how to write a repeating decimal as a fraction

This step may seem strange, because on the right side of the equation youre subtracting an infinite decimal from an infinite decimal. All trademarks are property of their respective trademark owners. x &= 4.1+0.0454 +0.0000454 + 0.0000000454 + \cdots\\ If you're working with numbers that end in a 0 or 5, divide them by 5. 10x &= 39.1111111. For example, heres how you convert the repeating decimals, To gain insight into why this trick works, here is a step-by-step way to convert a repeating decimal to a fraction using algebra. You can then simplify the fraction if needed. thing as 0.7777 and I could just keep going wikiHow is a wiki, similar to Wikipedia, which means that many of our articles are co-written by multiple authors. The numerator is a whole number greater than 0 . Math, Praxis A quick trick for converting a repeating decimal is to place the repeating numbers in the numerator of a fraction over the same number of 9s, and then reduce if necessary. To start, set the decimal equal to a variable. Rational numbers, when written as decimals, are either terminating or non-terminating, repeating decimals. subtract x from 10x? What is the definition of a repeating decimal? In this video, I want .

As another example, convert the fraction

to a decimal by dividing:

As in the previous example, the pattern of numbers in the answer repeats itself and will do so indefinitely. x &= 0.023 + 0.00023 + 0.0000023 + \cdots\\ Multiply the decimal by 10 and subtract the original decimal from it. To convert repeating decimals to fractions: Convert \(\color{red}{0.8888}\)to a fraction. Figure out the recurring digits in the given decimal number. Write \(4.1\overline{454}\) as a fraction. Suppose you want to convert the decimal. Then keep multiplying both the numerator (top number) and denominator (bottom number) by 10 until both are whole numbers. 72 Since we have "72" as the repeating part, we will . &=\frac{23}{990}. The decimal is 0.703703, and the notation for a repeating decimal like this is to write the numbers that repeat and then put a line above them. How do I convert a repeating decimal to a fraction? Divide both sides by 9 to get. x &= 0.34 + 0.0034 + 0.000034 + \cdots\\ This article teaches you how to Convert Repeating Decimals to Fractions in a few simple steps. You can also say the decimal aloud. Direct link to ( )'s post i now right, Posted 8 months ago. &= 34 \times \left( \frac{1}{100^{1}} + \frac{1}{100^{2}} + \frac{1}{100^{3}} + \cdots \right). Direct link to mikeblack3rd's post i am a 7 yr old, Posted 3 days ago. We can simplify 3.3/9 by first multiplying top and bottom by 10 (getting rid of the decimal) to get 33/90, then dividing top and bottom by 3 to get 11/30. To create this article, 20 people, some anonymous, worked to edit and improve it over time. The formula to convert this type of repeating decimal to a fraction is given by: a b c d = Repeated term Number of 9's for the repeated term Example 1: Convert 0. Mark is also author of several other successful For Dummies books.

Mark Zegarelli earned degrees in mathematics and English from Rutgers University. However, it does not always work out that nicely. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33722,"title":"Basic Math","slug":"basic-math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33722"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Converting fractions to repeating decimals","target":"#tab1"},{"label":"Converting repeating decimals to fractions","target":"#tab2"}],"relatedArticles":{"fromBook":[],"fromCategory":[{"articleId":291491,"title":"Teaching Your Kids New Math (K-5) For Dummies Cheat Sheet","slug":"teaching-your-kids-new-math-k-5-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/291491"}},{"articleId":253710,"title":"Pre-Algebra Practice Questions: Comparing Fractions Using Cross-Multiplication","slug":"pre-algebra-practice-questions-comparing-fractions-using-cross-multiplication","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/253710"}},{"articleId":249996,"title":"Pre-Algebra Practice Questions: Solving Simple Algebraic Equations","slug":"pre-algebra-practice-questions-solving-simple-algebraic-equations","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249996"}},{"articleId":249986,"title":"Pre-Algebra Practice Questions: Isolating x in an Equation","slug":"pre-algebra-practice-questions-isolating-x-equation","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249986"}},{"articleId":249980,"title":"Pre-Algebra Practice Questions: Rearranging Equations to Isolate x","slug":"pre-algebra-practice-questions-rearranging-equations-isolate-x","categoryList":["academics-the-arts","math","basic-math"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/249980"}}]},"hasRelatedBookFromSearch":true,"relatedBook":{"bookId":281978,"slug":"basic-math-pre-algebra-for-dummies-2nd-edition","isbn":"9781119293637","categoryList":["academics-the-arts","math","basic-math"],"amazon":{"default":"https://www.amazon.com/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119293634-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119293634/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/covers/9781119293637.jpg","width":250,"height":350},"title":"Basic Math & Pre-Algebra For Dummies","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"\n

Mark Zegarelli earned degrees in mathematics and English from Rutgers University.