Write down the decimal expansions of the following rational numbers by writing their denominators in the form of $2^m \times 5^n$, where m, and n, are the non-negative integers.
$\frac{3}{8}$

Given: 

The given rational number is $\frac{3}{8}$.

To do: 

Here, we have to write the decimal expansion of the given rational number by writing its denominator in the form of $2^m \times 5^n$, where m, and n, are non-negative integers.

Solution:

$\frac{3}{8}=\frac{3}{2^3}$

We can see that $8=2^3$ is of the form $2^m \times 5^n$, where $m = 3$ and $n = 0$.

This implies,

The given rational number has a terminating decimal expansion.

Multiply the numerator and denominator by $5^3$ so that the denominator becomes a multiple of $10^r$, where r is any positive integer. 

Therefore,

$\frac{3}{8}=\frac{3}{2^3}$

$=\frac{3\times5^3}{2^3\times5^3}$

$=\frac{3\times125}{(2\times5)^3}$

$=\frac{375}{10^3}$

$=\frac{375}{1000}$

$=0.375$

The decimal expansion of the given rational number is $0.375$.