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.

\[\frac{14588}{625}\]

Answer 1

The given number is \[\frac{14588}{625}\].

Clearly, 625 = 5⁴ is of the form 2^m × 5ⁿ, where m = 0 and n = 4.

So, the given number has terminating decimal expansion.

\[\therefore \frac{14588}{625} = \frac{14588 \times 2^4}{2^4 \times 5^4} = \frac{14588 \times 16}{\left( 2 \times 5 \right)^4} = \frac{233408}{\left( 10 \right)^4} = \frac{233408}{10000} = 23 . 3408\]