{"id":138,"date":"2022-04-12T12:12:38","date_gmt":"2022-04-12T12:12:38","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=138"},"modified":"2025-02-23T09:12:36","modified_gmt":"2025-02-23T09:12:36","slug":"g-3-multiply-numbers-written-in-scientific-notation","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/g-3-multiply-numbers-written-in-scientific-notation\/","title":{"rendered":"G.3 Multiply 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>Multiply 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\">Very&nbsp;large or very small numbers can be written in&nbsp;scientific&nbsp;notation&nbsp;to make them easier to work with. Numbers in scientific notation are written as the product of two&nbsp;factors.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">The&nbsp;<strong>first&nbsp;factor<\/strong>&nbsp;is always a number greater than or equal to&nbsp;1&nbsp;but less than&nbsp;10.<\/li>\n\n\n\n<li class=\"has-large-font-size\">The&nbsp;<strong>second&nbsp;factor<\/strong>&nbsp;is always a&nbsp;power&nbsp;of&nbsp;10.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">For&nbsp;example, you can write the number&nbsp;39,000,000&nbsp;in scientific notation as&nbsp;<strong>3.9<\/strong>\u00d7<strong>10\u2077<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color\" id=\"yui_3_18_1_1_1669863087676_2617\" style=\"color:#1b07ac\">Multiplying&nbsp;numbers&nbsp;in&nbsp;scientific&nbsp;notation<\/h3>\n\n\n\n<p class=\"has-large-font-size\">You&nbsp;can follow these steps to multiply numbers in scientific&nbsp;notation:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Rewrite&nbsp;the multiplication expression to group the first factors and the powers of&nbsp;10.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Multiply&nbsp;the first&nbsp;factors.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Multiply&nbsp;the powers of&nbsp;10&nbsp;using the&nbsp;product&nbsp;of&nbsp;powers&nbsp;property.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Rewrite&nbsp;the product to be in proper scientific notation, if&nbsp;needed.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-large-font-size\">Let&#8217;s try it! Multiply (1.5\u00d710\u2075)\u00d7(6.8\u00d710\u2077).<\/p>\n\n\n\n<p class=\"has-large-font-size\">           (1.5\u00d710\u2075)\u00d7(6.8\u00d710\u2077)<\/p>\n\n\n\n<p class=\"has-large-font-size\">               =  (1.5\u00d76.8)\u00d7(10\u2075\u00d710\u2077) &#8212;&#8212;-&gt; Group the first factors and the powers of 10.<\/p>\n\n\n\n<p class=\"has-large-font-size\">               = 10.2\u00d7(10\u2075\u00d710\u2077)   &#8212;&#8212;&#8211;&gt;Multiply&nbsp;the first&nbsp;factors.<\/p>\n\n\n\n<p class=\"has-large-font-size\">               = 10.2\u00d710\u2075\u207a\u2077   &#8212;-&gt; Multiply&nbsp;the powers of&nbsp;10&nbsp;using the product of powers&nbsp;property.<\/p>\n\n\n\n<p class=\"has-large-font-size\">               = 10.2\u00d710\u00b9\u00b2<\/p>\n\n\n\n<p class=\"has-large-font-size\">Since&nbsp;the first factor in the product,&nbsp;10.2,&nbsp;is greater than&nbsp;10,&nbsp;the product is not written in proper scientific form. Rewrite the product so the first factor is greater than&nbsp;1&nbsp;but less than&nbsp;10.<\/p>\n\n\n\n<p class=\"has-large-font-size\">10.2\u00d710\u00b9\u00b2<\/p>\n\n\n\n<p class=\"has-large-font-size\">      = 1.02\u00d710\u00d710\u00b9\u00b2    &#8212;&#8212;&gt;Rewrite 10.2 as 1.02\u00d710.<\/p>\n\n\n\n<p class=\"has-large-font-size\">      = 1.02\u00d7(10\u00d710\u00b9\u00b2)    &#8212;&#8211;&gt;Multiply 10\u00d710\u00b9\u00b2.<\/p>\n\n\n\n<p class=\"has-large-font-size\">      =1.02\u00d710\u00b9\u00b3<\/p>\n\n\n\n<p class=\"has-large-font-size\">So, 10.2\u00d710\u00b9\u00b2 = 1.02\u00d710\u00b9\u00b3, and (1.5\u00d710\u2075)\u00d7(6.8\u00d710\u2077) = 1.02\u00d710\u00b9\u00b3.<\/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-f639b4e7088d59bff3b49663296215a9\" style=\"background-color:#e9ed9d\"><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-180f244053a21be22d75ab300b6b5375\"><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-de23182384b4221761332acb35840d58\" style=\"color:#b00012\"><strong>Multiply.<\/strong><\/p>\n\n\n\n<p>(2 \u00d7 10<sup>5<\/sup> )(3 \u00d7 10<sup>3<\/sup>)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5 \u00d7 10<sup>15<\/sup><\/li>\n\n\n\n<li>6 \u00d7 10<sup>15<\/sup><\/li>\n\n\n\n<li>5 \u00d7 10<sup>8<\/sup><\/li>\n\n\n\n<li>6 \u00d7 10<sup>8<\/sup><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Multiply.<\/p>\n\n\n\n<p>(2 \u00d7 10<sup>5<\/sup> )(3 \u00d7 10<sup>3<\/sup>)<\/p>\n\n\n\n<p>(2 .3) \u00d7 (10<sup>5<\/sup> .10<sup>3<\/sup>) Group the first factors and the power of 10<\/p>\n\n\n\n<p>6 \u00d7 (10<sup>5<\/sup> .10<sup>3<\/sup>) Multiply the first factors<\/p>\n\n\n\n<p>6 \u00d7 10<sup>5+3<\/sup> Multiply the powers of 10 , remembering to add the exponents<\/p>\n\n\n\n<p>6 \u00d7 10<sup>8<\/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-036ee1dc54e612ef834ea11b475d6543\" style=\"background-color:#feb1ee\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><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-dc74cd4867f39e606c536eb513dbe2d1\" style=\"color:#b00012\"><strong>Multiply.&nbsp;Write your answer in scientific&nbsp;notation.<\/strong><\/p>\n\n\n\n<p>(1 \u00d7 10<sup>2<\/sup> )(6 \u00d710<sup>1<\/sup>) = ____________<\/p>\n<\/div><\/div>\n\n\n\n<p>Multiply.<\/p>\n\n\n\n<p>(1 \u00d7 10<sup>2<\/sup> )(6 \u00d7 10<sup>1<\/sup>)<\/p>\n\n\n\n<p>(1 .6) \u00d7 (10<sup>2<\/sup> .10<sup>1<\/sup>) Group the first factors and the power of 10<\/p>\n\n\n\n<p>6 \u00d7 (10<sup>2<\/sup> .10<sup>1<\/sup>) Multiply the first factors<\/p>\n\n\n\n<p>6 \u00d7 10<sup>2+1<\/sup> Multiply the powers of 10 , remembering to add the exponents<\/p>\n\n\n\n<p>6 \u00d7 10<sup>3<\/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-af94a478c790d6dbd0d8c67bd338bf16\" style=\"background-color:#acf2af\"><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-d0f0c819215f240901867ad2e085feba\"><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-2840ae9e0e3cb3bb7e2b107f4be0268f\" style=\"color:#b00012\"><strong>Multiply<\/strong>.<\/p>\n\n\n\n<p>(3 \u00d7 10<sup>1<\/sup> )(3 \u00d7 10<sup>1<\/sup>)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4 \u00d7 10<sup>1<\/sup><\/li>\n\n\n\n<li>9 \u00d7 10<sup>2<\/sup><\/li>\n\n\n\n<li>4 \u00d7 10<sup>2<\/sup><\/li>\n\n\n\n<li>9 \u00d7 10<sup>1<\/sup><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Multiply.<\/p>\n\n\n\n<p>(3 \u00d7 10<sup>1<\/sup> )(3 \u00d7 10<sup>1<\/sup>)<\/p>\n\n\n\n<p>(3 .3) \u00d7 (10<sup>1<\/sup> .10<sup>1<\/sup>) Group the first factors and the power of 10<\/p>\n\n\n\n<p>9 \u00d7 (10<sup>1<\/sup> .10<sup>1<\/sup>) Multiply the first factors<\/p>\n\n\n\n<p>9 \u00d7 10<sup>1+1<\/sup> Multiply the powers of 10 , remembering to add the exponents<\/p>\n\n\n\n<p>9 \u00d7 10<sup>2<\/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\/79919\/653\/915\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-313.png\" alt=\"\" class=\"wp-image-9643\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-313.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-313-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-313-150x150.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\/129\/589\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-320.png\" alt=\"\" class=\"wp-image-9644\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-320.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-320-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-320-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiply numbers written in scientific notation key notes : Very&nbsp;large or very small numbers can be written in&nbsp;scientific&nbsp;notation&nbsp;to make them easier to work with. Numbers in scientific notation are written as the product of two&nbsp;factors. For&nbsp;example, you can write the number&nbsp;39,000,000&nbsp;in scientific notation as&nbsp;3.9\u00d710\u2077. Multiplying&nbsp;numbers&nbsp;in&nbsp;scientific&nbsp;notation You&nbsp;can follow these steps to multiply numbers in scientific&nbsp;notation: Let&#8217;s<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/g-3-multiply-numbers-written-in-scientific-notation\/\">Continue reading <span class=\"screen-reader-text\">&#8220;G.3 Multiply 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-138","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\/138","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=138"}],"version-history":[{"count":31,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/138\/revisions"}],"predecessor-version":[{"id":19983,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/138\/revisions\/19983"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}