MCQ
The simplest for of $0.\overline{32}$ is:
- A$\frac{16}{45}$
- B$\frac{32}{99}$
- ✓$\frac{29}{90}$
- DNone of these.
✓
Answer
Correct option: C.
$\frac{29}{90}$
Let $\text{x}=0.\overline{32}$
Then, $\text{x}=0.3222 \ ...(\text{i})$
$\therefore10\text{x}=3.222 \ ...(\text{ii})$
and $100\text{x}=32.222 \ ...(\text{iii})$
On subtracting $(ii)$ from $(iii),$ we get
$90\text{x}=29$
$\Rightarrow\text{x}=\frac{29}{90}$
Hence, the correct option is $(c).$
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