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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. 129 2 2 × 5 7 - Mathematics

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Question

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.\[\frac{129}{2^2 \times 5^7}\]

Numerical
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Solution

The given number is \[\frac{129}{2^2 \times 5^7}\] 

Clearly, 22 × 5is of the form 2m × 5n, where m = 2 and n = 7.
So, the given number has terminating decimal expansion.

\[\therefore \frac{129}{2^2 \times 5^7} = \frac{129 \times 2^5}{2^2 \times 5^7 \times 2^5} = \frac{129 \times 32}{\left( 2 \times 5 \right)^7} = \frac{4182}{\left( 10 \right)^7} = \frac{4182}{10000000} = 0 . 0004182\]
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Chapter 1: Real Numbers - Exercise 1.6 [Page 56]

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RD Sharma Mathematics [English] Class 10
Chapter 1 Real Numbers
Exercise 1.6 | Q 2.5 | Page 56

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