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.

\[\frac{7}{80}\]

Answer 1

The given number is \[\frac{7}{80}\].

Clearly, 80 = 2⁴ × 5 is of the form 2^m × 5ⁿ, where m = 4 and n = 1.

So, the given number has terminating decimal expansion.

\[\therefore \frac{7}{80} = \frac{7 \times 5^3}{2^4 \times 5 \times 5^3} = \frac{7 \times 125}{\left( 2 \times 5 \right)^4} = \frac{875}{\left( 10 \right)^4} = \frac{875}{10000} = 0 . 0875\]