Question

Write down the decimal expression of $\frac{16}{3125}$without actual division.

Answer 1

Convert into decimal.

The given fraction $\frac{16}{3125}$can be written as,

$\frac{16}{3125}=\frac{16}{5^5}$

To solve the above expression without actual division. first, we have to make the denominator order of $10$.

Multiply numerator and denominator of $\frac{16}{5^5}$ by $2^5$.

$$\begin{gathered} \frac{16}{5^5}\times \frac{2^5}{2^5}=\frac{16\times 32}{{10}^5}\left[\because a^m\times b^m={\left(ab\right)}^m\right] \\ =\frac{512}{100000} \\ =0.00512 \end{gathered}$$

Hence, the required decimal number is $0.00512$.