{"id":233802,"date":"2025-06-13T12:20:24","date_gmt":"2025-06-13T12:20:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233802"},"modified":"2025-06-13T12:20:27","modified_gmt":"2025-06-13T12:20:27","slug":"0-94-0-94-express-the-given-repeating-decimal-quotient-of-integers-possible-reduce-lowest-terms","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/0-94-0-94-express-the-given-repeating-decimal-quotient-of-integers-possible-reduce-lowest-terms\/","title":{"rendered":"0.94 = 0.94 Express the given repeating decimal quotient of integers possible , reduce lowest terms"},"content":{"rendered":"\n
0.94 = 0.94 Express the given repeating decimal quotient of integers possible , reduce lowest terms<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n\n\n\n\n
\u2705 Step 1: Let x equal the repeating decimal<\/strong><\/h3>\n\n\n\n
Let x = 0.949494…<\/strong><\/p>\n\n\n\n\n\n\n\n
\u2705 Step 2: Multiply x by 100<\/strong><\/h3>\n\n\n\n
Since the repeating part has two digits<\/strong> (“94”), we multiply both sides of the equation by 100<\/strong> to move the decimal point two places to the right:<\/p>\n\n\n\n
100x = 94.949494…<\/strong><\/p>\n\n\n\n\n\n\n\n
\u2705 Step 3: Subtract the original equation from this one<\/strong><\/h3>\n\n\n\n
Now subtract the original equation (x = 0.949494…<\/strong>) from the one we just created: 100x=94.949494…\u2212 x= 0.949494…99x=94\\begin{align*} 100x &= 94.949494… \\\\ – \\ \\ \\ x &= \\ \\ \\ 0.949494… \\\\ \\hline 99x &= 94 \\end{align*}100x\u2212 x99x\u200b=94.949494…= 0.949494…=94\u200b\u200b<\/p>\n\n\n\n\n\n\n\n
\u2705 Step 4: Solve for x<\/strong><\/h3>\n\n\n\n
x=9499x = \\frac{94}{99}x=9994\u200b<\/p>\n\n\n\n
\n\n\n\n
\u2705 Step 5: Reduce the fraction to lowest terms<\/strong><\/h3>\n\n\n\n
We now simplify 94\/99<\/strong>. Check if any common factors exist. The GCD of 94 and 99 is 1<\/strong>, so the fraction is already in lowest terms<\/strong>.<\/p>\n\n\n\n\n\n\n\n
To convert a repeating decimal into a fraction, we use algebra to isolate and eliminate the repeating part. The decimal 0.94\u0305 means that the digits \u201c94\u201d repeat indefinitely, forming the sequence 0.949494…, and so on. Our goal is to express this as a fraction of two integers in lowest terms.<\/p>\n\n\n\n
We begin by assigning a variable to the decimal: let x = 0.949494…. Since the repeating block is two digits long, we multiply both sides of the equation by 100 (a power of 10 with two zeros) to shift the decimal point two places to the right. This gives us 100x = 94.949494….<\/p>\n\n\n\n
Now we subtract the original x = 0.949494… from 100x = 94.949494…, which eliminates the repeating part of the decimal:<\/p>\n\n\n\n
100x \u2013 x = 94.949494… \u2013 0.949494…, resulting in 99x = 94.<\/p>\n\n\n\n
Next, we solve for x by dividing both sides by 99:<\/p>\n\n\n\n
x = 94 \/ 99.<\/p>\n\n\n\n
The final step is to reduce the fraction to its lowest terms. To do this, we find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 94 and 99 is 1, so the fraction is already in its simplest form.<\/p>\n\n\n\n
Therefore, the repeating decimal 0.94\u0305 is exactly equal to the fraction 94\/99<\/strong>.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
0.94 = 0.94 Express the given repeating decimal quotient of integers possible , reduce lowest terms The Correct Answer and Explanation is: \u2705 Step 1: Let x equal the repeating decimal Letx = 0.949494… \u2705 Step 2: Multiply x by 100 Since the repeating part has two digits (“94”), we multiply both sides of the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-233802","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233802","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=233802"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233802\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233802"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233802"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233802"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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