{"id":156394,"date":"2022-03-26T01:42:32","date_gmt":"2022-03-25T20:12:32","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/decimal-number-system-definition-conversion-and-examples\/"},"modified":"2022-12-22T21:38:34","modified_gmt":"2022-12-22T16:08:34","slug":"decimal-number-system-definition-conversion-and-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/decimal-number-system\/","title":{"rendered":"Decimal Number System &#8211; Definition, Conversion 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\/decimal-number-system\/#What_is_the_Decimal_Number_System\" title=\"What is the Decimal Number System?\">What is the 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\/decimal-number-system\/#Decimal_Number_System_Definition\" title=\"Decimal Number System Definition\">Decimal Number System Definition<\/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\/decimal-number-system\/#How_to_read_Decimal_Numbers\" title=\"How to read Decimal Numbers?\">How to read Decimal Numbers?<\/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\/decimal-number-system\/#Conversion_in_Decimal_Number_System\" title=\"Conversion in Decimal Number System\">Conversion in Decimal Number System<\/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\/decimal-number-system\/#How_to_convert_Octal_to_Decimal\" title=\"How to convert Octal to Decimal?\">How to convert Octal to Decimal?<\/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\/decimal-number-system\/#How_to_convert_Hexadecimal_to_Decimal\" title=\"How to convert Hexadecimal to Decimal?\">How to convert Hexadecimal to Decimal?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/decimal-number-system\/#Conversion_of_Decimal_to_Other_System\" title=\"Conversion of Decimal to Other System\">Conversion of Decimal to Other System<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/decimal-number-system\/#How_to_convert_Decimal_to_Octal\" title=\"How to convert Decimal to Octal?\">How to convert Decimal to Octal?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/decimal-number-system\/#How_to_convert_Decimal_to_Hexadecimal\" title=\"How to convert Decimal to Hexadecimal?\">How to convert Decimal to Hexadecimal?<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_the_Decimal_Number_System\"><\/span>What is the Decimal Number System?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The decimal number system is a numbering system that uses 10 different symbols to represent numbers. These symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. In the decimal number system, each number is represented by a combination of these symbols. For example, the number 12 can be represented as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12. The number 11 can be represented as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156393 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/decimal-number-system-definition-conversion-and-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/decimal-number-system-definition-conversion-and-examples.jpg?v=1648239146 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/decimal-number-system-definition-conversion-and-examples-300x212.jpg?v=1648239146 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Decimal_Number_System_Definition\"><\/span>Decimal Number System Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The decimal number system is the most common number system in use today. It is a base 10 number system, which means that it uses 10 different symbols to represent numbers. The symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.<\/p>\n<p>In the decimal number system, each number is represented by a combination of these symbols. The number 1, for example, is represented by the symbol 1, the number 2 is represented by the symbol 2, and so on.<\/p>\n<p>The number 10, which is the base of the decimal number system, is represented by the symbol 10. This means that the number 10 can be represented by the combination of the symbols 1 and 0, the combination of the symbols 2 and 0, the combination of the symbols 3 and 0, and so on.<\/p>\n<p>The number 100, which is 10 times the number 10, is represented by the symbol 100. This means that the number 100 can be represented by the combination of the symbols 1 and 0, the combination of the symbols 2 and 0, the combination of the symbols 3 and 0, and so on, all the way up to the combination of the symbols 9 and 0.<\/p>\n<p>The number 1000, which is 10 times the number 100, is represented by the symbol 1000. This means that the number 1000 can be represented by the combination of the symbols 1 and 0, the combination of the symbols 2 and 0, the combination of the<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_read_Decimal_Numbers\"><\/span>How to read Decimal Numbers?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A decimal number is a number that is represented by a combination of a whole number and a decimal point. The whole number is written to the left of the decimal point and the decimal point is written to the right of the whole number. The number that is written to the right of the decimal point is the decimal component of the decimal number.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Conversion_in_Decimal_Number_System\"><\/span>Conversion in Decimal Number System<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In the decimal number system, the base is 10 and each digit is a power of 10. The number 123.456 is written as 1 multiplied by 102, plus 2 multiplied by 101, plus 3 multiplied by 100, plus 4 multiplied by 10-1, plus 5 multiplied by 10-2. The number can also be written as 1.23456, where each number represents 1, 2, 3, 4, 5, and 6 in the decimal number system.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_convert_Octal_to_Decimal\"><\/span>How to convert Octal to Decimal?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In order to convert octal to decimal, one needs to divide the octal number by 8 and then take the remainder.<\/p>\n<p>For example, if someone has the octal number 234, they would divide it by 8 to get the remainder of 2. This would mean that the decimal value for 234 is 14.<\/p>\n<p>If someone has the octal number 137, they would divide it by 8 to get the remainder of 5. This would mean that the decimal value for 137 is 9.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_convert_Hexadecimal_to_Decimal\"><\/span>How to convert Hexadecimal to Decimal?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To convert hexadecimal to decimal, divide the hexadecimal number by 16, and round down the result.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Conversion_of_Decimal_to_Other_System\"><\/span>Conversion of Decimal to Other System<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To convert decimal to other system, divide the decimal number by the base of the other system.<\/p>\n<p>Example:<\/p>\n<p>Convert decimal number 123 to binary<\/p>\n<p>123\/2 = 61<\/p>\n<p>The binary equivalent of 123 is 11100011.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_convert_Decimal_to_Octal\"><\/span>How to convert Decimal to Octal?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To convert decimal to octal, divide the decimal number by 8 and take the remainder. Write the quotient and the remainder together, using a dot to separate them. For example, to convert the decimal number 145 to octal, divide it by 8 and take the remainder:<\/p>\n<p>145 \u00f7 8 = 18 remainder 3<\/p>\n<p>18 . 3 = 22<\/p>\n<p>Therefore, the octal number for 145 is 22.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_convert_Decimal_to_Hexadecimal\"><\/span>How to convert Decimal to Hexadecimal?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To convert a decimal number to hexadecimal, divide the decimal number by 16 and take the remainder. Write the hexadecimal number as a string of hexadecimal digits, with each digit representing 4 bits. For example, the decimal number 1234 is converted to hexadecimal as follows:<\/p>\n<p>1234 \/ 16 = 76<\/p>\n<p>76 remainder 12<\/p>\n<p>1234 converted to hexadecimal is 4E2<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the Decimal Number System? The decimal number system is a numbering system that uses 10 different symbols to [&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":"Decimal Number System - Definition, Conversion and Examples","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Decimal Number System topic of maths in details explained by subject experts on infinitylearn.com. 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