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. 14588 625 - Mathematics

Numerical

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.\[\frac{14588}{625}\]

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Solution

The given number is \[\frac{14588}{625}\] Clearly, 625 = 5⁴ is of the form 2^m × 5ⁿ, where m = 0 and n = 4.

So, the given number has terminating decimal expansion.

\[\therefore \frac{14588}{625} = \frac{14588 \times 2^4}{2^4 \times 5^4} = \frac{14588 \times 16}{\left( 2 \times 5 \right)^4} = \frac{233408}{\left( 10 \right)^4} = \frac{233408}{10000} = 23 . 3408\]

Concept: Revisiting Rational Numbers and Their Decimal Expansions

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Chapter 1: Real Numbers - Exercise 1.6 [Page 56]

Q 2.4 Q 2.3 Q 2.5

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