To convert 0.4666…<\/strong> (where the 6 repeats) into a fraction:<\/p>\n\n\n\n Let Multiply both sides by 10 to move the decimal point one place right: Now subtract the original equation from this new equation: This simplifies to: Now divide both sides by 9: Since 4.2 is a decimal, convert it to a fraction: So: Now simplify 42\/90 by dividing both numerator and denominator by 6: Final answer: 0.4666… = 7\/15<\/strong><\/p>\n\n\n\n Repeating decimals can be expressed as fractions using algebraic methods. In this case, 0.4666… has one digit repeating: the number 6. First, we assign the decimal to a variable, calling it x<\/strong>. That gives us: To eliminate the repeating part, we multiply x<\/strong> by 10. This moves the decimal point one place to the right, giving us: Now, subtracting the original x = 0.4666…<\/strong> from this new expression allows the repeating parts to cancel out: To isolate x<\/strong>, divide both sides by 9: Now we deal with the decimal 4.2. It can be rewritten as a fraction: So: This fraction can be simplified. The greatest common divisor of 42 and 90 is 6. Dividing both by 6 gives: Therefore, the repeating decimal 0.4666… is equal to the fraction 7\/15<\/strong>.<\/p>\n\n\n\n What is 0.46 with 6 repeating as a fraction The Correct Answer and Explanation is: To convert 0.4666… (where the 6 repeats) into a fraction: Letx = 0.4666… Multiply both sides by 10 to move the decimal point one place right:10x = 4.666… Now subtract the original equation from this new equation:10x – x = […]<\/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-26055","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26055","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=26055"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26055\/revisions"}],"predecessor-version":[{"id":26057,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26055\/revisions\/26057"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26055"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26055"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26055"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
x = 0.4666…<\/strong><\/p>\n\n\n\n
10x = 4.666…<\/strong><\/p>\n\n\n\n
10x – x = 4.666… – 0.4666…<\/strong><\/p>\n\n\n\n
9x = 4.2<\/strong><\/p>\n\n\n\n
x = 4.2 \/ 9<\/strong><\/p>\n\n\n\n
4.2 = 42 \/ 10<\/strong><\/p>\n\n\n\n
x = (42 \/ 10) \u00f7 9 = 42 \/ (10 \u00d7 9) = 42 \/ 90<\/strong><\/p>\n\n\n\n
42 \u00f7 6 = 7<\/strong>
90 \u00f7 6 = 15<\/strong><\/p>\n\n\n\n
\n\n\n\nExplanation<\/h3>\n\n\n\n
x = 0.4666…<\/strong><\/p>\n\n\n\n
10x = 4.666…<\/strong><\/p>\n\n\n\n
10x – x = 4.666… – 0.4666…<\/strong>, which simplifies to:
9x = 4.2<\/strong><\/p>\n\n\n\n
x = 4.2 \u00f7 9<\/strong><\/p>\n\n\n\n
4.2 = 42\/10<\/strong><\/p>\n\n\n\n
x = (42\/10) \u00f7 9 = 42 \/ (10 \u00d7 9) = 42\/90<\/strong><\/p>\n\n\n\n
42 \u00f7 6 = 7, 90 \u00f7 6 = 15<\/strong>, so:
x = 7\/15<\/strong><\/p>\n\n\n\n![\"\"](\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-48.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"