Question
Short-Answer Questions:
Express $0.\bar4$ as a rational number in simplest form.
Express $0.\bar4$ as a rational number in simplest form.
✓
Answer
Let $\text{x}=0.\bar4$ then,
$\text{x}=0.4444\dots\ \ \dots(\text{i})$
$\therefore\text{10x}=4.444\dots\ \ \dots(\text{ii})$
On subtracting (i) from (ii), we get
$\text{9x}=4$
$\Rightarrow\text{x}=\frac{4}{9}$
Hence, $0.\bar4=\frac{4}{9}$
$\text{x}=0.4444\dots\ \ \dots(\text{i})$
$\therefore\text{10x}=4.444\dots\ \ \dots(\text{ii})$
On subtracting (i) from (ii), we get
$\text{9x}=4$
$\Rightarrow\text{x}=\frac{4}{9}$
Hence, $0.\bar4=\frac{4}{9}$
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