{"id":26969,"date":"2023-03-30T11:23:43","date_gmt":"2023-03-30T11:23:43","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26969"},"modified":"2024-02-05T15:33:11","modified_gmt":"2024-02-05T15:33:11","slug":"repeating-decimal-to-fraction-definition-steps-tricks-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/repeating-decimal-to-fraction","title":{"rendered":"Repeating Decimal to Fraction: Definition, Steps, Tricks, 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-927daea4-d049-4613-8bef-1bd82760a7f2\" 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\/repeating-decimal-to-fraction#0-what-is-repeating-decimal-to-fraction-conversion>What Is Repeating Decimal to Fraction Conversion?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/repeating-decimal-to-fraction#1-how-to-convert-repeating-decimal-to-fraction>How to Convert Repeating Decimal to Fraction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/repeating-decimal-to-fraction#8-repeating-decimal-to-fraction-chart>Repeating Decimal to Fraction Chart<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/repeating-decimal-to-fraction#10-solved-examples-of-repeating-decimal-to-fraction>Solved Examples of Repeating Decimal to Fraction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/repeating-decimal-to-fraction#11-practice-problems-on-repeating-decimal-to-fraction>Practice Problems on Repeating Decimal to Fraction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/repeating-decimal-to-fraction#12-frequently-asked-questions-on-repeating-decimal-to-fraction>Frequently Asked Questions on Repeating Decimal to Fraction<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-repeating-decimal-to-fraction-conversion\">What Is Repeating Decimal to Fraction Conversion?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Repeating decimal to fraction conversion is used to express a repeating or recurring decimal in the form of a fraction.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">To convert a \u201cterminating decimal\u201d to a fraction, we simply count the number of digits after the decimal point (which are finite); then, we multiply and divide by the appropriate power of ten.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example:<\/strong> $0.75 = 0.75 \\times \\frac{100}{100} = \\frac{75}{100} = \\frac{3}{4}$&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">This is pretty simple, isn\u2019t it? But what about repeating decimals where we cannot count the number of digits after the decimal point?&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">A repeating decimal (or a recurring decimal) is a decimal number in which a single digit or a group of digits after the decimal point is repeated infinitely.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Examples of repeating decimals:<\/strong>&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$0.4545454545\u2026  = 0.\\overline{45}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$2.333333\u2026  = 2.\\overline{3}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$14.35353535&#8230;  = 14.\\overline{35}$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">So, how to write a repeating decimal as a fraction? Let\u2019s find out!<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimal-fractions-using-equivalence\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_convert_to_equi_frac_to_add_pt.png\" alt=\"Add Decimal Fractions Using Equivalence Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Decimal Fractions Using Equivalence Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimals-greater-than-1-using-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_add_sub_add_dec_greater_than_1_models_pt.png\" alt=\"Add Decimals (Greater than 1) Using Model Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Decimals (Greater than 1) Using Model Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimals-less-than-1-using-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_add_sub_add_dec_less_than_1_models_pt.png\" alt=\"Add Decimals (Less than 1) Using Model Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Decimals (Less than 1) Using Model Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimals-with-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_add_sub_add_dec_with_regrouping_pt.png\" alt=\"Add Decimals with Regrouping Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Decimals with Regrouping Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimals-without-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_add_sub_add_dec_without_regrouping_pt.png\" alt=\"Add Decimals without Regrouping Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Decimals without Regrouping Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-fractions-using-models\" 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\/fractions_add_unlike_models_pt.png\" alt=\"Add Fractions using Models 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 Fractions using Models 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-fractions-with-the-aid-of-a-number-line\" 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\/fractions_add_like_frac_sum_greater_than_1_nl_pt.png\" alt=\"Add Fractions WIth the Aid of a Number LIne 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 Fractions WIth the Aid of a Number LIne 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-like-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\/fractions_add_like_frac_sum_upto_1_pt.png\" alt=\"Add Like 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\">Add Like 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\/add-like-fractions-greater-than-1\" 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\/fractions_find_sum_pt.png\" alt=\"Add Like Fractions Greater than 1 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 Like Fractions Greater than 1 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-like-fractions-to-get-a-sum-greater-than-1\" 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\/fractions_add_like_frac_sum_greater_than_1_pt.png\" alt=\"Add Like Fractions to Get a Sum Greater than 1 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 Like Fractions to Get a Sum Greater than 1 Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-how-to-convert-repeating-decimal-to-fraction\">How to Convert Repeating Decimal to Fraction<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Repeating or Recurring decimals have a repetitive pattern in the digits after the decimal point. With repeating decimals, it is not possible to count the number of decimal places as it is infinite. So, we follow simple steps to convert repeating decimals to fractions.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"2-single-repeating-digit\">Single Repeating Digit<\/h3>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: <\/strong>Convert 0.33333\u2026 to a fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1:<\/strong> Identify the repeating digits and the number of repeating digits in the given decimal number.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, the repeating digit is 3.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Number of repeating digits $= 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2:<\/strong> Equate the decimal number to some variable.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, we assume $x = 0.3333&#8230;$&nbsp; \u2026(1)<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3:<\/strong> First ensure that only the repeating digits come after the decimal point. Then<\/p>\n\n\n\n<p class=\"eplus-wrapper\">multiply both the sides of the equation by a power of ten equal to the number of repeating digits.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = 0.3333&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$10x = 10 \\times 0.3333&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, after multiplying 0.3333&#8230; with 10, the decimal point will shift one position to the right.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$10x = 3.3333&#8230;$ \u2026(2)<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4:<\/strong> We subtract the equation (1) from the equation (2). In this case, we get&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$10x \\;-\\; x = 3.3333&#8230; \\;- \\;0.3333&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$9x = 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 5:<\/strong> Simplify to get the answer.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In this case, we get $x = \\frac{3}{9} = \\frac{1}{3}$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"3-multiple-repeating-digits\">Multiple Repeating Digits<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Now, let us convert a multi-digit repeating decimal to a fraction.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: Convert 5.232323&#8230; to a fraction.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1:<\/strong> The repeating digits in the given decimal number are 23.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The number of repeating digits $= 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2:<\/strong> Let $x = 5.232323&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3:<\/strong> There are two repeating digits. Multiply the above equation by $10^2 = 100$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We will get&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$100x = 10 \\times 0 5.232323&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Shift the decimal point two places to the right.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$100x = 523.232323&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4:<\/strong> Subtract $x = 5.232323&#8230;.$ from $100x = 523.232323&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We will get $99x = 518$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 5:<\/strong> $x = \\frac{518}{99}$&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-non-repeating-digits-followed-by-repeating-digits\">Non-Repeating Digits Followed by Repeating Digits<\/h3>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: Convert 7.324242\u2026 to a fraction.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1: <\/strong>Repeating digits $= 42$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Note that 3 is not repeating.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2: <\/strong>Let $x = 7.3424242&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s first shift the non-repeating digit 3 to the left side of the decimal point by multiplying both sides by 10.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In this case, we get $10x = 73.424242&#8230;$                     \u2013 (1)<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3:<\/strong> Multiply both the sides by the power of 10 equal to the number of repeating digits.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In this case, we get $100x = 7342.424242&#8230;$                     \u2013 (2)<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 4:<\/strong> Subtracting (1) from (2), we get&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1000x \\;-\\; 10x = 7342.424242&#8230; \\;-\\; 73.424242&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow 990x = 7269$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow x = \\frac{7269}{990} = \\frac{2423}{330}$<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-horizontal-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-horizontal-addition.jpeg\" alt=\"Add a Whole and a Decimal Number with Regrouping: Horizontal Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-missing-digits\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-with-regrouping-missing-digits.jpeg\" alt=\"Add a Whole and a Decimal Number with Regrouping: Missing Digits Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a 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class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-without-regrouping-vertical-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-without-regrouping-vertical-addition.jpeg\" alt=\"Add a Whole and a Decimal Number without Regrouping: Vertical Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-a-whole-and-a-decimal-number-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-horizontal-addition.jpeg\" alt=\"Add a Whole and a Decimal Number: 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-horizontal-timed-practice\" 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-horizontal-timed-practice.jpeg\" alt=\"Add a Whole and a Decimal Number: Horizontal Timed Practice\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            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=\"5-repeating-decimal-to-fraction-tricks\">Repeating Decimal to Fraction: Tricks<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">There is an easy trick to convert a repeating decimal to the fraction form. Write the repeating digits as the numerator over the same number of 9s.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"6-repeating-decimal-of-the-form-0overlinepqrs\">Repeating Decimal of the Form $0.\\overline{pqrs}$<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">This trick is applicable only for repeating decimals having only repeating digits after the decimal point.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can write a formula to convert such decimals to fractions as<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$0.\\overline{pqrs} = \\frac{Repeated\\; digit\\; or\\; digits}{Number\\; of\\; 9&#8217;s\\; Equal\\; to\\; the\\; Number\\; of\\; Repeated\\; Digits}&nbsp;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong><em>Converting a fraction to a repeating decimal examples based on this trick:<\/em><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1:<\/strong> $0.2222&#8230; = \\frac{2}{9}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">There is only 1 repeating digit, 2. So, the denominator will be 9.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: <\/strong>$0.323232&#8230; = \\frac{32}{99}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">There are 2 repeating digits, 3 and 2. So, the numerator will be 32, and two 9\u2019s or 99 will come in the denominator.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 3: <\/strong>$0.999&#8230; = \\frac{9}{9} = 1$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"7-repeating-decimal-of-the-form-0pqoverliners\">Repeating Decimal of the Form $0.pq&#8230;\\overline{rs}$<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Here, the decimal consists of some non-repeating digits followed by the repeating digits.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The formula to convert such decimals to fractions is<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$0.pq&#8230;\\overline{rs} = \\frac{pqrs \\;-\\; pq}{No.\\; of\\; 9&#8217;s\\; equal\\; to\\; repeating\\; terms\\; followed\\; by\\; no.\\; of\\; 0&#8217;s\\; equal\\; to\\; non\u2012repeating\\; terms}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong><em>Converting a fraction to a repeating decimal examples based on this trick:<\/em><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: <\/strong>0.12757575\u2026<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$0.12757575\u2026 = \\frac{1275 \\;-\\; 12}{9900} = \\frac{1263}{9900}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2:<\/strong> $0.00345345\u2026 = 0.00\\overline{345}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$0.00\\overline{345} = \\frac{345 &#8211; 00}{99900} = \\frac{345}{99900}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-repeating-decimal-to-fraction-chart\">Repeating Decimal to Fraction Chart<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The chart given below will help to convert some repeating decimals to a fraction.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"346\" height=\"304\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/repeating-decimal-to-fraction-conversion.png\" alt=\"Repeating decimal to fraction conversion\" class=\"wp-image-37164\" title=\"Repeating decimal to fraction conversion\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/repeating-decimal-to-fraction-conversion.png 346w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/repeating-decimal-to-fraction-conversion-300x264.png 300w\" sizes=\"auto, (max-width: 346px) 100vw, 346px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-facts-about-repeating-decimal-to-fraction\">Facts about Repeating Decimal to Fraction<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Rational numbers are of the form $pq; q \\neq 0, p$ and $q$ are integers. Repeating decimals are considered as rational numbers since any repeating decimal can always be written in the form of a fraction.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: <\/strong>$0.5555\u2026 = 0.\\overline{5} = \\frac{5}{9}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-solved-examples-of-repeating-decimal-to-fraction\">Solved Examples of Repeating Decimal to Fraction<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Convert 1.8888&#8230; to fraction.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let $x = 1.8888&#8230;$                                                       \u2014 (1)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiplying both the sides by 10, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$10x = 18.8888&#8230;$                                                       \u2014 (2)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Subtracting (1) from (2), we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$10x \\;-\\; x = 18.888&#8230;\\;-\\;1.888&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$9x = 17$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = \\frac{17}{9}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. <\/strong><strong>What fraction is equivalent to the repeating decimal number 0.434343&#8230;?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let $x=0.434343&#8230;$                                          \u2014 (1)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiplying both the sides by 100, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$100x = 43.434343&#8230;.$                                    \u2014 (2)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Subtracting (1) from (2), we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$100x\\;-\\;x = 43.4343&#8230;\\;-\\;0.4343&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$99x = 43$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = \\frac{43}{99}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Convert 0.567567567\u2026 to fraction.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let $x = 0.567567567&#8230;..$                                       \u2014 (1)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiplying both the sides by 1000, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1000x = 567.567567&#8230;.$                                       \u2014 (2)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Subtracting (1) from (2), we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1000x \\;-\\; x = 567.567567567&#8230;\\;-\\;0.567567567&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$999x = 567$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = \\frac{567}{999} = \\frac{189}{333} = \\frac{63}{111} = \\frac{21}{37}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. <\/strong><strong>Which fraction is equivalent to 2.34444&#8230;?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let $x = 2.34444&#8230;$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiply both the sides by 10 so that all the repeating digits come after the decimal point.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$10x = 23.4444&#8230;$                        \u2014 (1)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiplying both sides by 10&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$100x = 234.4444&#8230;$                          \u2014 (2)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Subtracting (1) from (2), we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$100x\\;-\\;10x = 234.444&#8230;\\;-\\;23.444&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$90x = 211$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = \\frac{21}{190}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. <\/strong><strong>What fraction is equivalent to the repeating decimal number 24.579579&#8230;?<\/strong><strong>&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let $x = 24.579579&#8230;$                                     \u2014 (1)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiplying both the sides by 1000<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1000x = 24579.579579&#8230;$                          \u2014 (2)<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Subtracting (1) from (2), we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1000x \\;-\\; x = 24579.579579&#8230; \\;-\\; 24.579579&#8230;$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$999x = 24555$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = \\frac{24555}{999} = \\frac{8185}{333}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-practice-problems-on-repeating-decimal-to-fraction\">Practice Problems on Repeating Decimal to Fraction<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Repeating Decimal to Fraction: Definition, Steps, Tricks, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">On converting 6.7777\u2026 into a fraction, we get ____<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{73}{9}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{61}{9}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{67}{9}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{60}{9}$<\/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: $\\frac{61}{9}$<br\/>Let $x = 6.7777...$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 10<br>\r\n$10x = 67.7777...$ \t\t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$10x \\;-\\; x = 67.7777...\\;-\\;6.7777...$<br>\r\n$9x = 61$<br>\r\n$x = \\frac{61}{9}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following is the correct fraction for 0.696969\u2026.?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{6}{9}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{20}{33}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{67}{99}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{69}{99}$<\/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: $\\frac{69}{99}$<br\/>Let $x = 0.696969...$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$100x = 69.696969...$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$100x \\;-\\; x = 69.696969... \\;-\\; 0.696969...$<br>\r\n$99x = 69$<br>\r\n$x = \\frac{69}{99}$<\/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\">On converting 0.67777.... into a fraction, we get ____<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{67}{90}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{67}{99}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{61}{99}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{61}{90}$<\/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: $\\frac{61}{99}$<br\/>Let $x = 0.67777.....$<br> \r\nMultiplying both the sides by 10<br>\r\n$10x = 6.7777....$\t\t\t\t \u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$100x = 67.7777....$\t\t\t \u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$100x \\;-\\; 10x = 67.7777.... \\;-\\; 6.7777....$<br>\r\n$90x = 61$\r\n$x = \\frac{61}{90}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">On converting 41.323232\u2026 into a fraction, we get ___.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{4091}{99}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{4132}{99}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{4091}{90}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{4132}{90}$<\/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: $\\frac{4091}{99}$<br\/>Let $x = 41.323232...$ \t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$100x = 4132.323232...$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$100x\\;-\\;x = 4132.323232.. \\;-\\; 41.323232...$<br>\r\n$99x = 4091$<br>\r\n$x = \\frac{4091}{99}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Which of the following is the correct fraction for 0.1233333\u2026?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1239}{99}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{111}{900}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{37}{999}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{37}{330}$<\/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: $\\frac{111}{900}$<br\/>Let $x = 0.123333...$ <br>\r\nMultiplying both the sides by 100<br>\r\n$100x = 12.3333...$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$1000x = 123.3333...$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$1000x \\;-\\; 100x = 123.3333... \\;-\\; 12.3333...$<br>\r\n$900x = 111$<br>\r\n$x = \\frac{111}{900}$<\/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\": \"Repeating Decimal to Fraction: Definition, Steps, Tricks, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Repeating Decimal to Fraction\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"On converting 6.7777\u2026 into a fraction, we get ____\",\n                    \"text\": \"On converting 6.7777\u2026 into a fraction, we get ____\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Let $$x = 6.7777...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 10<br>\r\n$$10x = 67.7777...$$ \t\t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$10x \\\\;-\\\\; x = 67.7777...\\\\;-\\\\;6.7777...$$<br>\r\n$$9x = 61$$<br>\r\n$$x = \\\\frac{61}{9}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{73}{9}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 6.7777...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 10<br>\r\n$$10x = 67.7777...$$ \t\t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$10x \\\\;-\\\\; x = 67.7777...\\\\;-\\\\;6.7777...$$<br>\r\n$$9x = 61$$<br>\r\n$$x = \\\\frac{61}{9}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{67}{9}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 6.7777...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 10<br>\r\n$$10x = 67.7777...$$ \t\t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$10x \\\\;-\\\\; x = 67.7777...\\\\;-\\\\;6.7777...$$<br>\r\n$$9x = 61$$<br>\r\n$$x = \\\\frac{61}{9}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{60}{9}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 6.7777...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 10<br>\r\n$$10x = 67.7777...$$ \t\t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$10x \\\\;-\\\\; x = 67.7777...\\\\;-\\\\;6.7777...$$<br>\r\n$$9x = 61$$<br>\r\n$$x = \\\\frac{61}{9}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{61}{9}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let $$x = 6.7777...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 10<br>\r\n$$10x = 67.7777...$$ \t\t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$10x \\\\;-\\\\; x = 67.7777...\\\\;-\\\\;6.7777...$$<br>\r\n$$9x = 61$$<br>\r\n$$x = \\\\frac{61}{9}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let $$x = 6.7777...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 10<br>\r\n$$10x = 67.7777...$$ \t\t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$10x \\\\;-\\\\; x = 67.7777...\\\\;-\\\\;6.7777...$$<br>\r\n$$9x = 61$$<br>\r\n$$x = \\\\frac{61}{9}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is the correct fraction for 0.696969\u2026.?\",\n                    \"text\": \"Which of the following is the correct fraction for 0.696969\u2026.?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Let $$x = 0.696969...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 69.696969...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; x = 69.696969... \\\\;-\\\\; 0.696969...$$<br>\r\n$$99x = 69$$<br>\r\n$$x = \\\\frac{69}{99}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{6}{9}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 0.696969...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 69.696969...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; x = 69.696969... \\\\;-\\\\; 0.696969...$$<br>\r\n$$99x = 69$$<br>\r\n$$x = \\\\frac{69}{99}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{20}{33}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 0.696969...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 69.696969...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; x = 69.696969... \\\\;-\\\\; 0.696969...$$<br>\r\n$$99x = 69$$<br>\r\n$$x = \\\\frac{69}{99}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{67}{99}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 0.696969...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 69.696969...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; x = 69.696969... \\\\;-\\\\; 0.696969...$$<br>\r\n$$99x = 69$$<br>\r\n$$x = \\\\frac{69}{99}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{69}{99}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let $$x = 0.696969...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 69.696969...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; x = 69.696969... \\\\;-\\\\; 0.696969...$$<br>\r\n$$99x = 69$$<br>\r\n$$x = \\\\frac{69}{99}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let $$x = 0.696969...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 69.696969...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; x = 69.696969... \\\\;-\\\\; 0.696969...$$<br>\r\n$$99x = 69$$<br>\r\n$$x = \\\\frac{69}{99}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"On converting 0.67777.... into a fraction, we get ____\",\n                    \"text\": \"On converting 0.67777.... into a fraction, we get ____\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Let $$x = 0.67777.....$$<br> \r\nMultiplying both the sides by 10<br>\r\n$$10x = 6.7777....$$\t\t\t\t \u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$100x = 67.7777....$$\t\t\t \u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; 10x = 67.7777.... \\\\;-\\\\; 6.7777....$$<br>\r\n$$90x = 61$$\r\n$$x = \\\\frac{61}{90}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{67}{90}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 0.67777.....$$<br> \r\nMultiplying both the sides by 10<br>\r\n$$10x = 6.7777....$$\t\t\t\t \u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$100x = 67.7777....$$\t\t\t \u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; 10x = 67.7777.... \\\\;-\\\\; 6.7777....$$<br>\r\n$$90x = 61$$\r\n$$x = \\\\frac{61}{90}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{67}{99}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 0.67777.....$$<br> \r\nMultiplying both the sides by 10<br>\r\n$$10x = 6.7777....$$\t\t\t\t \u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$100x = 67.7777....$$\t\t\t \u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; 10x = 67.7777.... \\\\;-\\\\; 6.7777....$$<br>\r\n$$90x = 61$$\r\n$$x = \\\\frac{61}{90}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{61}{90}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 0.67777.....$$<br> \r\nMultiplying both the sides by 10<br>\r\n$$10x = 6.7777....$$\t\t\t\t \u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$100x = 67.7777....$$\t\t\t \u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; 10x = 67.7777.... \\\\;-\\\\; 6.7777....$$<br>\r\n$$90x = 61$$\r\n$$x = \\\\frac{61}{90}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{61}{99}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let $$x = 0.67777.....$$<br> \r\nMultiplying both the sides by 10<br>\r\n$$10x = 6.7777....$$\t\t\t\t \u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$100x = 67.7777....$$\t\t\t \u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; 10x = 67.7777.... \\\\;-\\\\; 6.7777....$$<br>\r\n$$90x = 61$$\r\n$$x = \\\\frac{61}{90}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let $$x = 0.67777.....$$<br> \r\nMultiplying both the sides by 10<br>\r\n$$10x = 6.7777....$$\t\t\t\t \u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$100x = 67.7777....$$\t\t\t \u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x \\\\;-\\\\; 10x = 67.7777.... \\\\;-\\\\; 6.7777....$$<br>\r\n$$90x = 61$$\r\n$$x = \\\\frac{61}{90}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"On converting 41.323232\u2026 into a fraction, we get ___.\",\n                    \"text\": \"On converting 41.323232\u2026 into a fraction, we get ___.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Let $$x = 41.323232...$$ \t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 4132.323232...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x\\\\;-\\\\;x = 4132.323232.. \\\\;-\\\\; 41.323232...$$<br>\r\n$$99x = 4091$$<br>\r\n$$x = \\\\frac{4091}{99}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{4132}{99}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 41.323232...$$ \t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 4132.323232...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x\\\\;-\\\\;x = 4132.323232.. \\\\;-\\\\; 41.323232...$$<br>\r\n$$99x = 4091$$<br>\r\n$$x = \\\\frac{4091}{99}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{4091}{90}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 41.323232...$$ \t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 4132.323232...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x\\\\;-\\\\;x = 4132.323232.. \\\\;-\\\\; 41.323232...$$<br>\r\n$$99x = 4091$$<br>\r\n$$x = \\\\frac{4091}{99}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{4132}{90}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 41.323232...$$ \t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 4132.323232...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x\\\\;-\\\\;x = 4132.323232.. \\\\;-\\\\; 41.323232...$$<br>\r\n$$99x = 4091$$<br>\r\n$$x = \\\\frac{4091}{99}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{4091}{99}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let $$x = 41.323232...$$ \t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 4132.323232...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x\\\\;-\\\\;x = 4132.323232.. \\\\;-\\\\; 41.323232...$$<br>\r\n$$99x = 4091$$<br>\r\n$$x = \\\\frac{4091}{99}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let $$x = 41.323232...$$ \t\t\t\u2014 (1)<br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 4132.323232...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$100x\\\\;-\\\\;x = 4132.323232.. \\\\;-\\\\; 41.323232...$$<br>\r\n$$99x = 4091$$<br>\r\n$$x = \\\\frac{4091}{99}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is the correct fraction for 0.1233333\u2026?\",\n                    \"text\": \"Which of the following is the correct fraction for 0.1233333\u2026?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Let $$x = 0.123333...$$ <br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 12.3333...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$1000x = 123.3333...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$1000x \\\\;-\\\\; 100x = 123.3333... \\\\;-\\\\; 12.3333...$$<br>\r\n$$900x = 111$$<br>\r\n$$x = \\\\frac{111}{900}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1239}{99}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 0.123333...$$ <br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 12.3333...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$1000x = 123.3333...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$1000x \\\\;-\\\\; 100x = 123.3333... \\\\;-\\\\; 12.3333...$$<br>\r\n$$900x = 111$$<br>\r\n$$x = \\\\frac{111}{900}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{37}{999}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 0.123333...$$ <br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 12.3333...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$1000x = 123.3333...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$1000x \\\\;-\\\\; 100x = 123.3333... \\\\;-\\\\; 12.3333...$$<br>\r\n$$900x = 111$$<br>\r\n$$x = \\\\frac{111}{900}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{37}{330}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let $$x = 0.123333...$$ <br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 12.3333...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$1000x = 123.3333...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$1000x \\\\;-\\\\; 100x = 123.3333... \\\\;-\\\\; 12.3333...$$<br>\r\n$$900x = 111$$<br>\r\n$$x = \\\\frac{111}{900}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{111}{900}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let $$x = 0.123333...$$ <br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 12.3333...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$1000x = 123.3333...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$1000x \\\\;-\\\\; 100x = 123.3333... \\\\;-\\\\; 12.3333...$$<br>\r\n$$900x = 111$$<br>\r\n$$x = \\\\frac{111}{900}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let $$x = 0.123333...$$ <br>\r\nMultiplying both the sides by 100<br>\r\n$$100x = 12.3333...$$ \t\t\t\t\u2014 (1)<br>\r\nMultiplying both sides by 10<br>\r\n$$1000x = 123.3333...$$ \t\t\t\u2014 (2)<br>\r\nSubtracting (1) from (2), we get<br>\r\n$$1000x \\\\;-\\\\; 100x = 123.3333... \\\\;-\\\\; 12.3333...$$<br>\r\n$$900x = 111$$<br>\r\n$$x = \\\\frac{111}{900}$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-frequently-asked-questions-on-repeating-decimal-to-fraction\">Frequently Asked Questions on Repeating Decimal to Fraction<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-cf41dee6-570f-47f6-a000-8bfb45fc2223\" 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-cf41dee6-570f-47f6-a000-8bfb45fc2223\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cf41dee6-570f-47f6-a000-8bfb45fc2223\"><strong>Can we convert non-terminating and non-repeating decimals to a fraction?<\/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-cf41dee6-570f-47f6-a000-8bfb45fc2223\">\n\n<p class=\"eplus-wrapper\">No, we can never convert a non terminating decimal to a fraction. They are irrational 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-1-cf41dee6-570f-47f6-a000-8bfb45fc2223\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cf41dee6-570f-47f6-a000-8bfb45fc2223\"><strong>What is the difference between terminating and non-terminating decimal expansion?<\/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-cf41dee6-570f-47f6-a000-8bfb45fc2223\">\n\n<p class=\"eplus-wrapper\">Fractions can be converted into decimals by dividing the numerator by the denominator. Terminating decimal expansion is the expansion in which the remainder $= 0$ and non-terminating decimal expansion is the expansion in which the remainder $\\neq 0$.<\/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-cf41dee6-570f-47f6-a000-8bfb45fc2223\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cf41dee6-570f-47f6-a000-8bfb45fc2223\"><strong>How to convert fractions to decimals?<\/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-cf41dee6-570f-47f6-a000-8bfb45fc2223\">\n\n<p class=\"eplus-wrapper\">Fractions can be converted into decimals by dividing the numerator by the denominator.<\/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-cf41dee6-570f-47f6-a000-8bfb45fc2223\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cf41dee6-570f-47f6-a000-8bfb45fc2223\"><strong>How do we represent the non-terminating repeating decimal expansion?<\/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-cf41dee6-570f-47f6-a000-8bfb45fc2223\">\n\n<p class=\"eplus-wrapper\">We represent the non terminating repeating decimal expansion using a bar. For example, 0.232323\u2026 can be represented as $\\overline{0.23}$.<\/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-cf41dee6-570f-47f6-a000-8bfb45fc2223\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cf41dee6-570f-47f6-a000-8bfb45fc2223\"><strong>What is a mixed recurring 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-4-cf41dee6-570f-47f6-a000-8bfb45fc2223\">\n\n<p class=\"eplus-wrapper\">A decimal in which at least one of the digits after the decimal point is non-repeated and some digits are repeated is known as a <strong>mixed recurring decimal<\/strong>.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example: 3.45777\u2026<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Repeating Decimal to Fraction Conversion? Repeating decimal to fraction conversion is used to express a repeating or recurring decimal in the form of a fraction. To convert a \u201cterminating decimal\u201d to a fraction, we simply count the number of digits after the decimal point (which are finite); then, we multiply and divide by &#8230; <a title=\"Repeating Decimal to Fraction: Definition, Steps, Tricks, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/repeating-decimal-to-fraction\" aria-label=\"More on Repeating Decimal to Fraction: Definition, Steps, Tricks, 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-26969","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\/26969","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=26969"}],"version-history":[{"count":15,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26969\/revisions"}],"predecessor-version":[{"id":39931,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26969\/revisions\/39931"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26969"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26969"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26969"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}