{"id":217279,"date":"2025-05-21T12:03:08","date_gmt":"2025-05-21T12:03:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=217279"},"modified":"2025-05-21T12:03:11","modified_gmt":"2025-05-21T12:03:11","slug":"determine-the-number-of-significant-digits-in-each-number-and-write-the-specific-significant-digits","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/21\/determine-the-number-of-significant-digits-in-each-number-and-write-the-specific-significant-digits\/","title":{"rendered":"Determine the number of significant digits in each number, and write the specific significant digits."},"content":{"rendered":"\n<p>Determine the number of significant digits in each number, and write the specific significant digits.<\/p>\n\n\n\n<p>405000<br>0.0098<br>39.999999<br>13.00<br>80,000,089<br>55,430.00<br>0.000033<br>620.03080<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Sure! Let&#8217;s analyze each number to determine the number of significant digits and list the specific significant digits.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">1. <strong>405000<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Significant digits:<\/strong> 3 (4, 0, 5)<\/li>\n\n\n\n<li><strong>Explanation:<\/strong> The trailing zeros in this number are ambiguous without additional formatting (like a decimal point). Typically, if there is no decimal point, trailing zeros are not considered significant. So, only 4, 0, and 5 are significant here.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">2. <strong>0.0098<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Significant digits:<\/strong> 2 (9, 8)<\/li>\n\n\n\n<li><strong>Explanation:<\/strong> Leading zeros are never significant; they only indicate the position of the decimal point. So only the digits 9 and 8 are significant.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">3. <strong>39.999999<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Significant digits:<\/strong> 8 (3, 9, 9, 9, 9, 9, 9, 9)<\/li>\n\n\n\n<li><strong>Explanation:<\/strong> All digits in a decimal number are significant, including trailing zeros. Here, 8 digits are significant.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">4. <strong>13.00<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Significant digits:<\/strong> 4 (1, 3, 0, 0)<\/li>\n\n\n\n<li><strong>Explanation:<\/strong> The zeros after the decimal point are significant because they indicate precision.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">5. <strong>80,000,089<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Significant digits:<\/strong> 8 (8, 0, 0, 0, 0, 0, 8, 9)<\/li>\n\n\n\n<li><strong>Explanation:<\/strong> All non-zero digits and any zeros between non-zero digits are significant. Here, the zeros between 8 and 8 are significant as they occur between significant digits. Trailing zeros would be significant only if there was a decimal point, but here zeros are between 8&#8217;s.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">6. <strong>55,430.00<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Significant digits:<\/strong> 7 (5, 5, 4, 3, 0, 0, 0)<\/li>\n\n\n\n<li><strong>Explanation:<\/strong> The zeros after the decimal point are significant, indicating precision. All digits are significant.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">7. <strong>0.000033<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Significant digits:<\/strong> 2 (3, 3)<\/li>\n\n\n\n<li><strong>Explanation:<\/strong> Leading zeros are not significant; only the digits 3 and 3 are significant.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">8. <strong>620.03080<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Significant digits:<\/strong> 8 (6, 2, 0, 0, 3, 0, 8, 0)<\/li>\n\n\n\n<li><strong>Explanation:<\/strong> All digits including zeros between non-zero digits and trailing zeros after a decimal point are significant.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Summary Table:<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Number<\/th><th>Significant Digits<\/th><th>Digits<\/th><\/tr><\/thead><tbody><tr><td>405000<\/td><td>3<\/td><td>4, 0, 5<\/td><\/tr><tr><td>0.0098<\/td><td>2<\/td><td>9, 8<\/td><\/tr><tr><td>39.999999<\/td><td>8<\/td><td>3, 9, 9, 9, 9, 9, 9, 9<\/td><\/tr><tr><td>13.00<\/td><td>4<\/td><td>1, 3, 0, 0<\/td><\/tr><tr><td>80,000,089<\/td><td>8<\/td><td>8, 0, 0, 0, 0, 0, 8, 9<\/td><\/tr><tr><td>55,430.00<\/td><td>7<\/td><td>5, 5, 4, 3, 0, 0, 0<\/td><\/tr><tr><td>0.000033<\/td><td>2<\/td><td>3, 3<\/td><\/tr><tr><td>620.03080<\/td><td>8<\/td><td>6, 2, 0, 0, 3, 0, 8, 0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300+ words):<\/h3>\n\n\n\n<p>The concept of significant digits (or significant figures) is fundamental in science and mathematics to express the precision of a measured or calculated number. Significant digits include all the digits in a number that contribute to its accuracy, including all non-zero digits, zeros between significant digits, and trailing zeros in decimal numbers.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Non-zero digits<\/strong> are always significant. For example, digits like 4, 5, 9, and 3 in numbers are always counted.<\/li>\n\n\n\n<li><strong>Leading zeros<\/strong>, which are zeros before any non-zero digit, serve only as placeholders to locate the decimal point and are <strong>not significant<\/strong>. For example, in 0.0098, the zeros before 9 are not significant, so only two significant digits exist (9 and 8).<\/li>\n\n\n\n<li><strong>Captive zeros<\/strong> (zeros between non-zero digits) are significant. For example, in 80,000,089, all zeros between the first 8 and the last digits are significant because they are sandwiched between significant digits.<\/li>\n\n\n\n<li><strong>Trailing zeros<\/strong> have special rules:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If trailing zeros are after a decimal point, they are significant because they show precision. For example, 13.00 has four significant digits, including the zeros.<\/li>\n\n\n\n<li>If trailing zeros are before a decimal point (e.g., 405000 without a decimal), those zeros are often not significant unless otherwise specified by scientific notation or a decimal point.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Decimal points<\/strong> make trailing zeros significant. For example, 55,430.00 contains trailing zeros after the decimal point, so they are significant, making a total of 7 significant digits.<\/li>\n<\/ol>\n\n\n\n<p>Understanding significant digits ensures accuracy in scientific calculations and conveys the precision of measurements. It helps avoid overstating precision and allows consistent communication of data reliability.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Determine the number of significant digits in each number, and write the specific significant digits. 4050000.009839.99999913.0080,000,08955,430.000.000033620.03080 The Correct Answer and Explanation is: Sure! Let&#8217;s analyze each number to determine the number of significant digits and list the specific significant digits. 1. 405000 2. 0.0098 3. 39.999999 4. 13.00 5. 80,000,089 6. 55,430.00 7. 0.000033 8. [&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-217279","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217279","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=217279"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217279\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=217279"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=217279"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=217279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}