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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. 13 125 - Mathematics

Numerical

Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where, mn are non-negative integers.\[\frac{13}{125}\]

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Solution

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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APPEARS IN

RD Sharma Class 10 Maths
Chapter 1 Real Numbers
Exercise 1.6 | Q 2.2 | Page 56
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