{"id":136,"date":"2022-04-12T12:12:15","date_gmt":"2022-04-12T12:12:15","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=136"},"modified":"2025-02-23T09:09:46","modified_gmt":"2025-02-23T09:09:46","slug":"g-2-compare-numbers-written-in-scientific-notation","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/g-2-compare-numbers-written-in-scientific-notation\/","title":{"rendered":"G.2 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<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-869a5c0b6b78055316c8d0186252dcbd\" style=\"color:#74008b\"><strong>key notes :<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">You&nbsp;can compare two numbers written in scientific notation by following these&nbsp;steps:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-large-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-large-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<\/ol>\n\n\n\n<p class=\"has-large-font-size\">Let&#8217;s&nbsp;try it! Compare&nbsp;4.7\u00d710\u2078&nbsp;and&nbsp;3.6\u00d710\u2079.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Start by comparing the powers of 10. Since 10\u2078 &lt; 10\u2079, then 4.7\u00d710\u2078 &lt; 3.6\u00d710\u2079. <\/p>\n\n\n\n<p class=\"has-large-font-size\">You can see why this works by rewriting each number in standard form.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"> 4.7\u00d710\u2078 = 470,000,000 <\/li>\n\n\n\n<li class=\"has-large-font-size\">3.6\u00d710\u2079 = 3,600,000,000 <\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">\ud83c\udff9Since 470,000,000&lt;3,600,000,000, then 4.7\u00d710\u2078 &lt; 3.6\u00d710\u2079.<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color\" id=\"yui_3_18_1_1_1669859779744_2732\" style=\"color:#000170\">Another&nbsp;example:<\/h4>\n\n\n\n<p class=\"has-large-font-size\">Compare&nbsp;5.1\u00d710\u207b\u2077&nbsp;and&nbsp;2.8\u00d710\u207b\u2077.<\/p>\n\n\n\n<p class=\"has-large-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-large-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-large-font-size\">You&nbsp;can see why this works by rewriting each number in standard&nbsp;form.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">5.1\u00d710\u207b\u2077 = 0.00000051<\/li>\n\n\n\n<li class=\"has-large-font-size\">2.8\u00d710\u207b\u2077 = 0.00000028<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">\ud83c\udff9Since&nbsp;0.00000051 &gt; 0.00000028,&nbsp;then 5.1\u00d710\u207b\u2077 &gt; 2.8\u00d710\u207b\u2077 <\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-7c43e0815413ce413f47e9c72a542ff3\" style=\"background-color:#f6abab\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-b0dca409b073eea910936d279d81e678\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-fe4c1408b322d9904bcaabf387d69cba\" style=\"color:#b00012\"><strong>Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-3.png\" alt=\"\" class=\"wp-image-12818\" style=\"width:372px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-3.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-3-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\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>2.95 \u00d7&nbsp;<strong>10<\/strong><sup><strong>3<\/strong><\/sup>&nbsp;&nbsp;? 2.95 \u00d7&nbsp;<strong>10<\/strong><sup><strong>1<\/strong><\/sup><\/p>\n\n\n\n<p>\u200b10<sup>3<\/sup>&nbsp;is larger than&nbsp;10<sup>1<\/sup>, so the first number is larger.<\/p>\n\n\n\n<p>2.95 \u00d7&nbsp;10<sup>3<\/sup>&nbsp;&gt; 2.95 \u00d7&nbsp;10<sup>1<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-0f97c230d2b8fd90a5b44162a199d053\" style=\"background-color:#a8f9b0\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-f4447a7fcc4befd2ae2ceacd8f4718f2\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-fe4c1408b322d9904bcaabf387d69cba\" style=\"color:#b00012\"><strong>Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-2.png\" alt=\"\" class=\"wp-image-12816\" style=\"width:436px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-2.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-2-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Express the second number in standard form. Look at&nbsp;10<sup>4<\/sup>. The 10 is raised to the power of 4. You want to move the decimal point 4 places to the right. First, write extra zeroes to the right of the decimal point. Remember that writing extra zeroes to the right of a decimal does not change its value.<\/p>\n\n\n\n<p>3.86 = 3.8600<\/p>\n\n\n\n<p>Now move the decimal point 4 places to the right.<\/p>\n\n\n\n<p>3.8600&nbsp;\u2192&nbsp;38,600.<\/p>\n\n\n\n<p>3.86 \u00d7&nbsp;10<sup>4<\/sup>&nbsp;= 38,600<\/p>\n\n\n\n<p>Compare the two numbers.<\/p>\n\n\n\n<p>38,600 = 38,600<\/p>\n\n\n\n<p>38,600 = 3.86 \u00d7&nbsp;10<sup>4<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-16c54d77c6d034216f28bf816d68d2c8\" style=\"background-color:#e9a9e9\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-5a4196665ab9e4d6b8da770ca1161413\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-fe4c1408b322d9904bcaabf387d69cba\" style=\"color:#b00012\"><strong>Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-4.png\" alt=\"\" class=\"wp-image-12820\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-4.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-4-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\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>1.4 \u00d7&nbsp;<strong>10<\/strong><sup><strong>4<\/strong><\/sup>&nbsp;?&nbsp;1.4 \u00d7&nbsp;<strong>10<\/strong><sup><strong>3<\/strong><\/sup><\/p>\n\n\n\n<p>\u200b10<sup>4<\/sup>&nbsp;is larger than&nbsp;10<sup>3<\/sup>, so the first number is larger.<\/p>\n\n\n\n<p>1.4 \u00d7&nbsp;10<sup>4<\/sup>&nbsp;&gt; 1.4 \u00d7&nbsp;10<sup>3<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!<\/strong><\/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\/899\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-314.png\" alt=\"\" class=\"wp-image-9646\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-314.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-314-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-314-150x150.png 150w\" 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\/79761\/114\/933\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-321.png\" alt=\"\" class=\"wp-image-9647\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-321.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-321-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-321-150x150.png 150w\" 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 key notes : You&nbsp;can compare two numbers written in scientific notation by following these&nbsp;steps: Let&#8217;s&nbsp;try it! Compare&nbsp;4.7\u00d710\u2078&nbsp;and&nbsp;3.6\u00d710\u2079. Start by comparing the powers of 10. Since 10\u2078 &lt; 10\u2079, then 4.7\u00d710\u2078 &lt; 3.6\u00d710\u2079. You can see why this works by rewriting each number in standard form. \ud83c\udff9Since 470,000,000&lt;3,600,000,000, then 4.7\u00d710\u2078<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/g-2-compare-numbers-written-in-scientific-notation\/\">Continue reading <span class=\"screen-reader-text\">&#8220;G.2 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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-136","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/136","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=136"}],"version-history":[{"count":32,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/136\/revisions"}],"predecessor-version":[{"id":19982,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/136\/revisions\/19982"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=136"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}