Question

giá trị x thỏa mãn [0.(37)+0.(7)]x=0.1(6) dưới dạng phân số tối giản nhé

Answer 1

\(\left[0,\left(37\right)+0,\left(7\right)\right]x=0,1\left(6\right)\)

\(\Rightarrow\left[\frac{37}{99}+\frac{7}{9}\right]x=0,1+0,0\left(6\right)\)

\(\Rightarrow\frac{38}{33}.x=\frac{1}{10}+\frac{6}{90}\)

\(\Rightarrow\frac{38}{33}.x=\frac{1}{6}\)

\(\Rightarrow x=\frac{1}{6}:\frac{38}{33}=\frac{1}{6}.\frac{33}{38}\)

\(\Rightarrow x=\frac{11}{76}\)

Vậy \(x=\frac{11}{76}\)