Question

Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2^m × 5ⁿ, where m, n are non-negative integers.

\[\frac{3}{8}\]

Answer 1

The given number is \[\frac{3}{8}\]

Clearly, 8 = 2³ is of the form 2^m × 5ⁿ, where m = 3 and n = 0.

So, the given number has terminating decimal expansion.

\[\therefore \frac{3}{8} = \frac{3 \times 5^3}{2^3 \times 5^3} = \frac{3 \times 125}{\left( 2 \times 5 \right)^3} = \frac{375}{\left( 10 \right)^3} = \frac{375}{1000} = 0 . 375\]