Is 5.33333\u2026.. (3 continuing) rational or irrational?<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n Correct Answer: Rational<\/strong><\/p>\n\n\n\n The number 5.33333…<\/strong> (with the digit 3 repeating infinitely) is a rational number<\/strong>.<\/p>\n\n\n\n To determine whether a number is rational or irrational, we must first understand what these terms mean.<\/p>\n\n\n\n A rational number<\/strong> is any number that can be expressed as a ratio of two integers<\/strong>, i.e., in the form a\/b<\/strong>, where a<\/strong> and b<\/strong> are integers and b \u2260 0<\/strong>. In contrast, an irrational number<\/strong> cannot<\/strong> be written as a simple fraction. Irrational numbers have non-repeating, non-terminating decimal expansions (like \u221a2 or \u03c0).<\/p>\n\n\n\n Now, consider the number 5.33333…<\/strong>, where the digit 3 repeats forever. This is a repeating decimal<\/strong>, and repeating decimals are always rational<\/strong> because they can be converted into a fraction.<\/p>\n\n\n\n Let\u2019s demonstrate how to write 5.33333… as a fraction:<\/p>\n\n\n\n Let x = 5.33333…<\/strong><\/p>\n\n\n\n We isolate the repeating part by multiplying x by 10 (since the repeating part is just one digit):<\/p>\n\n\n\n 10x = 53.33333…<\/p>\n\n\n\n Now subtract the original equation (x = 5.33333…) from this:<\/p>\n\n\n\n 10x \u2013 x = 53.33333… \u2013 5.33333…<\/p>\n\n\n\n This simplifies to:<\/p>\n\n\n\n 9x = 48<\/p>\n\n\n\n Now solve for x:<\/p>\n\n\n\n x = 48 \/ 9<\/p>\n\n\n\n Simplify the fraction:<\/p>\n\n\n\n x = 16 \/ 3<\/p>\n\n\n\n So, 5.33333… = 16\/3<\/strong>, which is a ratio of two integers. This proves that the number is rational<\/strong>.<\/p>\n\n\n\n It is important not to confuse non-terminating decimals with irrational numbers. Only non-repeating, non-terminating decimals are irrational. Since 5.33333…<\/strong> has a repeating pattern, it fits the definition of a rational number.<\/p>\n\n\n\n In conclusion, 5.33333… is rational<\/strong> because it can be written exactly as the fraction 16\/3<\/strong>, and any decimal that repeats is always rational.<\/p>\n","protected":false},"excerpt":{"rendered":" Is 5.33333\u2026.. (3 continuing) rational or irrational? The correct answer and explanation is: Correct Answer: Rational The number 5.33333… (with the digit 3 repeating infinitely) is a rational number. Explanation (Approximately 300 words): To determine whether a number is rational or irrational, we must first understand what these terms mean. A rational number is any […]<\/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-19140","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19140","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=19140"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19140\/revisions"}],"predecessor-version":[{"id":19142,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19140\/revisions\/19142"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=19140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=19140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=19140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation (Approximately 300 words):<\/h3>\n\n\n\n