{"id":98,"date":"2022-04-12T12:06:26","date_gmt":"2022-04-12T12:06:26","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=98"},"modified":"2025-10-29T06:42:34","modified_gmt":"2025-10-29T06:42:34","slug":"f-5-exponents-with-decimal-and-fractional-bases","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/f-5-exponents-with-decimal-and-fractional-bases\/","title":{"rendered":"F.5 Exponents with decimal and fractional bases"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Exponents with decimal and fractional bases<\/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\/DAG3Jtq-kew\/hxZ_bIoFPAprFJS1eXct2g\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAG3Jtq-kew&#x2F;hxZ_bIoFPAprFJS1eXct2g&#x2F;watch?utm_content=DAG3Jtq-kew&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Design<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-09eb8d27d0d70f35bd20b1cf47293f11\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color has-large-font-size wp-elements-a93b27cc42f8fd8433bad83baec3405c\">\ud83c\udf1f <strong>Exponents with Decimal and Fractional Bases<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udd39 <strong>What is an Exponent?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>An <strong>exponent<\/strong> shows how many times a number (called the base) is multiplied by itself.<\/p>\n\n\n\n<p><strong>\ud83d\udc49 Example:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">3<sup>2<\/sup>=3\u00d73=9<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udd39 <strong>Decimal Bases<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>A <strong>decimal base<\/strong> is a number that contains a decimal point.<\/p>\n\n\n\n<p>When a decimal base is raised to a power, we multiply the base by itself as many times as the exponent shows.<\/p>\n\n\n\n<p>\u2728 <strong>Examples:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(0.2)<sup>2<\/sup>=0.2\u00d70.2=0.04<\/li>\n\n\n\n<li>(0.5)<sup>3<\/sup>=0.5\u00d70.5\u00d70.5=0.125<\/li>\n<\/ol>\n\n\n\n<p>\ud83d\udc49 <strong>Tip:<\/strong> The result becomes smaller as you multiply decimals less than 1.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udd39 <strong>Fractional Bases<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>A <strong>fractional base<\/strong> is a number written in the form a\/b\u200b.<\/p>\n\n\n\n<p>When raised to a power, both the <strong>numerator<\/strong> and the <strong>denominator<\/strong> are raised to that power.<\/p>\n\n\n\n<p>\u2728 <strong>Examples:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(2\/3)2=2<sup>2<\/sup>\/3<sup>2<\/sup>=4\/9<\/li>\n\n\n\n<li>(1\/4)<sup>3<\/sup>=1<sup>3<\/sup>\/4<sup>3<\/sup>=1\/64<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udd39<strong> Negative Exponents<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>A <strong>negative exponent<\/strong> means we take the <strong>reciprocal<\/strong> of the base and make the exponent positive.<\/p>\n\n\n\n<p>\u2728 <strong>Examples:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(0.2)<sup>\u22121<\/sup>=1\/0.2=5<\/li>\n\n\n\n<li>(3\/4)<sup>\u22122<\/sup>=(4\/3)<sup>2<\/sup>=16\/9<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udd39 <strong>Zero Exponent Rule<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Any <strong>non-zero number<\/strong> raised to the power of <strong>0<\/strong> equals <strong>1<\/strong>.<\/p>\n\n\n\n<p>\u2728 <strong>Examples:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(0.5)<sup>0<\/sup>=1<\/li>\n\n\n\n<li>(2\/3)<sup>0<\/sup>=1<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td>\ud83d\udd39 <strong>Comparing Decimal and Fractional Bases<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Both decimals and fractions less than 1 become <strong>smaller<\/strong> as the exponent increases.<\/li>\n\n\n\n<li>Example: (0.5)<sup>2<\/sup>=0.25 and (1\/2)<sup>2<\/sup>=1\/4\u200b, which are the same value.<\/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:#000060\"><tbody><tr><td>\ud83d\udd39 <strong>Real-Life Applications \ud83d\udca1<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Calculating <strong>interest rates<\/strong> and <strong>growth\/decay<\/strong> in financial problems.<\/li>\n\n\n\n<li>Finding <strong>areas and volumes<\/strong> when measurements are in decimals or fractions.<\/li>\n\n\n\n<li>Used in <strong>scientific notation<\/strong> for very small numbers (like (1.2\u00d710<sup>\u22123<\/sup>)<sup>2<\/sup>).<\/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:#000060\"><tbody><tr><td>\ud83e\udde0 <strong>Quick Practice<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(0.3)<sup>3<\/sup>=?<\/li>\n\n\n\n<li>(2\/5)<sup>2<\/sup>=?<\/li>\n\n\n\n<li>(0.4)<sup>\u22122<\/sup>=?<\/li>\n\n\n\n<li>(3\/4)<sup>0<\/sup>=?<\/li>\n<\/ol>\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-normal-font-size wp-elements-6ef9e1a6bbad5c875c6d00c529e17cf3\" style=\"background-color:#a6ddf9\"><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-text-color has-background has-link-color wp-elements-3981e5326178c8200c77638d2a259e85\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Evaluate. Write your answer as a fraction or whole number.<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-8e260c11954794e15f8fb38e7c9df52f\">(1\/2)<sup>4<\/sup>&nbsp;=____<\/p>\n<\/div><\/div>\n\n\n\n<p>(1\/2)<sup>4<\/sup>&nbsp;= 1\/2 \u00d7 1\/2 \u00d7 1\/2 \u00d7 1\/2<\/p>\n\n\n\n<p>          = 1\/2.2.2.2<\/p>\n\n\n\n<p>          = 1\/16<\/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-normal-font-size wp-elements-bec0bc99d69fb6d6c30b0a4a8eca911d\" style=\"background-color:#bbf9d2\"><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-text-color has-background has-link-color wp-elements-5c9032068a43f3051b0ac2a236d56eb4\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Evaluate. Write your answer as a decimal or whole number.<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-241adff46eb7a7d65c43a2aeb8e17467\">(0.03)<sup>4<\/sup>&nbsp;=____<\/p>\n<\/div><\/div>\n\n\n\n<p>The base is 0.03 and the exponent is 4. Use 0.03 as a factor 4 times.<\/p>\n\n\n\n<figure id=\"yui_3_18_1_1_1664766677917_325\" class=\"wp-block-table\"><table><tbody><tr><td>(0.03)<sup>4<\/sup><\/td><td>&nbsp;=&nbsp;<\/td><td>0.03 \u00b7 0.03 \u00b7 0.03 \u00b7 0.03<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">         = 0.00000081<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group\"><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-text-color has-background has-link-color has-normal-font-size wp-elements-408ac3bce6ebcca01e519287711e2570\" style=\"background-color:#f1dddd\"><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-text-color has-background has-link-color wp-elements-7b0eae157cb7ded0a61394357eb538a0\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>Evaluate. Write your answer as a decimal or whole number.<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-f8dfc5a567f62613294eb16481533987\">(0.01)<sup>4<\/sup> =_______<\/p>\n<\/div><\/div>\n\n\n\n<p>The base is 0.01 and the exponent is 4. Use 0.01 as a factor 4 times.<\/p>\n\n\n\n<p>(0.01)4 = 0.01 \u00b7 0.01 \u00b7 0.01 \u00b7 0.01<\/p>\n\n\n\n<p>= 0.00000001<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/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\/77974\/125\/379\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-293.png\" alt=\"\" class=\"wp-image-9571\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-293.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-293-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-293-150x150.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\/33847\/845\/722\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-300.png\" alt=\"\" class=\"wp-image-9572\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-300.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-300-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-300-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Exponents with decimal and fractional bases Design by Delta publications Key Notes : \ud83c\udf1f Exponents with Decimal and Fractional Bases \ud83d\udd39 What is an Exponent? An exponent shows how many times a number (called the base) is multiplied by itself. \ud83d\udc49 Example: 32=3\u00d73=9 \ud83d\udd39 Decimal Bases A decimal base is a number that contains a<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/f-5-exponents-with-decimal-and-fractional-bases\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.5 Exponents with decimal and fractional bases&#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-98","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\/98","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=98"}],"version-history":[{"count":25,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/98\/revisions"}],"predecessor-version":[{"id":22045,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/98\/revisions\/22045"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=98"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}