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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. 7 80 - Mathematics

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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, mn are non-negative integers.\[\frac{7}{80}\]

संख्यात्मक

उत्तर

The given number is \[\frac{7}{80}\] Clearly, 80 = 24 × 5 is of the form 2m × 5n, where m = 4 and n = 1.

So, the given number has terminating decimal expansion.

\[\therefore \frac{7}{80} = \frac{7 \times 5^3}{2^4 \times 5 \times 5^3} = \frac{7 \times 125}{\left( 2 \times 5 \right)^4} = \frac{875}{\left( 10 \right)^4} = \frac{875}{10000} = 0 . 0875\]
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पाठ 1: Real Numbers - Exercise 1.6 [पृष्ठ ५६]

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आरडी शर्मा Mathematics [English] Class 10
पाठ 1 Real Numbers
Exercise 1.6 | Q 2.3 | पृष्ठ ५६

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