Let x=0.15\u203ex = 0.\\overline{15}x=0.15, which represents the repeating decimal 0.151515\u20260.151515\\ldots0.151515\u2026.<\/p>\n\n\n\n
Step 1: Set up the equation<\/h3>\n\n\n\n
Let x=0.15\u203ex = 0.\\overline{15}x=0.15.<\/p>\n\n\n\n
Step 2: Multiply both sides by a power of 10 to shift the decimal<\/h3>\n\n\n\n
Since the decimal repeats every two digits, multiply both sides of the equation by 100 to shift the decimal point two places to the right:100x=15.15\u203e100x = 15.\\overline{15}100x=15.15<\/p>\n\n\n\n
Step 3: Subtract the original equation from the new equation<\/h3>\n\n\n\n
Now, subtract the original equation x=0.15\u203ex = 0.\\overline{15}x=0.15 from the new equation 100x=15.15\u203e100x = 15.\\overline{15}100x=15.15:100x\u2212x=15.15\u203e\u22120.15\u203e100x – x = 15.\\overline{15} – 0.\\overline{15}100x\u2212x=15.15\u22120.1599x=1599x = 1599x=15<\/p>\n\n\n\n
Step 4: Solve for xxx<\/h3>\n\n\n\n
Now solve for xxx by dividing both sides by 99:x=1599x = \\frac{15}{99}x=9915\u200b<\/p>\n\n\n\n
Step 5: Simplify the fraction<\/h3>\n\n\n\n
To simplify the fraction 1599\\frac{15}{99}9915\u200b, divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3:x=15\u00f7399\u00f73=533x = \\frac{15 \\div 3}{99 \\div 3} = \\frac{5}{33}x=99\u00f7315\u00f73\u200b=335\u200b<\/p>\n\n\n\n
Thus, the repeating decimal 0.15\u203e0.\\overline{15}0.15 can be expressed as the ratio of two integers:x=533x = \\frac{5}{33}x=335\u200b<\/p>\n\n\n\n
Conclusion:<\/h3>\n\n\n\n
The repeating decimal 0.15\u203e0.\\overline{15}0.15 is equivalent to the fraction 533\\frac{5}{33}335\u200b.<\/p>\n\n\n\n Express the repeating decimal as the ratio of two integers. \\overline{0.15} = 0.151515\u2026 The ratio of two integers is (Type an integer or a simplified fraction. The Correct Answer and Explanation is: Let x=0.15\u203ex = 0.\\overline{15}x=0.15, which represents the repeating decimal 0.151515\u20260.151515\\ldots0.151515\u2026. Step 1: Set up the equation Let x=0.15\u203ex = 0.\\overline{15}x=0.15. Step 2: Multiply […]<\/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-45344","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45344","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=45344"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45344\/revisions"}],"predecessor-version":[{"id":45346,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45344\/revisions\/45346"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=45344"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=45344"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=45344"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-14.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"