{"id":20438,"date":"2025-06-14T12:46:13","date_gmt":"2025-06-14T12:46:13","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=20438"},"modified":"2025-06-14T12:46:21","modified_gmt":"2025-06-14T12:46:21","slug":"write-the-decimal-number-0-83333333-as-a-rational-number","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/write-the-decimal-number-0-83333333-as-a-rational-number\/","title":{"rendered":"write the decimal number 0.83333333 as a rational number"},"content":{"rendered":"\n<p>write the decimal number 0.83333333 as a rational number<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>The decimal number <strong>0.83333333<\/strong> can be expressed as a rational number in fraction form.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify the repeating decimal<\/h3>\n\n\n\n<p>The decimal 0.83333333&#8230; can be seen as:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>0.8 (which is 8 tenths), plus<\/li>\n\n\n\n<li>0.03333333&#8230; (a repeating decimal)<\/li>\n<\/ul>\n\n\n\n<p>The repeating part is the digit <strong>3<\/strong>, repeating infinitely.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Express the decimal as sum of parts<\/h3>\n\n\n\n<p>We write: 0.83333333&#8230;=0.8+0.03333333&#8230;0.83333333&#8230; = 0.8 + 0.03333333&#8230;<\/p>\n\n\n\n<p>We already know 0.8 = 810=45\\frac{8}{10} = \\frac{4}{5}.<\/p>\n\n\n\n<p>Now focus on 0.03333333&#8230;0.03333333&#8230;.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Express the repeating decimal 0.0333333&#8230;0.0333333&#8230; as a fraction<\/h3>\n\n\n\n<p>Let x=0.0333333&#8230;x = 0.0333333&#8230;.<\/p>\n\n\n\n<p>Multiply xx by 10: 10x=0.3333333&#8230;10x = 0.3333333&#8230;<\/p>\n\n\n\n<p>We know that 0.3333&#8230;0.3333&#8230; (repeating 3) equals 13\\frac{1}{3}.<\/p>\n\n\n\n<p>So: 10x=13\u2005\u200a\u27f9\u2005\u200ax=13010x = \\frac{1}{3} \\implies x = \\frac{1}{30}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Add the two parts as fractions<\/h3>\n\n\n\n<p>Recall: 0.83333333&#8230;=45+1300.83333333&#8230; = \\frac{4}{5} + \\frac{1}{30}<\/p>\n\n\n\n<p>Find a common denominator, which is 30: 45=2430\\frac{4}{5} = \\frac{24}{30}<\/p>\n\n\n\n<p>Add: 2430+130=2530\\frac{24}{30} + \\frac{1}{30} = \\frac{25}{30}<\/p>\n\n\n\n<p>Simplify the fraction: 2530=56\\frac{25}{30} = \\frac{5}{6}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final answer:<\/h3>\n\n\n\n<p>0.83333333&#8230;=560.83333333&#8230; = \\frac{5}{6}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Decimal numbers that repeat infinitely, such as 0.3333&#8230;, 0.6666&#8230;, or 0.8333333&#8230;, can be expressed exactly as fractions, also called rational numbers. A rational number is any number that can be written as the ratio of two integers pq\\frac{p}{q}, where q\u22600q \\neq 0.<\/p>\n\n\n\n<p>The decimal 0.83333333&#8230; consists of a non-repeating part (0.8) followed by a repeating part (0.03333&#8230;). To convert such a decimal, you break it down into these two parts and convert each to fractions separately.<\/p>\n\n\n\n<p>The repeating decimal 0.3333&#8230; is well known to equal 13\\frac{1}{3}. Since in our case, the repeating 3 starts after one decimal place (i.e., it is 0.03 repeating), multiplying by 10 shifts the decimal point right so that the repeating part becomes 0.3333&#8230;, allowing us to isolate the repeating decimal as a fraction.<\/p>\n\n\n\n<p>Once each part is converted, adding the fractions gives the overall rational number equivalent.<\/p>\n\n\n\n<p>In conclusion, the repeating decimal 0.8333333&#8230;0.8333333&#8230; is exactly 56\\frac{5}{6}, which means the decimal is just the decimal form of that fraction.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>write the decimal number 0.83333333 as a rational number The correct answer and explanation is: The decimal number 0.83333333 can be expressed as a rational number in fraction form. Step 1: Identify the repeating decimal The decimal 0.83333333&#8230; can be seen as: The repeating part is the digit 3, repeating infinitely. Step 2: Express the [&hellip;]<\/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-20438","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20438","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=20438"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20438\/revisions"}],"predecessor-version":[{"id":20439,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20438\/revisions\/20439"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=20438"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=20438"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=20438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}