Question

The decimal expression of 21/24 will terminate after how many places of decimal ? Answer without doing actual division .​

Answer 1

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$⟾ \: \frac{21}{24}$

$= \frac{3 \times 7}{2 \times 2 \times 2 \times 3}$

$= \frac{7}{2 \times 2 \times 2}$

$= \frac{7}{ {2}^{3} } = \frac{7 \times {5}^{3} }{ {2}^{3} {5}^{3} }$

$= \frac{7 \times 125}{103}$

$= \frac{875}{1000} = 0.875$

Therefore, 21/24 will terminate after 3 decimal.