Question

Without actual division state whether the following rational number has a terminating or a non terminating repeating decimal 17/8

Answer 1

$\frac{17}{8} = \frac{17}{2 \times 2 \times 2} = \red{\frac{17}{ {2}^{3} } }$

$\green{\frac{17}{8}}$ will have a terminating decimal expansion.

⭐ This is because whenever the denominator of a rational number is of the form $\green{{2}^{m}×{5}^{n}}$ OR $\green{{2}^{m}}$ OR $\green{{5}^{n}}$ then the rational number has terminating decimal expansion.

Answer 2

this is your answer