{"id":134,"date":"2022-04-12T12:11:59","date_gmt":"2022-04-12T12:11:59","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=134"},"modified":"2025-02-23T09:08:01","modified_gmt":"2025-02-23T09:08:01","slug":"g-1-convert-between-standard-and-scientific-notation","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/g-1-convert-between-standard-and-scientific-notation\/","title":{"rendered":"G.1 Convert between standard and scientific notation"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Convert between standard and scientific notation<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-28d136ae4331e7eb05ec8e1cb71ebcde\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<p class=\"has-large-font-size\">\ud83c\udff9 Scientific notation:<\/p>\n\n\n\n<p class=\"has-large-font-size\">You&nbsp;can use scientific notation to write very large or very small numbers. Here are some&nbsp;examples.<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>4,000,000<\/strong>&nbsp;in scientific notation is&nbsp;4\u00d7<strong>106<\/strong>.<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>0.00007<\/strong>&nbsp;in scientific notation is&nbsp;7\u00d7<strong>10<\/strong>\u2013<strong>5<\/strong>.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Writing&nbsp;numbers in scientific notation can make them easier to work&nbsp;with.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color\" id=\"yui_3_18_1_1_1669859779744_2666\" style=\"color:#0e0075\">How&nbsp;do&nbsp;you&nbsp;read&nbsp;numbers&nbsp;in&nbsp;scientific&nbsp;notation?<\/h3>\n\n\n\n<p class=\"has-large-font-size\">You&nbsp;can interpret scientific notation by converting the number to standard form. Just follow the rules for multiplying by a&nbsp;power&nbsp;of&nbsp;10.&nbsp;When you multiply by a power of&nbsp;10,&nbsp;the exponent in the power of 10 tells you how many places to move the decimal point. Follow these&nbsp;rules:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">If&nbsp;the exponent is positive, move the decimal point&nbsp;<strong>to<\/strong><strong>&nbsp;the&nbsp;<\/strong><strong>right<\/strong>.<\/li>\n\n\n\n<li class=\"has-large-font-size\">If&nbsp;the exponent is negative, move the decimal point&nbsp;<strong>to<\/strong><strong>&nbsp;the&nbsp;<\/strong><strong>left<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">Let&#8217;s&nbsp;try it! The planet Neptune is about&nbsp;2.78\u00d710\u2079&nbsp;miles from the sun. Write&nbsp;&nbsp;2.78\u00d710\u2079&nbsp;in standard&nbsp;form.<\/p>\n\n\n\n<p class=\"has-large-font-size\">The&nbsp;exponent in&nbsp;<strong>10\u2079&nbsp;<\/strong>&nbsp;is positive&nbsp;9,&nbsp;so move the decimal point&nbsp;9&nbsp;places to the&nbsp;right.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.ixl.com\/~media\/2\/Z0LaMM0GN7knBp6pIal9o2ZgMLpc9T5LFq64fxg1QxGCSs3drXY_FS9NS8gKbxsayUD4iTb4rqrvcEV6ARlu2A.svg\" alt=\"The number two point seven eight zero zero zero zero zero zero zero is shown. Under the number, there are nine arrows showing the decimal point moving between decimal places. The arrows start between the two and the seven and point right, with the last arrow pointing to the right of the last zero. The arrows are labeled with the numbers one through nine. Next to that number is an arrow pointing to the number two billion seven hundred eighty million.\"\/><\/figure>\n\n\n\n<p class=\"has-large-font-size\">So,&nbsp;<strong>2.78<\/strong>\u00d7<strong>10\u2079&nbsp;<\/strong>in standard form is&nbsp;2,780,000,000.<\/p>\n\n\n\n<h5 class=\"wp-block-heading has-large-font-size\" id=\"yui_3_18_1_1_1669859779744_2814\">Another&nbsp;example: <\/h5>\n\n\n\n<p class=\"has-large-font-size\">The&nbsp;average grain of sand weighs about&nbsp;<strong>4.4\u00d710\u207b\u2076<\/strong>&nbsp;kilograms. Write&nbsp;4.4\u00d710\u20136&nbsp;in standard&nbsp;form.<\/p>\n\n\n\n<p class=\"has-large-font-size\">The&nbsp;exponent in&nbsp;<strong><strong>10\u207b\u2076<\/strong><\/strong> is negative&nbsp;6,&nbsp;so move the decimal point&nbsp;6&nbsp;places to the&nbsp;left.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/www.ixl.com\/~media\/2\/Q-nwZo6tYMiytg4_ZuvxILbhqIdwcvP9JtXPNWCNgEPzQQBR_4KCeBgw3ybYLdGVllmIoiCYnFRMioGCWy0E1w.svg\" alt=\"The number zero zero zero zero zero zero four point four is shown. Under the number, there are six arrows showing the decimal point moving between decimal places. The arrows start after the between the two fours and point left, with the last arrow pointing between the first two zeros. The arrows are labeled with the numbers one through six. Next to that number is an arrow pointing to the number zero point zero zero zero zero zero four four.\" style=\"width:476px;height:auto\"\/><\/figure>\n\n\n\n<p class=\"has-large-font-size\">So,&nbsp;<strong>4.4<\/strong>\u00d7<strong><strong><strong>10\u207b\u2076<\/strong><\/strong><\/strong>&nbsp;in standard form is&nbsp;0.0000044.<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color\" id=\"yui_3_18_1_1_1669859779744_2829\" style=\"color:#940808\">How&nbsp;do&nbsp;you&nbsp;write&nbsp;numbers&nbsp;in&nbsp;scientific&nbsp;notation?<\/h4>\n\n\n\n<p class=\"has-large-font-size\">You&nbsp;can write numbers in scientific notation by writing them as a 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<\/strong><strong>&nbsp;<\/strong><strong>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<\/strong><strong>&nbsp;<\/strong><strong>factor<\/strong>&nbsp;is always a power 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;561,000,000&nbsp;in scientific notation as&nbsp;<strong>5.61<\/strong>\u00d7<strong>10\u2078<\/strong>.<\/p>\n\n\n\n<p class=\"has-large-font-size\">To&nbsp;determine the two factors, follow these&nbsp;steps:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Move<\/strong><strong>&nbsp;the decimal point in the&nbsp;<\/strong><strong>number<\/strong>&nbsp;until you get a number greater than or equal to&nbsp;1&nbsp;but less than&nbsp;10.&nbsp;This will be the first&nbsp;factor.<\/li>\n\n\n\n<li class=\"has-large-font-size\"><strong>Count<\/strong><strong>&nbsp;how many places, and in which direction, you moved the decimal&nbsp;<\/strong><strong>point.<\/strong>&nbsp;This will tell you the exponent in the power of&nbsp;10.&nbsp;If you moved the decimal point to the left, your exponent will be positive. If you moved the decimal point to the right, your exponent will be&nbsp;negative.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-large-font-size\">\ud83c\udff9 Let&#8217;s&nbsp;try it! Write&nbsp;0.000095&nbsp;in scientific&nbsp;notation.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Start&nbsp;by writing the first factor. Move the decimal point between&nbsp;9&nbsp;and&nbsp;5.&nbsp;The first factor is&nbsp;<strong>9.5<\/strong>.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Then,&nbsp;determine the exponent in the power of&nbsp;10.&nbsp;Count the number of places the decimal point moved to make&nbsp;<strong>9.5<\/strong>.&nbsp;Since you&#8217;ll need to move the decimal to the right, use a negative&nbsp;exponent.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized is-style-default\"><img decoding=\"async\" src=\"https:\/\/www.ixl.com\/~media\/2\/MIPOnAW-Z2RVRGdi8W-VeLQ59nZK8hvfHnzH43jCBPMl-UxfOC6DYQ6wacdHcbONq2G81Y9cmeNfIGi3_omI8A.svg\" alt=\"The number zero point zero zero zero zero nine five is shown. Under the number, there are five arrows showing the decimal point moving between decimal places. The arrows start between the first two zeros and point right, ending with the last arrow pointing between nine and five. The arrows are labeled with the numbers one through five. Next to that number is an arrow pointing to the number nine point five.\" style=\"width:294px;height:auto\"\/><\/figure>\n\n\n\n<p class=\"has-large-font-size\">The&nbsp;decim10\u207b\u2075.<\/p>\n\n\n\n<p class=\"has-large-font-size\">So,&nbsp;the number&nbsp;0.000095&nbsp;in scientific notation is&nbsp;<strong>9.5<\/strong>\u00d7<strong>10\u207b\u2075<\/strong>.<\/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-background has-large-font-size\" style=\"background-color:#f0a7a7\"><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-7167e15425dcf06f369d8d64efb0673d\" style=\"color:#b00012\"><strong>How do you write 30 in scientific notation?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-1-1.png\" alt=\"\" class=\"wp-image-12793\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-1-1.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-1-1-300x45.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Move the decimal point to the left until the number is between 1 and 10. Count how many places you move the decimal point.<\/p>\n\n\n\n<p>30&nbsp;\u2192&nbsp;3.0<br>You moved the decimal point 1 place to the left. The power of 10 is&nbsp;10<sup>1<\/sup>.<\/p>\n\n\n\n<p>30 = 3.0 \u00d7&nbsp;10<sup>1<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#a8ecb4\"><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-69ff78ba935ddf63bd77ae844f7d84ad\" style=\"color:#b00012\"><strong>How do you write 623 in scientific notation?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-1-2.png\" alt=\"\" class=\"wp-image-12797\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-1-2.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-1-2-300x45.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Move the decimal point to the left until the number is between 1 and 10. Count how many places you move the decimal point.<\/p>\n\n\n\n<p>623&nbsp;\u2192&nbsp;6.23<br>You moved the decimal point 2 places to the left. The power of 10 is&nbsp;10<sup>2<\/sup>.<\/p>\n\n\n\n<p>623 = 6.23 \u00d7&nbsp;10<sup>2<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f29feb\"><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-c6f424c68bb9b4d7ac24f341e8729d90\" style=\"color:#b00012\"><strong>How do you write 67,000 in scientific notation?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-1-3.png\" alt=\"\" class=\"wp-image-12799\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-1-3.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-1-3-300x45.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Move the decimal point to the left until the number is between 1 and 10. Count how many places you move the decimal point.<\/p>\n\n\n\n<p>67,000&nbsp;\u2192&nbsp;6.70<br>You moved the decimal point 4 places to the left. The power of 10 is&nbsp;10<sup>4<\/sup>.<\/p>\n\n\n\n<p>67,000 = 6.70 \u00d7&nbsp;10<sup>4<\/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\/371\/516\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-315.png\" alt=\"\" class=\"wp-image-9649\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-315.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-315-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-315-150x150.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\/090\/718\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-322.png\" alt=\"\" class=\"wp-image-9650\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-322.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-322-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-322-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Convert between standard and scientific notation key notes : \ud83c\udff9 Scientific notation: You&nbsp;can use scientific notation to write very large or very small numbers. Here are some&nbsp;examples. 4,000,000&nbsp;in scientific notation is&nbsp;4\u00d7106. 0.00007&nbsp;in scientific notation is&nbsp;7\u00d710\u20135. Writing&nbsp;numbers in scientific notation can make them easier to work&nbsp;with. How&nbsp;do&nbsp;you&nbsp;read&nbsp;numbers&nbsp;in&nbsp;scientific&nbsp;notation? You&nbsp;can interpret scientific notation by converting the number to<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/g-1-convert-between-standard-and-scientific-notation\/\">Continue reading <span class=\"screen-reader-text\">&#8220;G.1 Convert between standard and 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-134","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\/134","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=134"}],"version-history":[{"count":33,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/134\/revisions"}],"predecessor-version":[{"id":19981,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/134\/revisions\/19981"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}