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.

\[\frac{13}{125}\]

Answer 1

The given number is \[\frac{13}{125}\].

Clearly, 125 = 5³ is of the form 2^m × 5ⁿ, where m = 0 and n = 3.

So, the given number has terminating decimal expansion.

\[\therefore \frac{13}{125} = \frac{13 \times 2^3}{2^3 \times 5^3} = \frac{13 \times 8}{\left( 2 \times 5 \right)^3} = \frac{104}{\left( 10 \right)^3} = \frac{104}{1000} = 0 . 104\]