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# Recurring Decimals Help watch

1. Can someone help me with this question, please?
“Hence, or otherwise, write the recurring decimal 0.481818181… as a fraction.”
The first part of the question was to prove that the recurring decimal 0.818181.. can be written as 9/11.
2. multiply it by 10 to get 4.818181. since they give you 9/11, you know that 4.818181 is 53/11 (cause its 4 and 9/11 turned into an improper fraction) then you just multiply the denominator by 10 so 0.48181 is 53/110. hope that made sense!!
3. (Original post by yourlocalflop)
multiply it by 10 to get 4.818181. since they give you 9/11, you know that 4.818181 is 53/11 (cause its 4 and 9/11 turned into an improper fraction) then you just multiply the denominator by 10 so 0.48181 is 53/110. hope that made sense!!
Thank you very much, glad for someone to have at least solved it for me!
4. Simple explanation:

x = 0.48181
10x = 4.8181
100x= 48.1818
1000x = 481.8181

Both 10x and 1000x have the same recurring numbers after the decimal point so,
1000x 481.8181
-10x 4.8181
= 477
= 990x
so... the fraction is 477/990 which can be simplified to 53/110

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Updated: February 11, 2018
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