Express each of the following as a rational number: (a) 4.125<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n Correct Answer:<\/strong> A rational number<\/strong> is any number that can be expressed as a fraction<\/strong> ab\\dfrac{a}{b}, where aa<\/strong> and bb<\/strong> are integers and b\u22600b \\neq 0<\/strong>. In other words, any decimal that terminates<\/strong> or repeats<\/strong> is a rational number because it can be written as a ratio of two integers.<\/p>\n\n\n\n Now let’s convert the decimal 4.125<\/strong> to a fraction:<\/p>\n\n\n\n 4.125 is a terminating decimal<\/strong> because it ends after a few digits. This type of decimal can easily be written as a fraction.<\/p>\n\n\n\n The decimal part 0.125<\/strong> has three digits after the decimal point, so we multiply it by 1000<\/strong> to eliminate the decimal: 4.125=412510004.125 = \\frac{4125}{1000}<\/p>\n\n\n\n Now simplify 41251000\\frac{4125}{1000} by dividing both the numerator and denominator by their greatest common divisor (GCD)<\/strong>.<\/p>\n\n\n\n The GCD of 4125 and 1000 is 125<\/strong>. 4125\u00f71251000\u00f7125=338\\frac{4125 \\div 125}{1000 \\div 125} = \\frac{33}{8}<\/p>\n\n\n\n 4.125=3384.125 = \\frac{33}{8}<\/p>\n\n\n\n This confirms that 4.125 is a rational number because it can be written as a simple fraction.<\/p>\n\n\n\n Therefore, 4.125 expressed as a rational number is 338\\dfrac{33}{8}<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Express each of the following as a rational number: (a) 4.125 The correct answer and explanation is: Correct Answer:(a) 4.125=3384.125 = \\dfrac{33}{8} Explanation (300 words): A rational number is any number that can be expressed as a fraction ab\\dfrac{a}{b}, where aa and bb are integers and b\u22600b \\neq 0. In other words, any decimal that […]<\/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-21784","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21784","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=21784"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21784\/revisions"}],"predecessor-version":[{"id":21785,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21784\/revisions\/21785"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=21784"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=21784"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=21784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
(a) 4.125=3384.125 = \\dfrac{33}{8}<\/p>\n\n\n\n
\n\n\n\nExplanation (300 words):<\/h3>\n\n\n\n
Step 1: Identify the decimal type<\/h4>\n\n\n\n
Step 2: Convert to fraction<\/h4>\n\n\n\n
Step 3: Simplify the fraction<\/h4>\n\n\n\n
Step 4: Final Answer<\/h4>\n\n\n\n
\n\n\n\nSummary:<\/h3>\n\n\n\n
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