Question
Short-Answer Questions:
Express $0.\overline{23}$ as a rational number in simplest form.
Express $0.\overline{23}$ as a rational number in simplest form.
✓
Answer
Let $\text{x}=0.\overline{23}$ then,
$\text{x}=0.232323\dots\ \ \dots(\text{i})$
$\therefore\text{100x}=23.2323\dots\ \ \dots(\text{ii})$
On subtracting (i) from (ii), we get
$\text{99x}=23$
$\Rightarrow\text{x}=\frac{23}{99}$
Hence, $0.\overline{23}=\frac{23}{99}$
$\text{x}=0.232323\dots\ \ \dots(\text{i})$
$\therefore\text{100x}=23.2323\dots\ \ \dots(\text{ii})$
On subtracting (i) from (ii), we get
$\text{99x}=23$
$\Rightarrow\text{x}=\frac{23}{99}$
Hence, $0.\overline{23}=\frac{23}{99}$
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