{"id":154680,"date":"2022-03-25T23:48:13","date_gmt":"2022-03-25T18:18:13","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/non-terminating-repeating-decimals-are-rationals-explanation-and-examples\/"},"modified":"2022-12-31T15:52:06","modified_gmt":"2022-12-31T10:22:06","slug":"non-terminating-repeating-decimals-are-rationals-explanation-and-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/non-terminating-repeating-decimals-are-rationals\/","title":{"rendered":"Non-Terminating Repeating Decimals are Rationals &#8211; Explanation and Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/non-terminating-repeating-decimals-are-rationals\/#Non-Terminating_Repeating_Decimals\" title=\"Non-Terminating Repeating Decimals\">Non-Terminating Repeating Decimals<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/non-terminating-repeating-decimals-are-rationals\/#Rational_Numbers\" title=\"Rational Numbers\">Rational Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/non-terminating-repeating-decimals-are-rationals\/#Rational_Numbers_as_Terminating_and_Non-Terminating_Decimals\" title=\"Rational Numbers as Terminating and Non-Terminating Decimals\">Rational Numbers as Terminating and Non-Terminating Decimals<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/non-terminating-repeating-decimals-are-rationals\/#Converting_a_Terminating_Decimal_into_a_Fraction\" title=\"Converting a Terminating Decimal into a Fraction\">Converting a Terminating Decimal into a Fraction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/non-terminating-repeating-decimals-are-rationals\/#Converting_a_Non-Terminating_Decimal_into_a_Fraction\" title=\"Converting a Non-Terminating Decimal into a Fraction\">Converting a Non-Terminating Decimal into a Fraction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/non-terminating-repeating-decimals-are-rationals\/#Converting_a_Non-Terminating_Repeating_Decimal_into_a_Fraction\" title=\"Converting a Non-Terminating Repeating Decimal into a Fraction\">Converting a Non-Terminating Repeating Decimal into a Fraction<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Non-Terminating_Repeating_Decimals\"><\/span>Non-Terminating Repeating Decimals<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Non-terminating repeating decimals are decimals that do not have a finite number of digits that repeat. For example, the decimal 0.333333&#8230;, which is equal to the fraction 1\/3, is a non-terminating repeating decimal. The digits 3, 3, 3, 3, 3, 3, 3, &#8230; keep repeating forever.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154679 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/nonterminating-repeating-decimals-are-rationals-explanation-and-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/nonterminating-repeating-decimals-are-rationals-explanation-and-examples.jpg?v=1648232291 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/nonterminating-repeating-decimals-are-rationals-explanation-and-examples-300x212.jpg?v=1648232291 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Rational_Numbers\"><\/span>Rational Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. So, for example, the rational number 3\/4 can be written as the fraction 3\/4, and the rational number -5\/6 can be written as the fraction -5\/6.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Rational_Numbers_as_Terminating_and_Non-Terminating_Decimals\"><\/span>Rational Numbers as Terminating and Non-Terminating Decimals<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Rational numbers can be expressed as terminating decimals or non-terminating decimals. A terminating decimal is a rational number that has a finite number of digits after the decimal point. A non-terminating decimal is a rational number that does not have a finite number of digits after the decimal point.<\/p>\n<p>Some examples of terminating decimals are 0.5, 0.7, and 0.9. Some examples of non-terminating decimals are 0.6, 0.333, and 0.142857.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Converting_a_Terminating_Decimal_into_a_Fraction\"><\/span>Converting a Terminating Decimal into a Fraction<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To convert a terminating decimal into a fraction, divide the number by 10 and place the result over 10.<\/p>\n<p>For example, to convert the number 0.234 into a fraction, divide 0.234 by 10 and place the result over 10.<\/p>\n<p>0.234 \u00f7 10 = 0.023<\/p>\n<p>The fraction is 0.023 or 2\/10.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Converting_a_Non-Terminating_Decimal_into_a_Fraction\"><\/span>Converting a Non-Terminating Decimal into a Fraction<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To convert a non-terminating decimal into a fraction, divide the number by the power of 10 that is equal to the number of digits after the decimal point.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Converting_a_Non-Terminating_Repeating_Decimal_into_a_Fraction\"><\/span>Converting a Non-Terminating Repeating Decimal into a Fraction<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To convert a non-terminating repeating decimal into a fraction, divide the decimal number by the number that represents the place value of the repeating decimal.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Non-Terminating Repeating Decimals Non-terminating repeating decimals are decimals that do not have a finite number of digits that repeat. 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