To convert 3.22\u203e3.2 \\overline{2}3.22 (where the “2” repeats indefinitely) into a fraction, we can follow these steps:<\/p>\n\n\n\n
Step 1: Represent the number as xxx<\/h3>\n\n\n\n
Let x=3.22\u203ex = 3.2 \\overline{2}x=3.22, which means x=3.22222\u2026x = 3.22222\\ldotsx=3.22222\u2026.<\/p>\n\n\n\n
Step 2: Eliminate the repeating decimal<\/h3>\n\n\n\n
To eliminate the repeating decimal, multiply both sides of the equation by 10. This will shift the decimal point one place to the right:10x=32.22222\u202610x = 32.22222\\ldots10x=32.22222\u2026<\/p>\n\n\n\n
Notice that the decimal part is still the same as in xxx, so we can now set up another equation.<\/p>\n\n\n\n
Step 3: Subtract the original equation from this new one<\/h3>\n\n\n\n
Now, subtract the original equation x=3.22222\u2026x = 3.22222\\ldotsx=3.22222\u2026 from the equation 10x=32.22222\u202610x = 32.22222\\ldots10x=32.22222\u2026:10x\u2212x=32.22222\u2026\u22123.22222\u202610x – x = 32.22222\\ldots – 3.22222\\ldots10x\u2212x=32.22222\u2026\u22123.22222\u2026<\/p>\n\n\n\n
This simplifies to:9x=299x = 299x=29<\/p>\n\n\n\n
Step 4: Solve for xxx<\/h3>\n\n\n\n
Now, solve for xxx by dividing both sides by 9:x=299x = \\frac{29}{9}x=929\u200b<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
So, 3.22\u203e=2993.2 \\overline{2} = \\frac{29}{9}3.22=929\u200b.<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
The repeating decimal 3.22\u203e3.2 \\overline{2}3.22 is a rational number, which means it can be expressed as a fraction. By setting up an equation and eliminating the repeating part through multiplication and subtraction, we found that the fraction representation of 3.22\u203e3.2 \\overline{2}3.22 is 299\\frac{29}{9}929\u200b. This method can be applied to any repeating decimal to convert it into a fraction.<\/p>\n\n\n\n How do you convert 3.2 (2 repeating) as a fraction? The Correct Answer and Explanation is: To convert 3.22\u203e3.2 \\overline{2}3.22 (where the “2” repeats indefinitely) into a fraction, we can follow these steps: Step 1: Represent the number as xxx Let x=3.22\u203ex = 3.2 \\overline{2}x=3.22, which means x=3.22222\u2026x = 3.22222\\ldotsx=3.22222\u2026. Step 2: Eliminate the repeating […]<\/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-45713","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45713","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=45713"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45713\/revisions"}],"predecessor-version":[{"id":45715,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45713\/revisions\/45715"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=45713"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=45713"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=45713"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-62.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"