Convert 1.16666666667 to a fraction.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To convert the decimal (1.16666666667) into a fraction, we start by separating the whole number part from the decimal part. The whole number part is (1), and the decimal part is (0.16666666667).<\/p>\n\n\n\n The decimal (0.16666666667) is a repeating decimal, where the digit (6) repeats indefinitely. This can be represented as (0.16\\overline{6}).<\/p>\n\n\n\n Let (x = 0.16666666667).<\/p>\n\n\n\n To eliminate the repeating part, we can multiply (x) by (10) (to shift the decimal point one place to the right): Next, we subtract the first equation from the second: Now, we can solve for (x) by dividing both sides by (9): Now that we have the fractional part, we can combine it with the whole number part: Thus, the decimal (1.16666666667) can be expressed as the fraction (\\frac{7}{6}).<\/p>\n\n\n\n In conclusion, converting repeating decimals to fractions involves recognizing the repeating pattern, setting up an equation, eliminating the repeating part through subtraction, and finally simplifying the result. This process reveals that (1.16666666667) is equivalent to the fraction (\\frac{7}{6}), which can also be expressed as an improper fraction, indicating that it is slightly more than (1).<\/p>\n","protected":false},"excerpt":{"rendered":" Convert 1.16666666667 to a fraction. The Correct Answer and Explanation is: To convert the decimal (1.16666666667) into a fraction, we start by separating the whole number part from the decimal part. The whole number part is (1), and the decimal part is (0.16666666667). Step 1: Converting the Decimal Part The decimal (0.16666666667) is a repeating […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"","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-160149","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160149","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=160149"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160149\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=160149"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=160149"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=160149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Converting the Decimal Part<\/h3>\n\n\n\n
Step 2: Setting Up the Equation<\/h3>\n\n\n\n
[
10x = 1.66666666667
]
Now we have two equations:<\/p>\n\n\n\n\n
Step 3: Subtracting the Equations<\/h3>\n\n\n\n
[
10x – x = 1.66666666667 – 0.16666666667
]
This simplifies to:
[
9x = 1.5
]<\/p>\n\n\n\nStep 4: Solving for (x)<\/h3>\n\n\n\n
[
x = \\frac{1.5}{9}
]
To simplify (\\frac{1.5}{9}), we can multiply the numerator and the denominator by (10) to eliminate the decimal:
[
x = \\frac{15}{90}
]
Now, we simplify (\\frac{15}{90}):
[
x = \\frac{1}{6}
]<\/p>\n\n\n\nStep 5: Combining with the Whole Number<\/h3>\n\n\n\n
[
1 + \\frac{1}{6} = \\frac{6}{6} + \\frac{1}{6} = \\frac{7}{6}
]<\/p>\n\n\n\nFinal Result<\/h3>\n\n\n\n