Question

Write the denominator of the rational number 257/5000 in the form 2m x 5n, where, are non-negative integers. Hence, write its decimal expansion, without actual division. ​

Answer 1

Answer:

$\frac{257}{5000}$

Denominator = 5000

$Factor \: \: of \: \: 5000= 2×2×2×5×5×5×5 \\ \\ = {2}^{3} \times {5}^{4} \\ \\ where \: n \: and \: m \: are \: \: 3\: \: \: and \: \: 4$

$\frac{257}{1000} = \frac{257}{ {2}^{3} \times {5}^{4} } \\ \\ multiply \: and \: \: devide \: \: by \: 2 \\ \\ = \frac{257 \times 2}{2 \times 2 {}^{3} \times {5}^{4} } \\ \\ = \frac{514}{(2 \times 5) {}^{4} } \\ \\ = \frac{514}{ {10}^{4} } \\ \\ = \frac{514}{10000} \\ \\ = 0.0514$