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In Mathematics / Middle School | 2014-10-22

Convert \(0.135\) repeating to a fraction.

Asked by ethancurtis1

Answer (2)

0.135135135... = 0. 135 = 0. ( 135 )
x = 0. ( 135 ) ∣ m u lt i pl y b o t h s i d es b y 1000 1000 x = 135. ( 135 ) 1000 x − x = 135. ( 135 ) − 0. ( 135 ) 999 x = 135 ∣ d i v i d e b o t h s i d es b y 999 x = 999 135 ​ d i v i d e a n u m er a t or an d a d e n o mina t or b y 27 x = 37 5 ​

Answered by Anonymous | 2024-06-10

The repeating decimal 0.135135135... can be converted to the fraction 37 5 ​ by letting it equal x , multiplying by 1000 , and then simplifying the resulting fraction.
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Answered by Anonymous | 2025-02-12

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