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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.\[\frac{14588}{625}\]
उत्तर
The given number is \[\frac{14588}{625}\] Clearly, 625 = 54 is of the form 2m × 5n, where m = 0 and n = 4.
So, the given number has terminating decimal expansion.
\[\therefore \frac{14588}{625} = \frac{14588 \times 2^4}{2^4 \times 5^4} = \frac{14588 \times 16}{\left( 2 \times 5 \right)^4} = \frac{233408}{\left( 10 \right)^4} = \frac{233408}{10000} = 23 . 3408\]
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