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Without Actually Performing the Long Division,23 8 - Mathematics

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Question

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.

\[\frac{23}{8}\]
Numerical

Solution

The given number is \[\frac{23}{8}\] Here, \[8 = 2^3\] and 2 is not a factor of 23.

So, the given number is in its simplest form.
Now,
\[8 = 2^3\]   is of the form
\[2^m \times 5^n\]  where m = 3 and n = 0.
So, the given number has a terminating decimal expansion.
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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 1.1 | Page 56

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