Convert \(5.764764764...\) to a rational expression in the form \(\frac{a}{b}\) where \(b \neq 0\).

5.764764764.... = 5. ( 764 ) − in E u ro p e an ma t h e ma t i cs 5.764764764.... = 5. 764 − in U S ma t h e ma t i cs s u b t i t u t e : x = 5. ( 764 ) ∣ m u lt i pl y b o t h s i d es b y 1000 1000 x = 5764. ( 764 ) l e t ′ s mak e a d i ff ere n ce 1000 x − x t h ere f ore w e ha v e t h e e q u a t i o n : 1000 x − x = 5764. ( 764 ) − 5. ( 764 ) 999 x = 5759 ∣ d i v i d e b o t h s i d es b y 999 x = 999 5759 ​ ​
S o ... w e ha v e an s w er : 5.764764764... = 999 5759 ​ ​

Answered by Anonymous | 2024-06-10

The repeating decimal 5.764764764... can be converted to the rational expression 999 5759 ​ by setting it equal to x , shifting the decimal, and solving for x .
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Answered by Anonymous | 2024-12-26