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प्रश्न
Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where, m, n are non-negative integers.\[\frac{13}{125}\]
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उत्तर
The given number is \[\frac{13}{125}\].
Clearly, 125 = 53 is of the form 2m × 5n, where m = 0 and n = 3.
So, the given number has terminating decimal expansion.
\[\therefore \frac{13}{125} = \frac{13 \times 2^3}{2^3 \times 5^3} = \frac{13 \times 8}{\left( 2 \times 5 \right)^3} = \frac{104}{\left( 10 \right)^3} = \frac{104}{1000} = 0 . 104\]
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