Question

without actually performing the long division state weather the following rational number will have a terminating decimal expansion or a non terminating repeating decimal expansion : (1) 15/1600​

Answer 1

$\bold\pink{answer \: 0.009375 }\\ = > \frac{15}{1600} \\ prime\: factorization\\ = > \frac{15}{ {2}^{6} \times {5}^{2} } \\ = > \frac{15 \times {5}^{4} }{ {2}^{6} \times {5}^{2} \times {5}^{4} } \: - - - mutiplying \: both \: by \: {5}^{4} \\ = > \frac{9375}{ {10}^{6} } \\ = > \frac{9375}{1000000} \\ \\ \huge\mathcal\red {answer = > 0.009375} \\ \\ hope \: it \: helps \\ thanks$

Answer 2

Step-by-step explanation:

Factorize the denominator we get 1600=2×2×2×2×2×2×5×5=26×52

so denominator is in form of 2n×5m

Hence 15 /1600  is  terminating.