213\u2026.= 4.213, 2.34343434\u2026.= 2.34, 1.9999999\u2026.= 1.9$, etc.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In these examples, one or more than one digit after the decimal keeps repeating.&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Non-recurring Non-terminating Decimal Numbers<\/strong>: In these decimal numbers, the digits after the decimal point are infinite as well as non-repeating. This means the digits after the decimal place digits don\u2019t follow a specific pattern.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">For example, 3.23447452\u2026, 1.36098757\u2026, 0.9374940\u2026, etc.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Such decimals fall under the category of irrational numbers.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s see the steps for long division where we divide 11 by 9. Here, the process of long division goes on. The remainder never becomes 0.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"619\" height=\"657\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/non-terminating-decimal-example.png\" alt=\"Non-terminating decimal example\" class=\"wp-image-36928\" title=\"Non-terminating decimal example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/non-terminating-decimal-example.png 619w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/non-terminating-decimal-example-283x300.png 283w\" sizes=\"auto, (max-width: 619px) 100vw, 619px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-facts-related-to-terminating-decimals\">Facts Related to Terminating Decimals<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Pi $(\\pi) = 3.14159&#8230;$ is a non-terminating and non-repeating decimal number. It is an irrational number.&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Recurring decimal numbers can be written by putting a bar sign or dots over the digits repeating after the decimal point. Example: $1.66666\u2026.= 1.6$<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Decimal numbers are of two types: terminating decimal numbers and non-terminating decimal numbers. Terminating decimals and non-terminating but recurring decimal numbers are called rational numbers and can be expressed as $\\frac{P}{q}, q \\neq 0$, $p$ and $q$ are integers. On the other hand, non-terminating and non-recurring decimals are called irrational numbers and cannot be expressed in the rational form. Let\u2019s solve a few examples based on the concept of terminating decimals.<br><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-solved-examples-on-terminating-decimals\">Solved Examples on Terminating Decimals<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Out of the given fractions <\/strong>$\\frac{7}{5}, \\frac{5}{15}, \\frac{7}{42}$<strong>, and <\/strong>$\\frac{4}{10}$<strong> , which one will result in a terminating decimal?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The fractions can be expressed as:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{7}{5} = 1.4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{5}{15} = 0.333&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{7}{42} = 1.666\u2026$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{4}{10} = 0.4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the fraction resulting in terminating decimals are $\\frac{4}{10}$ and $\\frac{7}{5}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Is the decimal number 1.111 a terminating decimal?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Terminating decimal is a decimal that has an end-digit.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The decimal 1.111 is a terminating decimal since it has a finite number of digits after the decimal point.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Any rational number with its denominator in the form of _______, where <\/strong><strong><em>m<\/em><\/strong><strong> and <\/strong><strong><em>n<\/em><\/strong><strong> are non-negative integers is a terminating 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\">Any rational number with its denominator in the form of $2^m \\times 5^n$, where <em>m<\/em> and <em>n<\/em> are non-negative integers is a terminating decimal number, otherwise it is non-terminating.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. Find out whether 5.348 is a terminating or a non-terminating decimal.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The given decimal is 5.348.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiply and divide it by 1000, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$5.348 = \\frac{5.348 \\times 1000}{1000} = \\frac{5348}{1000}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">It\u2019s a terminating decimal because it can be expressed in the form of p\/q.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. Is <\/strong>$\\frac{4}{3}$<strong> a terminating or a non-terminating decimal?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>On dividing we get, $\\frac{4}{3} = 1.333333\u2026$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Which means it is a repeating decimal.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-practice-problems-on-terminating-decimals\">Practice Problems on Terminating Decimals<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Terminating Decimals - Definition, Theorem, 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\">A _______ is a terminating decimal number.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Natural number<\/div><div class=\"spq_answer_block\" data-value=\"1\">A whole number<\/div><div class=\"spq_answer_block\" data-value=\"2\">A rational number<\/div><div class=\"spq_answer_block\" data-value=\"3\">An integer<\/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: Natural number<br\/>A rational number is a terminating decimal number and can be expressed in the form of $\\frac{p}{q}$. <\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following is a terminating decimal?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">0.23232323...<\/div><div class=\"spq_answer_block\" data-value=\"1\">0.333333...<\/div><div class=\"spq_answer_block\" data-value=\"2\">0.8<\/div><div class=\"spq_answer_block\" data-value=\"3\">0.22222222...<\/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: 0.8<br\/>0.8 is a terminating decimal since it has only one digit after the decimal. <\/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\">Without using a calculator, find out which of the following fractions will change into a terminating decimal?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{2}{33}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{5}{69}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{10}{81}$<\/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: $\\frac{1}{10}$<br\/>Only $\\frac{1}{10}$ has a denominator of the form of $2^m \\times 5^n$. Any rational number with its denominator in the form of $2^m \\times 5^n$, where m and n are positive integers are terminating decimal numbers, otherwise they are non-terminating.<\/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\">Find the odd one out.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5.36363636\u2026<\/div><div class=\"spq_answer_block\" data-value=\"1\">0.234565432\u2026<\/div><div class=\"spq_answer_block\" data-value=\"2\">8.76<\/div><div class=\"spq_answer_block\" data-value=\"3\">3.03892657853164\u2026<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 8.76<br\/>8.76 is the odd one out as it is a terminating decimal. The rest are non-terminating decimals.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">A number is a non-terminating decimal number if ________________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">it has only 1 digit after the decimal point<\/div><div class=\"spq_answer_block\" data-value=\"1\">it has only no digit after the decimal point<\/div><div class=\"spq_answer_block\" data-value=\"2\">it has an infinite number of digits after the decimal point<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/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: it has an infinite number of digits after the decimal point<br\/>A number is a non-terminating decimal number if it has an infinite number of digits after the decimal point.<\/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\": \"Terminating Decimals - Definition, Theorem, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Terminating Decimals\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple 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number is a terminating decimal number and can be expressed in the form of $$\\\\frac{p}{q}$$. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A rational number\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A rational number is a terminating decimal number and can be expressed in the form of $$\\\\frac{p}{q}$$. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"An integer\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A rational number is a terminating decimal number and can be expressed in the form of $$\\\\frac{p}{q}$$. \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Natural number\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A rational number is a terminating decimal number and can be expressed in the form of $$\\\\frac{p}{q}$$. \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A rational number is a terminating decimal number and can be expressed in the form of $$\\\\frac{p}{q}$$. \"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is a terminating decimal?\",\n                    \"text\": \"Which of the following is a terminating decimal?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"0.8 is a terminating decimal since it has only one digit after the decimal. \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.23232323...\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"0.8 is a terminating decimal since it has only one digit after the decimal. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.333333...\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"0.8 is a terminating decimal since it has only one digit after the decimal. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.22222222...\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"0.8 is a terminating decimal since it has only one digit after the decimal. \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"0.8\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"0.8 is a terminating decimal since it has only one digit after the decimal. \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"0.8 is a terminating decimal since it has only one digit after the decimal. \"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Without using a calculator, find out which of the following fractions will change into a terminating decimal?\",\n                    \"text\": \"Without using a calculator, find out which of the following fractions will change into a terminating decimal?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Only $$\\\\frac{1}{10}$$ has a denominator of the form of $$2^m \\\\times 5^n$$. Any rational number with its denominator in the form of $$2^m \\\\times 5^n$$, where m and n are positive integers are terminating decimal numbers, otherwise they are non-terminating.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{2}{33}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Only $$\\\\frac{1}{10}$$ has a denominator of the form of $$2^m \\\\times 5^n$$. Any rational number with its denominator in the form of $$2^m \\\\times 5^n$$, where m and n are positive integers are terminating decimal numbers, otherwise they are non-terminating.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{5}{69}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Only $$\\\\frac{1}{10}$$ has a denominator of the form of $$2^m \\\\times 5^n$$. Any rational number with its denominator in the form of $$2^m \\\\times 5^n$$, where m and n are positive integers are terminating decimal numbers, otherwise they are non-terminating.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{10}{81}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Only $$\\\\frac{1}{10}$$ has a denominator of the form of $$2^m \\\\times 5^n$$. Any rational number with its denominator in the form of $$2^m \\\\times 5^n$$, where m and n are positive integers are terminating decimal numbers, otherwise they are non-terminating.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{10}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Only $$\\\\frac{1}{10}$$ has a denominator of the form of $$2^m \\\\times 5^n$$. Any rational number with its denominator in the form of $$2^m \\\\times 5^n$$, where m and n are positive integers are terminating decimal numbers, otherwise they are non-terminating.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Only $$\\\\frac{1}{10}$$ has a denominator of the form of $$2^m \\\\times 5^n$$. Any rational number with its denominator in the form of $$2^m \\\\times 5^n$$, where m and n are positive integers are terminating decimal numbers, otherwise they are non-terminating.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the odd one out.\",\n                    \"text\": \"Find the odd one out.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"8.76 is the odd one out as it is a terminating decimal. The rest are non-terminating decimals.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5.36363636\u2026\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"8.76 is the odd one out as it is a terminating decimal. The rest are non-terminating decimals.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.234565432\u2026\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"8.76 is the odd one out as it is a terminating decimal. The rest are non-terminating decimals.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3.03892657853164\u2026\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"8.76 is the odd one out as it is a terminating decimal. The rest are non-terminating decimals.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8.76\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"8.76 is the odd one out as it is a terminating decimal. The rest are non-terminating decimals.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"8.76 is the odd one out as it is a terminating decimal. The rest are non-terminating decimals.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A number is a non-terminating decimal number if ________________.\",\n                    \"text\": \"A number is a non-terminating decimal number if ________________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A number is a non-terminating decimal number if it has an infinite number of digits after the decimal point.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"it has only 1 digit after the decimal point\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A number is a non-terminating decimal number if it has an infinite number of digits after the decimal point.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"it has only no digit after the decimal point\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A number is a non-terminating decimal number if it has an infinite number of digits after the decimal point.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A number is a non-terminating decimal number if it has an infinite number of digits after the decimal point.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"it has an infinite number of digits after the decimal point\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A number is a non-terminating decimal number if it has an infinite number of digits after the decimal point.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A number is a non-terminating decimal number if it has an infinite number of digits after the decimal point.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-frequently-asked-questions-on-terminating-decimals\">Frequently Asked Questions on Terminating Decimals<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-30d938f8-2696-422e-bbca-d5b1a13eed4f\" 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-0-30d938f8-2696-422e-bbca-d5b1a13eed4f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-30d938f8-2696-422e-bbca-d5b1a13eed4f\"><strong>Where are decimals used in our day-to-day life?<\/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-0-30d938f8-2696-422e-bbca-d5b1a13eed4f\">\n\n<p class=\"eplus-wrapper\">Decimals are used in our day-to-day life in measurements like length, weight, and volume. We use decimals when precision in measurement is required.<\/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-1-30d938f8-2696-422e-bbca-d5b1a13eed4f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-30d938f8-2696-422e-bbca-d5b1a13eed4f\"><strong>Is the fraction <\/strong>$\\frac{1}{3}$<strong> equivalent to a terminating decimal?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-30d938f8-2696-422e-bbca-d5b1a13eed4f\">\n\n<p class=\"eplus-wrapper\">No, $\\frac{1}{3}$ is not equivalent to a terminating decimal.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{1}{3} = 0.333&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The digit 3 repeats infinitely. Therefore, the fraction $\\frac{1}{3}$ is equivalent to a recurring decimal.<\/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-2-30d938f8-2696-422e-bbca-d5b1a13eed4f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-30d938f8-2696-422e-bbca-d5b1a13eed4f\"><strong>Is a terminating decimal a rational number?<\/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-2-30d938f8-2696-422e-bbca-d5b1a13eed4f\">\n\n<p class=\"eplus-wrapper\">Yes, a rational number is a terminating decimal number and can be expressed in the form p\/q.<\/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-3-30d938f8-2696-422e-bbca-d5b1a13eed4f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-30d938f8-2696-422e-bbca-d5b1a13eed4f\"><strong>Is 1.5 terminating or non-terminating?<\/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-3-30d938f8-2696-422e-bbca-d5b1a13eed4f\">\n\n<p class=\"eplus-wrapper\">1.5 is a terminating decimal because it has just one digit after the decimal.<\/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-4-30d938f8-2696-422e-bbca-d5b1a13eed4f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-30d938f8-2696-422e-bbca-d5b1a13eed4f\"><strong>How to find if a number is terminating or non-terminating?<\/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-4-30d938f8-2696-422e-bbca-d5b1a13eed4f\">\n\n<p class=\"eplus-wrapper\">If after dividing the number we get the remainder as 0, it is a terminating decimal. If the remainder is not equal to zero, the decimal number is non-terminating.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is a Terminating Decimal? A terminating decimal is a decimal in which the digits after the decimal point terminate. This means that the digits after the decimal are finite in number. It is a decimal that has an end-digit. Terminating decimal examples: 17.28, 6.02, \u221222.45435, 0.45, etc. A decimal is a number that consists &#8230; <a title=\"Terminating Decimals &#8211; Definition, Theorem, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/terminating-decimal\" aria-label=\"More on Terminating Decimals &#8211; Definition, Theorem, 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-26469","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\/26469","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=26469"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26469\/revisions"}],"predecessor-version":[{"id":39917,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26469\/revisions\/39917"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26469"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26469"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26469"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}