{"id":2364,"date":"2020-12-22T10:49:11","date_gmt":"2020-12-22T05:19:11","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=2364"},"modified":"2020-12-22T18:02:17","modified_gmt":"2020-12-22T12:32:17","slug":"decimal-representation-rational-numbers","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/decimal-representation-rational-numbers\/","title":{"rendered":"Decimal Representation Of Rational Numbers"},"content":{"rendered":"<h2><strong>Decimal Representation Of <a href=\"https:\/\/www.aplustopper.com\/rational-number\/\">Rational Numbers<\/a><\/strong><\/h2>\n<p><strong>Example 1:<\/strong>\u00a0 \u00a0\u00a0Express \\(\\frac { 7 }{ 8 }\\)\u00a0in the decimal form by long division method.<br \/>\n<strong>Solution:<\/strong> \u00a0 \u00a0We have,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-136029\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-1.png\" alt=\"Decimal Representation Of Rational Numbers 1\" width=\"124\" height=\"171\" \/><br \/>\n\u2234\u00a0\\(\\frac { 7 }{ 8 }\\) = 0.875<\/p>\n<p><strong>Example 2:<\/strong>\u00a0 \u00a0\u00a0Convert \\(\\frac { 35 }{ 16 }\\)\u00a0into decimal form by long division\u00a0 method.<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>We have,\u00a0<strong>\u00a0<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-136033\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-2.png\" alt=\"Decimal Representation Of Rational Numbers 2\" width=\"176\" height=\"302\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-2.png 176w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-2-175x300.png 175w\" sizes=\"(max-width: 176px) 100vw, 176px\" \/><\/p>\n<p><strong>Example 3:<\/strong>\u00a0 \u00a0\u00a0Express \\(\\frac { 2157 }{ 625 }\\)\u00a0in the decimal form.<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>We have,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-136034\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-3.png\" alt=\"Decimal Representation Of Rational Numbers 3\" width=\"250\" height=\"298\" \/><\/p>\n<p><strong>Example 4:<\/strong>\u00a0 \u00a0\u00a0Express \\(\\frac { -17 }{ 8 }\\)\u00a0in decimal form by long division method.<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>In order to convert \\(\\frac { -17 }{ 8 }\\)\u00a0in the decimal form, we first express \\(\\frac { 17 }{ 8 }\\) in the decimal form and the decimal form of \\(\\frac { -17 }{ 8 }\\) will be negative of the decimal form of \\(\\frac { 17 }{ 8 }\\)<br \/>\nwe have,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-136035\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-4.png\" alt=\"Decimal Representation Of Rational Numbers 4\" width=\"193\" height=\"266\" \/><\/p>\n<p><strong>Example 5:<\/strong>\u00a0 \u00a0\u00a0Find the decimal representation of \\(\\frac { 8 }{ 3 }\\) .<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>By long division, we have<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-136036\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-5.png\" alt=\"Decimal Representation Of Rational Numbers 5\" width=\"212\" height=\"312\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-5.png 212w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-5-204x300.png 204w\" sizes=\"(max-width: 212px) 100vw, 212px\" \/><\/p>\n<p><strong>Example 6:<\/strong>\u00a0 \u00a0\u00a0Express \\(\\frac { 2 }{ 11 }\\)\u00a0as a decimal fraction.<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>By long division, we have<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-136038\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-6.png\" alt=\"Decimal Representation Of Rational Numbers 6\" width=\"240\" height=\"356\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-6.png 240w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-6-202x300.png 202w\" sizes=\"(max-width: 240px) 100vw, 240px\" \/><\/p>\n<p><strong>Example 7:<\/strong>\u00a0 \u00a0\u00a0Find the decimal representation of\u00a0\\(\\frac { -16 }{ 45 }\\)<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>By long division, we have<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-136039\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-7.png\" alt=\"Decimal Representation Of Rational Numbers 7\" width=\"233\" height=\"331\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-7.png 233w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-7-211x300.png 211w\" sizes=\"(max-width: 233px) 100vw, 233px\" \/><\/p>\n<p><strong>Example 8:<\/strong>\u00a0 \u00a0\u00a0Find the decimal representation of\u00a0\\(\\frac { 22 }{ 7 }\\)<br \/>\n<strong>Solution: \u00a0 \u00a0<\/strong>By long division, we have<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-136040\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-8.png\" alt=\"Decimal Representation Of Rational Numbers 8\" width=\"216\" height=\"623\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-8.png 216w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-8-104x300.png 104w\" sizes=\"(max-width: 216px) 100vw, 216px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-136041\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-9.png\" alt=\"Decimal Representation Of Rational Numbers 9\" width=\"332\" height=\"50\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-9.png 332w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-9-300x45.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\nSo division of rational number gives decimal expansion. This expansion represents two types<br \/>\n<strong>(A)<\/strong> Terminating (remainder = 0)<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-136042\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-10.png\" alt=\"Decimal Representation Of Rational Numbers 10\" width=\"320\" height=\"71\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-10.png 320w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-10-300x67.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nSo these are terminating and non repeating (recurring)<br \/>\n<strong>(B)<\/strong> Non terminating recurring (repeating)<br \/>\n(remainder \u2260\u00a00, but equal to devidend)<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-136043\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-11.png\" alt=\"Decimal Representation Of Rational Numbers 11\" width=\"343\" height=\"178\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-11.png 343w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-11-300x156.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><br \/>\nThese expansion are not finished but digits are continusely repeated so we use a line on those digits, called bar \\((\\bar{a})\\).<br \/>\nSo we can say that rational numbers are of the form either terminating, non repeating or non terminating repeating (recurring).<\/p>\n<p><a class=\"button-red\" title=\"Maths\" href=\"https:\/\/www.aplustopper.com\/maths\/\">Maths<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Decimal Representation Of Rational Numbers Example 1:\u00a0 \u00a0\u00a0Express \u00a0in the decimal form by long division method. Solution: \u00a0 \u00a0We have, \u2234\u00a0 = 0.875 Example 2:\u00a0 \u00a0\u00a0Convert \u00a0into decimal form by long division\u00a0 method. Solution: \u00a0 \u00a0We have,\u00a0\u00a0 Example 3:\u00a0 \u00a0\u00a0Express \u00a0in the decimal form. Solution: \u00a0 \u00a0We have, Example 4:\u00a0 \u00a0\u00a0Express \u00a0in decimal form by [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[1019,1023,1021,1022,55912,1018,55948,1020],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Decimal Representation Of Rational Numbers - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/decimal-representation-rational-numbers\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Decimal Representation Of Rational Numbers\" \/>\n<meta property=\"og:description\" content=\"Decimal Representation Of Rational Numbers Example 1:\u00a0 \u00a0\u00a0Express \u00a0in the decimal form by long division method. Solution: \u00a0 \u00a0We have, \u2234\u00a0 = 0.875 Example 2:\u00a0 \u00a0\u00a0Convert \u00a0into decimal form by long division\u00a0 method. Solution: \u00a0 \u00a0We have,\u00a0\u00a0 Example 3:\u00a0 \u00a0\u00a0Express \u00a0in the decimal form. 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Solution: \u00a0 \u00a0We have, \u2234\u00a0 = 0.875 Example 2:\u00a0 \u00a0\u00a0Convert \u00a0into decimal form by long division\u00a0 method. Solution: \u00a0 \u00a0We have,\u00a0\u00a0 Example 3:\u00a0 \u00a0\u00a0Express \u00a0in the decimal form. Solution: \u00a0 \u00a0We have, Example 4:\u00a0 \u00a0\u00a0Express \u00a0in decimal form by [&hellip;]","og_url":"https:\/\/www.aplustopper.com\/decimal-representation-rational-numbers\/","og_site_name":"A Plus Topper","article_publisher":"https:\/\/www.facebook.com\/aplustopper\/","article_published_time":"2020-12-22T05:19:11+00:00","article_modified_time":"2020-12-22T12:32:17+00:00","og_image":[{"url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-1.png"}],"twitter_card":"summary","twitter_misc":{"Written by":"Veerendra","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/www.aplustopper.com\/#organization","name":"Aplus Topper","url":"https:\/\/www.aplustopper.com\/","sameAs":["https:\/\/www.facebook.com\/aplustopper\/"],"logo":{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/#logo","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","width":1585,"height":375,"caption":"Aplus Topper"},"image":{"@id":"https:\/\/www.aplustopper.com\/#logo"}},{"@type":"WebSite","@id":"https:\/\/www.aplustopper.com\/#website","url":"https:\/\/www.aplustopper.com\/","name":"A Plus Topper","description":"Improve your Grades","publisher":{"@id":"https:\/\/www.aplustopper.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.aplustopper.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/decimal-representation-rational-numbers\/#primaryimage","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-1.png","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/Decimal-Representation-Of-Rational-Numbers-1.png","width":124,"height":171,"caption":"Decimal Representation Of Rational Numbers 1"},{"@type":"WebPage","@id":"https:\/\/www.aplustopper.com\/decimal-representation-rational-numbers\/#webpage","url":"https:\/\/www.aplustopper.com\/decimal-representation-rational-numbers\/","name":"Decimal Representation Of Rational Numbers - 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