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Without Actually Performing the Long Division,125 441 - Mathematics

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प्रश्न

Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

\[\frac{125}{441}\]
संख्यात्मक

उत्तर

The given number is \[\frac{125}{441}\]

Here, \[441 = 3^2 \times 7^2\]and none of 3 and 7 is a factor of 125.
So, the given number is in its simplest form.
Now,

\[441 = 3^2 \times 7^2\] is not of the form
\[2^m \times 5^n\] So, the given number has a non-terminating repeating decimal expansion.
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अध्याय 1: Real Numbers - Exercise 1.6 [पृष्ठ ५६]

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आरडी शर्मा Mathematics [English] Class 10
अध्याय 1 Real Numbers
Exercise 1.6 | Q 1.2 | पृष्ठ ५६

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