Find the value of $0.32 ¯ ¯¯¯¯ ¯ 58$

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Solution

Let $R = 0.32 ¯ 58$
expanding
$\Rightarrow R = 0.32585858 \dots (1)$

multiplying by 100
$100 R = 32.585858 \dots (2)$

multiplying by 1000
$1000 R = 3258.5858 \dots (3)$

Subtracting $(2)$ from $(3)$ , we get
$9900 R = 3226$

$∴ R = \frac{3226}{9900}$
Hence, $R = \frac{1613}{4950}$

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