Question

Write the denominator of the rational number $\frac{257}{5000}$ in the form $2^m\times 5^n$, where $m,n$ are non-negative integers. Hence, write the decimal expansion, without actual division.

Answer 1

The given number is $\frac{257}{5000}$.

Now, 5000 = 2³ × 5⁴

Clearly, 2 and 5 are factors of 5000.

The denominator can be written in the form of 2^m × 5ⁿ.

So, the given number has a terminating decimal expansion.

$\frac{257}{5000}=\frac{257}{5^4\times 2^3}\times \frac{2}{2}=\frac{514}{{10}^4}=\frac{514}{10000}=0.0514$