Question

which of the following has terminating decimal expansion with reason

$\frac{32}{1250}$


$\frac{7125}{3 \times 5 {}^{2} }$
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Answer 1

Hello....

32/1250= here 1250 factors r 2*5^4...

Hence it hv terminating expansion...

7125/3*5^2= here the denominator is not in the form of 2^m5^n....

Hence it hv non terminating expansion

Answer 2

Answer:

32/1250 can also be written as 32/(5×5×5×5×2) we know that we can write 1/5 as 0.2 and 1/2 as 0.5 Hence 1/1250 is 0.2×0.2×0.2×0.5 => 0.04 So 32/1250 is 0.128 . Hence it has terminating decimal expansion whereas 1/3 ×1/5 ×1/5 => 0.3333333 × 0.2 × 0.2 => 0.1333333 So 7125/ 5×5 ×3 => 285 ×25/25×3 =>285/3 hence it has non terminating repeating decimal expansion. Hope it helps you.