0.02 repeating as a fraction<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct answer is: (\\frac{2}{99})<\/strong><\/mark><\/p>\n\n\n\n To convert the repeating decimal (0.02\\overline{02}) into a fraction, we can use algebraic methods. Let’s denote the repeating decimal as (x):<\/p>\n\n\n\n [ To eliminate the repeating part, we can multiply (x) by (100) (because the repeat is two digits long):<\/p>\n\n\n\n [ Now, we have two equations:<\/p>\n\n\n\n Next, we subtract the first equation from the second:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ Now, we can solve for (x):<\/p>\n\n\n\n [ Thus, the fraction representation of the repeating decimal (0.02\\overline{02}) is (\\frac{2}{99}).<\/p>\n\n\n\n Repeating decimals are often converted into fractions to express them in a more manageable form. The process involves identifying the repeating segment and eliminating it through multiplication. By shifting the decimal point appropriately, we can create a solvable equation.<\/p>\n\n\n\n In our case, recognizing that (0.02\\overline{02}) has a two-digit repeat allowed us to multiply by (100), isolating the repeating decimal. This method can be applied to any repeating decimal, no matter the length of the repetition. The subtraction of the equations helps to simplify the problem, revealing the relationship between the repeating decimal and the constant values we derived.<\/p>\n\n\n\n Ultimately, the fraction (\\frac{2}{99}) is not only an exact representation of the repeating decimal but also allows us to understand the underlying mathematics involved in converting decimals to fractions.<\/p>\n","protected":false},"excerpt":{"rendered":" 0.02 repeating as a fraction The Correct Answer and Explanation is : The correct answer is: (\\frac{2}{99}) To convert the repeating decimal (0.02\\overline{02}) into a fraction, we can use algebraic methods. Let’s denote the repeating decimal as (x): [x = 0.02020202\\ldots] Step 1: Eliminate the Repeating Part To eliminate the repeating part, we can multiply […]<\/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-149276","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149276","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=149276"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149276\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=149276"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=149276"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=149276"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
x = 0.02020202\\ldots
]<\/p>\n\n\n\nStep 1: Eliminate the Repeating Part<\/h3>\n\n\n\n
100x = 2.02020202\\ldots
]<\/p>\n\n\n\nStep 2: Set Up the Equation<\/h3>\n\n\n\n
\n
Step 3: Subtract the Two Equations<\/h3>\n\n\n\n
100x – x = 2.02020202\\ldots – 0.02020202\\ldots
]<\/p>\n\n\n\n
99x = 2
]<\/p>\n\n\n\nStep 4: Solve for (x)<\/h3>\n\n\n\n
x = \\frac{2}{99}
]<\/p>\n\n\n\nStep 5: Conclusion<\/h3>\n\n\n\n
Explanation<\/h3>\n\n\n\n