{"id":156536,"date":"2022-03-26T01:51:58","date_gmt":"2022-03-25T20:21:58","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/expanded-form-with-decimals-definition-applications-and-examples\/"},"modified":"2024-12-13T14:12:06","modified_gmt":"2024-12-13T08:42:06","slug":"expanded-form-with-decimals-definition-applications-and-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/expanded-form-with-decimals\/","title":{"rendered":"Expanded Form with Decimals &#8211; Definition, Applications and Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/expanded-form-with-decimals\/#Introduction_to_Decimal_Number_System\" title=\"Introduction to Decimal Number System\">Introduction to Decimal Number System<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/expanded-form-with-decimals\/#The_Expanded_Form_of_Decimal_Numbers\" title=\"The Expanded Form of Decimal Numbers\">The Expanded Form of Decimal Numbers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/expanded-form-with-decimals\/#Decimal_Expansion_Definition\" title=\"Decimal Expansion Definition\">Decimal Expansion Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/expanded-form-with-decimals\/#How_to_Write_Decimals_in_Expanded_Form\" title=\"How to Write Decimals in Expanded Form?\">How to Write Decimals in Expanded Form?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/expanded-form-with-decimals\/#Applications_of_Expanded_Form_with_Decimals\" title=\"Applications of Expanded Form with Decimals\">Applications of Expanded Form with Decimals<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/expanded-form-with-decimals\/#Decimal_Expansion_Example\" title=\"Decimal Expansion Example\">Decimal Expansion Example<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_Decimal_Number_System\"><\/span>Introduction to Decimal Number System<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In mathematics, the decimal number system is the system in which every real number is represented by a unique sequence of digits, beginning with 0. The decimal number system is also called base 10 because it uses 10 digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Expanded Form with Decimals &#8211; Definition Applications and Examples.<\/p>\n<p>The number 26.789 can be represented in the decimal number system as 2,679. The number 26.789 can also be represented in the <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/binary-multiplication\/\">binary<\/a> number system as 11011.001. The number 26.789 can also be represented in the octal number system as 377.621. The number 26.789 can also be represented in the hexadecimal number system as 1a.bcd.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156535 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/expanded-form-with-decimals-definition-applications-and-examples.jpg\" alt=\"Expanded Form with Decimals - Definition, Applications and Examples\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/expanded-form-with-decimals-definition-applications-and-examples.jpg?v=1648239715 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/expanded-form-with-decimals-definition-applications-and-examples-300x212.jpg?v=1648239715 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Expanded_Form_of_Decimal_Numbers\"><\/span>The Expanded Form of Decimal Numbers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The expanded form of decimal numbers is a way to show a decimal number as a sum of its individual digits multiplied by their respective place values. For example, the number 123.456 can be written as 1 \u00d7 10^2 + 2 \u00d7 10^1 + 3 \u00d7 10^0 + 4 \u00d7 10^-1 + 5 \u00d7 10^-2.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Decimal_Expansion_Definition\"><\/span>Decimal Expansion Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A decimal expansion is a sequence of digits representing a real number that is written as a decimal. The decimal expansion of a number starts with the number&#8217;s digits to the left of the decimal point and continues with 0s to the right of the decimal point if necessary. For example, the decimal expansion of the number 2.3456 is 2.3456, 2.34, 2.3, 2.2, 2.1, 2.0, 1.9, 1.8, 1.7, 1.6, 1.5, 1.4, 1.3, 1.2, 1.1, 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Write_Decimals_in_Expanded_Form\"><\/span>How to Write Decimals in Expanded Form?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To write decimals in expanded form, divide the number by 10 and write the remainder above the decimal point. If there is no remainder, write a 0.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Applications_of_Expanded_Form_with_Decimals\"><\/span>Applications of Expanded Form with Decimals<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are a few different ways that expanded form with decimals can be used in the real world. One way is to use it to help with math operations. For example, if a student is trying to subtract two numbers and one of the numbers is in expanded form, the student can use the expanded form to help them solve the problem. Another way to use expanded form with decimals is to help students understand how decimals work. For example, a student might be learning about place value and how to read and write decimals in standard form. Expanded form can be a helpful tool for students as they learn these concepts.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Decimal_Expansion_Example\"><\/span>Decimal Expansion Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To understand the decimal expansion of a number, let&#8217;s look at the number 123.<\/p>\n<p>The number 123 can be written as 1.23 \u00d7 10^2. This means that the number 123 is equal to 1.23 multiplied by 100, or 1,230.<\/p>\n<p>The number 123 can also be written as 1.23 \u00d7 10^1. This means that the number 123 is equal to 1.23 multiplied by 10, or 123.<\/p>\n<p>The number 123 can also be written as 1.23 \u00d7 10^0. This means that the number 123 is equal to 1.23 multiplied by 1, or 123.<\/p>\n<p>The number 123 can also be written as 1.23 \u00d7 10^-1. This means that the number 123 is equal to 1.23 multiplied by 0.1, or 12.3.<\/p>\n<p>The number 123 can also be written as 1.23 \u00d7 10^-2. This means that the number 123 is equal to 1.23 multiplied by 0.01, or 1.23.<\/p>\n<p>Expanded Form with Decimals &#8211; Definition Applications and Examples.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction to Decimal Number System In mathematics, the decimal number system is the system in which every real number is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Expanded Form with Decimals - Definition Applications and Examples","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Expanded Form with Decimals - Definition Applications and Examples in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/expanded-form-with-decimals\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Expanded Form with Decimals - 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