{"id":26059,"date":"2025-06-19T09:47:22","date_gmt":"2025-06-19T09:47:22","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=26059"},"modified":"2025-06-19T09:47:25","modified_gmt":"2025-06-19T09:47:25","slug":"what-is-0-58-repeating-as-a-fraction","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/what-is-0-58-repeating-as-a-fraction\/","title":{"rendered":"What is 0.58 repeating as a fraction"},"content":{"rendered":"\n<p>What is 0.58 repeating as a fraction?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-light-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To convert 0.5858\u203e0.58\\overline{58}0.5858 (where 58 repeats) into a fraction, follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Let x=0.585858\u2026x = 0.585858\\ldotsx=0.585858\u2026<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Multiply both sides of the equation by 100<\/h3>\n\n\n\n<p>Since the repeating block has two digits, we multiply by 100 to shift the decimal point two places to the right:100x=58.585858\u2026100x = 58.585858\\ldots100x=58.585858\u2026<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Subtract the original x=0.585858\u2026x = 0.585858\\ldotsx=0.585858\u2026 from this new equation:<\/h3>\n\n\n\n<p>100x\u2212x=58.585858\u2026\u22120.585858\u2026100x &#8211; x = 58.585858\\ldots &#8211; 0.585858\\ldots100x\u2212x=58.585858\u2026\u22120.585858\u202699x=5899x = 5899x=58<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Solve for xxx<\/h3>\n\n\n\n<p>x=5899x = \\frac{58}{99}x=9958\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>5899\\boxed{\\frac{58}{99}}9958\u200b\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>Repeating decimals can be expressed as fractions using algebra. In this case, we are given a repeating decimal 0.585858\u20260.585858\\ldots0.585858\u2026 where the digits &#8220;58&#8221; repeat endlessly. The goal is to express this value as a fraction of two integers.<\/p>\n\n\n\n<p>We start by letting xxx represent the repeating decimal, so x=0.585858\u2026x = 0.585858\\ldotsx=0.585858\u2026. To eliminate the repeating portion, we multiply xxx by 100 because the repeating segment &#8220;58&#8221; has two digits. This multiplication moves the decimal point two places to the right and gives 100x=58.585858\u2026100x = 58.585858\\ldots100x=58.585858\u2026. Notice how the decimal part of 100x100x100x is the same as the decimal part of xxx, which allows us to eliminate the repeating digits through subtraction.<\/p>\n\n\n\n<p>Subtracting xxx from 100x100x100x removes the repeating part:100x\u2212x=58.585858\u2026\u22120.585858\u2026=58100x &#8211; x = 58.585858\\ldots &#8211; 0.585858\\ldots = 58100x\u2212x=58.585858\u2026\u22120.585858\u2026=58<\/p>\n\n\n\n<p>This results in 99x=5899x = 5899x=58, and by solving for xxx, we find x=5899x = \\frac{58}{99}x=9958\u200b. This fraction is already in its simplest form because 58 and 99 do not have any common factors besides 1.<\/p>\n\n\n\n<p>Therefore, the repeating decimal 0.585858\u20260.585858\\ldots0.585858\u2026 is exactly equal to the fraction 5899\\frac{58}{99}9958\u200b. This method works for any repeating decimal and allows you to convert it into a precise fractional representation.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-49.jpeg\" alt=\"\" class=\"wp-image-26060\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-49.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-49-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>What is 0.58 repeating as a fraction? The Correct Answer and Explanation is: To convert 0.5858\u203e0.58\\overline{58}0.5858 (where 58 repeats) into a fraction, follow these steps: Step 1: Let x=0.585858\u2026x = 0.585858\\ldotsx=0.585858\u2026 Step 2: Multiply both sides of the equation by 100 Since the repeating block has two digits, we multiply by 100 to shift the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-26059","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26059","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=26059"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26059\/revisions"}],"predecessor-version":[{"id":26061,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26059\/revisions\/26061"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26059"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26059"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26059"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}