{"id":18,"date":"2022-04-13T06:07:26","date_gmt":"2022-04-13T06:07:26","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=18"},"modified":"2025-11-20T06:31:50","modified_gmt":"2025-11-20T06:31:50","slug":"a-4-convert-between-decimals-and-fractions","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/a-4-convert-between-decimals-and-fractions\/","title":{"rendered":"A.4 Convert between decimals and fractions"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Convert between decimals and fractions<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-video\"><video controls src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/A.4-Convert-between-decimals-and-fractions.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Converting Decimals to Fractions<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Identify the Decimal Place:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Determine the place value of the decimal. For example, 0.75 is in the hundredths place.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Write as a Fraction:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Place the decimal number over its place value. For 0.75, write it as <sup>75<\/sup>\u2044<sub>100<\/sub>.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Simplify the Fraction:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li class=\"has-normal-font-size\">Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). For <sup>75<\/sup>\u2044<sub>100<\/sub>, the GCD is 25.<\/li>\n\n\n\n<li class=\"has-normal-font-size\">\u2077\u2075\u00f7\u00b2\u2075 \/ \u00b9\u2070\u2070\u00f7 \u00b2\u2075 = <sup>3<\/sup>\u2044<sub>4<\/sub><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-75\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/a-4-convert-between-decimals-and-fractions\/2\/\"><strong>Steps to Convert Repeating Decimals to Fractions<\/strong><\/a><\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Converting Fractions to Decimals<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Divide the Numerator by the Denominator:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li class=\"has-normal-font-size\">Perform the division to convert the fraction into a decimal. For example, for <sup>3<\/sup>\u2044<sub>4<\/sub> .<\/li>\n\n\n\n<li class=\"has-normal-font-size\">Divide 3 by 4, which equals 0.75.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Learn with an example<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#fabbca\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\ud83c\udfaf Write&nbsp;-0.2&nbsp;as a fraction.<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Start with 0.2.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Write the decimal as a fraction with 10 as the denominator. Reduce the fraction to simplest form.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">0.2 = 2\/10<\/p>\n\n\n\n<p class=\"has-normal-font-size\">= 2\u00f7&nbsp;2 \/ 10 \u00f7&nbsp;2<\/p>\n\n\n\n<p class=\"has-normal-font-size\">= 1\/5<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Now write a negative sign on each number:<\/p>\n\n\n\n<p class=\"has-normal-font-size\">-0.2 = -1\/5<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#c0f1f9\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\ud83c\udfaf Write -39\/50 &nbsp;as a decimal number.<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Start with 39\/50,<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Write an equivalent fraction with 100 as the denominator. Then write the decimal number.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">39\/50 = 39 x 2 \/ 50 x 2<\/p>\n\n\n\n<p class=\"has-normal-font-size\">= 78\/100<\/p>\n\n\n\n<p class=\"has-normal-font-size\">= 0.78<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Now write a negative sign on each number:<\/p>\n\n\n\n<p class=\"has-normal-font-size\">-39\/50 = -0.78<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#bcbdf5\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Write -0.09&nbsp;as a fraction.<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Start with 0.09.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Write the decimal as a fraction with 100 as the denominator.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">0.09 = 9\/100<\/p>\n\n\n\n<p class=\"has-normal-font-size\">9\/100 &nbsp;is written in simplest form.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Now write a negative sign on each number:<\/p>\n\n\n\n<p class=\"has-normal-font-size\">\u20130.09 = -9\/100<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s Practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/95327\/651\/665\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-2.png\" alt=\"\" class=\"wp-image-7080\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-2.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-2-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/75571\/258\/405\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-2.png\" alt=\"\" class=\"wp-image-7081\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-2.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-2-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<!--nextpage-->\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Steps to Convert Repeating Decimals to Fractions<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color has-normal-font-size wp-elements-eecfd7bb28040d0e37e1bc848a042ee7\" style=\"color:#000060\">Example: Convert 0.3\u203e to a Fraction<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Set Up an Equation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Let x=0.3\u203e<\/li>\n\n\n\n<li>This means x=0.3333<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong><strong>Multiply by 10 (or a power of 10) to Shift the Decimal Point:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Multiply both sides of the equation by 10 to shift the decimal point one place to the right.<\/li>\n\n\n\n<li>10x = 3.3333..<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong><strong>Subtract the Original Equation from the New Equation:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Subtract the original x from 10x to eliminate the repeating part.<\/li>\n\n\n\n<li>10x\u2212x=3.3333&#8230; \u2212 0.3333&#8230;<\/li>\n\n\n\n<li>9x=3.<\/li>\n<\/ul>\n\n\n\n<p><strong>Solve for x:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>x= <sup>3<\/sup>\u2044<sub>9<\/sub><\/li>\n\n\n\n<li>Simplify the fraction.<\/li>\n\n\n\n<li><strong>x= <sup>1<\/sup>\u2044<sub>3<\/sub><\/strong><\/li>\n\n\n\n<li><strong>So, 0.3\u203e= <sup>1<\/sup>\u2044<sub>3<\/sub><\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Example: Convert 0.8\u03051 to a Fraction<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Set Up an Equation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Let x=0.8\u03051<\/li>\n\n\n\n<li>This means x=0.818181&#8230;<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong><strong>Multiply by 100 (to Shift the Decimal Two Places):<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Multiply both sides of the equation by 100 to shift the decimal two places to the right.<\/li>\n\n\n\n<li>100x = 81.818181&#8230;<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong><strong>Subtract the Original Equation from the New Equation:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Subtract the original x from 100x to eliminate the repeating part.<\/li>\n\n\n\n<li>100x\u2212x = 81.818181&#8230;\u22120.818181&#8230;<\/li>\n\n\n\n<li>99x=81.<\/li>\n<\/ul>\n\n\n\n<p>Solve for x:<\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>x = <strong><sup>81<\/sup>\u2044<sub>99<\/sub><\/strong><\/li>\n\n\n\n<li>Simplify the fraction.<\/li>\n\n\n\n<li>x = <strong><sup>9<\/sup>\u2044<sub>11<\/sub><\/strong><\/li>\n<\/ul>\n\n\n\n<p>so, 0.8\u03051 = <strong><sup>9<\/sup>\u2044<sub>11<\/sub><\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>General Formula<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>For a repeating decimal 0.a\u0305<\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>x= 0.a\u0305<\/li>\n\n\n\n<li>Multiply by 10\u207f where n is the number of repeating digits.<\/li>\n\n\n\n<li>Subtract the original equation from the new equation.<\/li>\n\n\n\n<li>Solve for x and simplify.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong><strong>For a repeating decimal with a non-repeating part (e.g., 0.1\u03056):<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Set Up an Equation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Let x = 0.1\u03056<\/li>\n<\/ul>\n\n\n\n<p><strong>Multiply by a Power of 10 to Shift the Decimal Past the Non-Repeating Part:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Multiply both sides by 10: 10x =1.6\u0305<\/li>\n\n\n\n<li>Multiply both sides by 100 to shift past the repeating part: 100x=16.6\u203e<\/li>\n<\/ul>\n\n\n\n<p><strong>Subtract the Two Equations to Isolate the Repeating Part:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>100x\u221210x=16.6\u203e\u22121.6\u203e.<\/li>\n\n\n\n<li>90x=15.<\/li>\n<\/ul>\n\n\n\n<p>Solve for x:<\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>x = <strong><sup>15<\/sup>\u2044<sub>90<\/sub><\/strong><\/li>\n\n\n\n<li>Simplify: x=<strong><sup>15<\/sup>\u2044<sub>90<\/sub><\/strong><\/li>\n\n\n\n<li>x = <strong><sup>1<\/sup>\u2044<sub>6<\/sub><\/strong><\/li>\n<\/ul>\n\n\n\n<p>So, 0.16\u203e=<strong><sup>1<\/sup>\u2044<sub>6<\/sub><\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-dots\"\/>\n","protected":false},"excerpt":{"rendered":"<p>Convert between decimals and fractions key notes : Converting Decimals to Fractions Identify the Decimal Place: Write as a Fraction: Simplify the Fraction: Converting Fractions to Decimals Divide the Numerator by the Denominator: Learn with an example \ud83c\udfaf Write&nbsp;-0.2&nbsp;as a fraction. Start with 0.2. Write the decimal as a fraction with 10 as the denominator.<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/a-4-convert-between-decimals-and-fractions\/\">Continue reading <span class=\"screen-reader-text\">&#8220;A.4 Convert between decimals and fractions&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-18","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/18","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=18"}],"version-history":[{"count":35,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/18\/revisions"}],"predecessor-version":[{"id":18245,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/18\/revisions\/18245"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=18"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}