Question

Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or a non-terminating decimal expansion 27/16 *

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Answer 1

Answer:

Numbers are decimal places value

Answer 2

SOLUTION :-

The Denominator of the Fraction $\frac{27}{16}$ is 16

Prime Factorization of 16 is $\Rightarrow16 = 2 * 2 * 2 * 2 = 2^4$

As 16 has no other Prime Factors other than 2 and 5,

We can Conclude that $\frac{27}{16}$ is a Terminating Decimal....

VERIFICATION :-

$\Rightarrow \frac{27}{16} = \bold{1.6875}$

Hence,

It is also Verified that the Fraction 27/16 is a Terminating Decimal....