Decimal Expansion of a Number<\/h3>\n
Decimal Expansion of a Number is its representation in the base-10 system. In this System, each decimal place consists of digits 0-9 arranged such that each digit is multiplied by a power of 10 decreasing from left to right and a decimal place with 10^0 is the one’s place.<\/p>\n
Decimal Expansion of Number 1423.25 is defined as<\/p>\n
1423.25 = 1*103<\/sup>+4*102<\/sup>+2*101<\/sup>+3*100<\/sup>+2*10-1<\/sup>+5*10-2<\/sup><\/p>\n = 1000+400+20+3+0.2+0.05<\/p>\n Decimal Expansion of a Number may terminate and in such case, the number is called a regular number or finite decimal. At times, the Decimal Expansion of a Number may become periodic and in such case, it is called a repeating decimal. However, the expansion may continue infinitely without repeating and it is called an irrational number.<\/p>\n In the Expanded Form of Decimal Fractions, you will learn how to read and write the Decimal Numbers. Decimal Numbers can be written in expanded form using the Place Value Chart.<\/p>\n Let us understand the same by considering an example<\/p>\n 384.264<\/p>\n 384.264 = 3 \u00d7 100 + 8 \u00d7 10 + 4 \u00d7 1 + 2 \u00d7 \\(\\frac { 1 }{10 } \\) + 6 \u00d7 \\(\\frac { 1 }{100 } \\) + 4 \u00d7 \\(\\frac { 1 }{1000 } \\)<\/p>\n = 300+80+4+\\(\\frac { 2 }{10 } \\)+\\(\\frac { 6 }{100 } \\)+\\(\\frac { 4 }{1000 } \\)<\/p>\n 1. Write the decimal and fractional expansion of 334.252?<\/p>\n Solution:<\/p>\n In Decimal Expansion<\/p>\n 334.252 = 3*100+3*10+4*1+2*\\(\\frac { 1 }{10 } \\)+5*\\(\\frac { 1 }{100 } \\)+2*\\(\\frac { 1 }{1000 } \\)<\/p>\n = 300+30+4+\\(\\frac { 2 }{10 } \\)+\\(\\frac { 5 }{100 } \\) + \\(\\frac { 2 }{1000 } \\)<\/p>\n = 300+30+4+0.2+0.05+0.002<\/p>\n In Fractional Expansion<\/p>\n = 3*100+3*10+4*1+2*\\(\\frac { 1 }{10 } \\)+5*\\(\\frac { 1 }{100 } \\)+2*\\(\\frac { 1 }{1000 } \\)<\/p>\n = 300+30+4+\\(\\frac { 2 }{10 } \\)+\\(\\frac { 5 }{100 } \\) + \\(\\frac { 2 }{1000 } \\)<\/p>\n 2. Write the decimal and fractional expansion of 543.32?<\/p>\n Solution:<\/p>\n In Decimal Expansion<\/p>\n 543.32 = 5*100+4*10+3*1+3*\\(\\frac { 1 }{10 } \\)+2*\\(\\frac { 1 }{100 } \\)<\/p>\n = 500+40+3+\\(\\frac { 3 }{10 } \\)+\\(\\frac { 2 }{100 } \\)<\/p>\n = 500+40+3+0.3+0.02<\/p>\n In Fractional Expansion<\/p>\n = 5*100+4*10+3*1+3*\\(\\frac { 1 }{10 } \\)+2*\\(\\frac { 1 }{100 } \\)<\/p>\n = 500+40+3+\\(\\frac { 3 }{10 } \\)+\\(\\frac { 2 }{100 } \\)<\/p>\n 3. Write the Decimal and Fractional Expansion of 647.345?<\/p>\n Solution:<\/p>\n In Decimal Expansion<\/p>\n 647.345 = 6*100+4*10+7*1+3*\\(\\frac { 1 }{10 } \\)+4*\\(\\frac { 1 }{100 } \\)+5*\\(\\frac { 1 }{1000 } \\)<\/p>\n = 600+40+7+\\(\\frac { 3 }{10 } \\)+\\(\\frac { 4 }{100 } \\)+\\(\\frac { 5 }{1000 } \\)<\/p>\n = 600+40+7+0.3+0.04+0.005<\/p>\n In Fractional Expansion<\/p>\n 647.345 = 6*100+4*10+7*1+3*\\(\\frac { 1 }{10 } \\)+4*\\(\\frac { 1 }{100 } \\)+5*\\(\\frac { 1 }{1000 } \\)<\/p>\n = 600+40+7+\\(\\frac { 3 }{10 } \\)+\\(\\frac { 4 }{100 } \\)+\\(\\frac { 5 }{1000 } \\)<\/p>\n 1. What is Decimal in Expanded Form?<\/strong><\/p>\n Expanded form notation for the decimal numbers is the mathematical expression that shows the sum of the values of each digit in the number.<\/p>\n 2. What is the Decimal Expansion of Number 164.38?<\/strong><\/p>\n Decimal Number 164.38 can be written in expanded form by writing it as the sum of the place value of all the digits i.e. 1*100+6*10+4*1+3*\\(\\frac { 1 }{10 } \\)+8*\\(\\frac { 1 }{100 } \\) = 100+60+4+0.3+0.08<\/p>\n 3. What is the Fractional Expansion of Number 94.38?<\/strong><\/p>\n Fractional Expansion of Number 94.38 is 9*10+4*10+3*\\(\\frac { 1 }{10 } \\)+8*\\(\\frac { 1 }{100 } \\) which inturn results in 90+40+\\(\\frac { 3 }{10 } \\)+\\(\\frac { 8 }{100 } \\)<\/p>\n","protected":false},"excerpt":{"rendered":" In this article, you will learn about the Decimal and Fractional Expansion of a Decimal Number. Before Proceeding further know the definitions of Decimal, Fraction, and the Place Value Chart. A Decimal is any number in the base 10 number system and is used to separate units place from tenths place in decimal. The decimal … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":75344,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/03\/Fractional-and-Decimal-Expansion.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/74746"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=74746"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/74746\/revisions"}],"predecessor-version":[{"id":92211,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/74746\/revisions\/92211"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/75344"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=74746"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=74746"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=74746"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Fractional Expansion of Decimals<\/h3>\n
![\"Decimal](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/03\/Decimal-and-Fractional-Expansion.png\")
<\/p>\nSolved Examples on Decimal and Fractional Expansion<\/h3>\n
FAQ’s on Decimal and Fractional Expansion<\/h3>\n