{"id":249151,"date":"2025-07-09T03:49:07","date_gmt":"2025-07-09T03:49:07","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249151"},"modified":"2025-07-09T03:49:10","modified_gmt":"2025-07-09T03:49:10","slug":"given-two-decimal-numbers-0-5-and-0-4375","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/09\/given-two-decimal-numbers-0-5-and-0-4375\/","title":{"rendered":"Given two decimal numbers 0.5 and -0.4375"},"content":{"rendered":"\n<p>Given two decimal numbers 0.5 and -0.4375. (a) Multiply the numbers. (b) Converting to decimal to check the results. Show your workings.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this, we will first multiply the two decimal numbers, and then we will convert the result to check the accuracy.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part (a): Multiplying the Numbers<\/h3>\n\n\n\n<p>We are given the two decimal numbers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>0.50.50.5<\/li>\n\n\n\n<li>\u22120.4375-0.4375\u22120.4375<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 1: Multiply the absolute values<\/strong><\/p>\n\n\n\n<p>We start by multiplying the absolute values of the numbers:0.5\u00d70.4375=0.218750.5 \\times 0.4375 = 0.218750.5\u00d70.4375=0.21875<\/p>\n\n\n\n<p><strong>Step 2: Apply the sign<\/strong><\/p>\n\n\n\n<p>Since one number is positive and the other is negative, the product will be negative. So, the result of the multiplication is:0.5\u00d7(\u22120.4375)=\u22120.218750.5 \\times (-0.4375) = -0.218750.5\u00d7(\u22120.4375)=\u22120.21875<\/p>\n\n\n\n<p>So, the result of multiplying the numbers is \u22120.21875-0.21875\u22120.21875.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part (b): Converting to Decimal to Check the Result<\/h3>\n\n\n\n<p>Now, let&#8217;s convert the decimal result \u22120.21875-0.21875\u22120.21875 back to decimal form to verify.<\/p>\n\n\n\n<p>We can check the multiplication by converting the fraction \u22120.21875-0.21875\u22120.21875 into its fraction form. Here\u2019s how:<\/p>\n\n\n\n<p><strong>Step 1: Express \u22120.21875-0.21875\u22120.21875 as a fraction<\/strong><\/p>\n\n\n\n<p>We can express 0.218750.218750.21875 as a fraction. Since there are 5 decimal places, we write it as:0.21875=218751000000.21875 = \\frac{21875}{100000}0.21875=10000021875\u200b<\/p>\n\n\n\n<p>Simplifying the fraction:21875100000=732\\frac{21875}{100000} = \\frac{7}{32}10000021875\u200b=327\u200b<\/p>\n\n\n\n<p>So:\u22120.21875=\u2212732-0.21875 = -\\frac{7}{32}\u22120.21875=\u2212327\u200b<\/p>\n\n\n\n<p><strong>Step 2: Convert the product of 0.50.50.5 and \u22120.4375-0.4375\u22120.4375 to a fraction<\/strong><\/p>\n\n\n\n<p>Next, let&#8217;s convert both of the original decimal numbers into fractions:0.5=12,\u22120.4375=\u22127160.5 = \\frac{1}{2}, \\quad -0.4375 = -\\frac{7}{16}0.5=21\u200b,\u22120.4375=\u2212167\u200b<\/p>\n\n\n\n<p>Now, multiply the fractions:12\u00d7\u2212716=\u2212732\\frac{1}{2} \\times -\\frac{7}{16} = -\\frac{7}{32}21\u200b\u00d7\u2212167\u200b=\u2212327\u200b<\/p>\n\n\n\n<p>Thus, the product is indeed \u2212732-\\frac{7}{32}\u2212327\u200b, which is equivalent to \u22120.21875-0.21875\u22120.21875, confirming our multiplication result.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The product of 0.50.50.5 and \u22120.4375-0.4375\u22120.4375 is \u22120.21875-0.21875\u22120.21875, and by converting it back to a fraction, we verified the result.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-1094.jpeg\" alt=\"\" class=\"wp-image-249152\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Given two decimal numbers 0.5 and -0.4375. (a) Multiply the numbers. (b) Converting to decimal to check the results. Show your workings. The Correct Answer and Explanation is: To solve this, we will first multiply the two decimal numbers, and then we will convert the result to check the accuracy. Part (a): Multiplying the Numbers [&hellip;]<\/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-249151","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249151","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=249151"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249151\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}