{"id":25285,"date":"2025-06-18T22:06:33","date_gmt":"2025-06-18T22:06:33","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25285"},"modified":"2025-06-18T22:06:34","modified_gmt":"2025-06-18T22:06:34","slug":"rewrite-as-a-simplified-fraction-2-67-repeating","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/rewrite-as-a-simplified-fraction-2-67-repeating\/","title":{"rendered":"Rewrite as a simplified fraction 2.67 repeating"},"content":{"rendered":"\n<p>Rewrite as a simplified fraction 2.67 repeating<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Correct Answer:<\/h3>\n\n\n\n<p>The decimal <strong>2.67 repeating<\/strong> (written as <strong>2.6\u03057\u0305<\/strong>) can be written as the simplified fraction<br><strong>267100\\frac{267}{100}<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Explanation (300 words):<\/h3>\n\n\n\n<p>To convert a repeating decimal like <strong>2.67 repeating<\/strong> into a fraction, follow a systematic method. First, understand the notation:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>2.67 repeating<\/strong> means that both <strong>6<\/strong> and <strong>7<\/strong> repeat forever: 2.67676767\u20262.67676767\\ldots<\/li>\n<\/ul>\n\n\n\n<p>We can write this repeating decimal as a fraction using algebra:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Step 1: Let<\/strong> x=2.676767\u2026x = 2.676767\\ldots<\/p>\n\n\n\n<p><strong>Step 2: Multiply x by 100 (since two digits repeat):<\/strong> 100x=267.676767\u2026100x = 267.676767\\ldots<\/p>\n\n\n\n<p><strong>Step 3: Subtract the original x from this equation:<\/strong> 100x\u2212x=267.676767\u2026\u22122.676767\u2026\u21d299x=265100x &#8211; x = 267.676767\\ldots &#8211; 2.676767\\ldots \\Rightarrow 99x = 265<\/p>\n\n\n\n<p><strong>Step 4: Solve for x:<\/strong> x=26599x = \\frac{265}{99}<\/p>\n\n\n\n<p>So the repeating decimal <strong>2.676767&#8230;<\/strong> equals 26599\\frac{265}{99}<\/p>\n\n\n\n<p>\u2705 <strong>Now simplify if possible<\/strong>. But in this case, <strong>265 and 99 have no common factor other than 1<\/strong>, so this is already simplified.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd01 Alternate Method Using Long Decimal:<\/h3>\n\n\n\n<p>You can also convert by rewriting the decimal:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2.676767&#8230; = 2 + 0.676767&#8230;<\/li>\n\n\n\n<li>Convert 0.676767&#8230; to a fraction first:\n<ul class=\"wp-block-list\">\n<li>Let y = 0.676767&#8230;<\/li>\n\n\n\n<li>Then 100y = 67.676767&#8230;<\/li>\n\n\n\n<li>Subtract: 100y \u2212 y = 67.676767&#8230; \u2212 0.676767&#8230; = 67<\/li>\n\n\n\n<li>So 99y = 67 \u2192 y = 67\/99<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>Now add back the whole number:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 + 67\/99 = (2 \u00d7 99 + 67)\/99 = (198 + 67)\/99 = <strong>265\/99<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer:<\/h3>\n\n\n\n<p>26599\\boxed{\\frac{265}{99}}<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rewrite as a simplified fraction 2.67 repeating The correct answer and explanation is: \u2705 Correct Answer: The decimal 2.67 repeating (written as 2.6\u03057\u0305) can be written as the simplified fraction267100\\frac{267}{100} \u2705 Explanation (300 words): To convert a repeating decimal like 2.67 repeating into a fraction, follow a systematic method. First, understand the notation: We can [&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-25285","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25285","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=25285"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25285\/revisions"}],"predecessor-version":[{"id":25286,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25285\/revisions\/25286"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}