the repeating decimal, (0.overline{27}), is converted to the fraction (0.overline{27}=\frac{3}{x}). what is…
the repeating decimal, (0.overline{27}), is converted to the fraction (0.overline{27}=\frac{3}{x}). what is the value of (x) in the fraction?
Answer
Explanation:
Step1: Let (y = 0.\overline{27}).
Then (100y=27.\overline{27}) (multiplying by 100 as 2 - digit repeating part).
Step2: Subtract (y) from (100y).
(100y - y=27.\overline{27}-0.\overline{27}), so (99y = 27), and (y=\frac{27}{99}=\frac{3}{11}).
Answer:
11