{"id":28,"date":"2022-04-12T09:07:47","date_gmt":"2022-04-12T09:07:47","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=28"},"modified":"2025-08-19T18:03:10","modified_gmt":"2025-08-19T18:03:10","slug":"a-9-compare-numbers-written-in-scientific-notation","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/a-9-compare-numbers-written-in-scientific-notation\/","title":{"rendered":"A.9 Compare numbers written in scientific notation"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Compare numbers written in scientific notation<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAGv8WfiqV8\/AuMwMpQlb9ms7XnH8pBmeA\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGv8WfiqV8&#x2F;AuMwMpQlb9ms7XnH8pBmeA&#x2F;watch?utm_content=DAGv8WfiqV8&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">7th class &#8211; Compare numbers written in scientific notation<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">Key Notes:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000040\"><tbody><tr><td><strong>Scientific Notation :<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Numbers in scientific notation are expressed as a\u00d710na \\times 10^na\u00d710n, where aaa is a number between 1 and 10, and nnn is an integer.<\/li>\n\n\n\n<li>Example: 3.25\u00d71043.25 \\times 10^43.25\u00d7104 means 32,500.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000040\"><tbody><tr><td><strong><strong>Comparison Steps:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Compare the coefficients (the numbers aaa) directly.<\/p>\n\n\n\n<p>If the coefficients are equal, compare the exponents nnn:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Larger exponent means a larger number.<\/li>\n\n\n\n<li>Smaller exponent means a smaller number.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000040\"><tbody><tr><td><strong>Examples:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Compare 2.1\u00d71052.1 \\times 10^52.1\u00d7105 and 3.5\u00d71043.5 \\times 10^43.5\u00d7104:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Coefficient comparison: 2.1&gt;3.52.1 &gt; 3.52.1&gt;3.5 (so 2.1\u00d71052.1 \\times 10^52.1\u00d7105 is larger).<\/li>\n<\/ul>\n\n\n\n<p>Compare 4.2\u00d71034.2 \\times 10^34.2\u00d7103 and 4.5\u00d71034.5 \\times 10^34.5\u00d7103:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Coefficients are close, compare exponents: 4.2\u00d7103&lt;4.5\u00d71034.2 \\times 10^3 &lt; 4.5 \\times 10^34.2\u00d7103&lt;4.5\u00d7103 (so 4.5\u00d71034.5 \\times 10^34.5\u00d7103 is larger).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\">You&nbsp;can compare two numbers written in scientific notation by following these&nbsp;steps:<\/p>\n\n\n\n<ul id=\"yui_3_18_1_1_1721308284980_2568\" class=\"wp-block-list has-normal-font-size\">\n<li class=\"has-normal-font-size\"><strong>Compare<\/strong><strong>&nbsp;the powers of&nbsp;<\/strong><strong>10<\/strong><strong>.<\/strong>&nbsp;If one of the powers of&nbsp;10&nbsp;is greater than the other, that number is&nbsp;greater.<\/li>\n\n\n\n<li class=\"has-normal-font-size\"><strong>If<\/strong><strong>&nbsp;the powers of&nbsp;<\/strong><strong>10<\/strong><strong>&nbsp;are the same, compare the first&nbsp;<\/strong><strong>factors.<\/strong>&nbsp;If one of the first factors is greater than the other, that number is&nbsp;greater.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000040\"><tbody><tr><td><strong><strong>In any other situation<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-color has-normal-font-size\" style=\"color:#000060\">Let&#8217;s try it! Compare 4.7\u00d710\u2078 and 3.6\u00d710\u2079.<\/p>\n\n\n\n<p class=\"has-text-color has-normal-font-size\" style=\"color:#000060\">Start&nbsp;by comparing the powers of&nbsp;10.&nbsp;Since&nbsp;10\u2078 &lt; 10\u2079, then 4.7\u00d710\u2078 &lt; 3.6\u00d710\u2079.<\/p>\n\n\n\n<p class=\"has-text-color has-normal-font-size\" style=\"color:#000060\">You&nbsp;can see why this works by rewriting each number in standard&nbsp;form.<\/p>\n\n\n\n<p class=\"has-text-color has-normal-font-size\" style=\"color:#000060\">4.7\u00d710\u2078 = 470,000,000<\/p>\n\n\n\n<p class=\"has-text-color has-normal-font-size\" style=\"color:#000060\">3.6\u00d710\u2079 = 3,600,000,000<\/p>\n\n\n\n<p class=\"has-text-color has-normal-font-size\" style=\"color:#000060\">Since 470,000,000 &lt; 3,600,000,000, then 4.7\u00d710\u2078 &lt; 3.6\u00d710\u2079.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000040\"><tbody><tr><td><strong><strong>Another example<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-color has-normal-font-size\" style=\"color:#000060\">Compare 5.1\u00d710\u207b\u2077 and 2.8\u00d710\u207b\u2077.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Start&nbsp;by comparing the powers of&nbsp;10.&nbsp;Since they are the same, compare the first&nbsp;factors.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Compare the first factor in each number. Since 5.1 &gt; 2.8, then 5.1\u00d710\u207b\u2077 &gt; 2.8\u00d710\u207b\u2077.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">You&nbsp;can see why this works by rewriting each number in standard&nbsp;form.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">5.1\u00d710\u207b\u2077 =&nbsp;0.00000051.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">2.8\u00d710\u207b\u2077 =&nbsp;0.00000028.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Since 0.00000051 &gt; 0.00000028, then 5.1\u00d710\u207b\u2077 &gt; 2.8\u00d710\u207b\u2077.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000040\"><tbody><tr><td><strong><strong>Learn with an example<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#b4e3fb\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-normal-font-size\" style=\"color:#b00012\"><strong>Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-normal-font-size\" style=\"color:#b00012\"><strong>3 \u00d7&nbsp;10<sup>5<\/sup>&nbsp;____ 3.3 \u00d7&nbsp;10<sup>4<\/sup><\/strong><\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p class=\"has-normal-font-size\">Both numbers are in correct scientific notation, so you can compare them.<\/p>\n\n\n\n<p>Look at the powers of 10.<\/p>\n\n\n\n<p>3 \u00d7&nbsp;<strong>10<\/strong><sup><strong>5<\/strong><\/sup>&nbsp;____ 3.3 \u00d7&nbsp;<strong>10<\/strong><sup><strong>4<\/strong><\/sup><\/p>\n\n\n\n<p>\u200b10<sup>5<\/sup>&nbsp;is larger than&nbsp;10<sup>4<\/sup>, so the first number is larger.<\/p>\n\n\n\n<p>3 \u00d7&nbsp;10<sup>5<\/sup>&nbsp;<strong>&gt;<\/strong> 3.3 \u00d7&nbsp;10<sup>4<\/sup><\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#c4f9b7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-normal-font-size\" style=\"color:#b00012\"><strong>Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-normal-font-size\" style=\"color:#b00012\"><strong>300.3&nbsp;&nbsp;____  3.03 \u00d7&nbsp;10<sup>2<\/sup><\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Express the second number in standard form. Look at&nbsp;10<sup>2<\/sup>. The 10 is raised to the power of 2. Move the decimal point 2 places to the right.<\/p>\n\n\n\n<p>3.03&nbsp;\u2192&nbsp;303.<\/p>\n\n\n\n<p>3.03 \u00d7&nbsp;10<sup>2<\/sup>&nbsp;= 303<\/p>\n\n\n\n<p>Compare the two numbers.<\/p>\n\n\n\n<p>300.3 &lt; 303<\/p>\n\n\n\n<p>300.3 &lt; 3.03 \u00d7&nbsp;10<sup>2<\/sup><\/p>\n<\/div><\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#f6c6e4\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-normal-font-size\" style=\"color:#b00012\"><strong>Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-normal-font-size\" style=\"color:#b00012\"><strong>7.70 \u00d7&nbsp;10<sup>1<\/sup>&nbsp;______ 7.7 \u00d7&nbsp;10<sup>1<\/sup><\/strong><\/p>\n<\/div><\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p>Both numbers are in correct scientific notation, so you can compare them.<\/p>\n\n\n\n<p>Look at the powers of 10.<\/p>\n\n\n\n<p>7.70 \u00d7&nbsp;<strong>10<\/strong><sup><strong>1<\/strong><\/sup>&nbsp;___ 7.7 \u00d7&nbsp;<strong>10<\/strong><sup><strong>1<\/strong><\/sup><\/p>\n\n\n\n<p>The powers of 10 are the same, so next look at the coefficient parts.<\/p>\n\n\n\n<p><strong>7.70<\/strong>&nbsp;\u00d7&nbsp;10<sup>1<\/sup><strong>___<\/strong><strong>7.7<\/strong>&nbsp;\u00d7&nbsp;10<sup>1<\/sup><\/p>\n\n\n\n<p>The coefficients are the same, so the two numbers are equal.<\/p>\n\n\n\n<p>7.70 \u00d7&nbsp;10<sup>1<\/sup>&nbsp;<strong>=<\/strong> 7.7 \u00d7&nbsp;10<sup>1<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/75713\/175\/626\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-8.png\" alt=\"\" class=\"wp-image-6493\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-8.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-8-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-8-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-8-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/75610\/435\/658\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-8.png\" alt=\"\" class=\"wp-image-6494\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-8.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-8-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-8-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-8-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Compare numbers written in scientific notation 7th class &#8211; Compare numbers written in scientific notation by Delta publications Key Notes: Scientific Notation : Comparison Steps: Compare the coefficients (the numbers aaa) directly. If the coefficients are equal, compare the exponents nnn: Examples: Compare 2.1\u00d71052.1 \\times 10^52.1\u00d7105 and 3.5\u00d71043.5 \\times 10^43.5\u00d7104: Compare 4.2\u00d71034.2 \\times 10^34.2\u00d7103 and<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/a-9-compare-numbers-written-in-scientific-notation\/\">Continue reading <span class=\"screen-reader-text\">&#8220;A.9 Compare numbers written in scientific notation&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-28","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/28","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=28"}],"version-history":[{"count":30,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/28\/revisions"}],"predecessor-version":[{"id":16797,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/28\/revisions\/16797"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=28"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}