Question

Without actual division, find which of the following rational numbers are terminating decimals. (i) $\frac{17}{50}$ (ii) $\frac{13}{75}$ (iii) $\frac{7}{100}$.

Answer 1

(i) $\frac{17}{50}$
Denominator is 50 = 2×5×5 = 2×$5^2$.
Hence, denominator doesn't have any factor other than 2 or 5. So, the number is terminating.

(ii) $\frac{13}{75}$
Denominator is 75 = 3×5×5 = 3×$5^2$.
Hence, denominator has factor other than 2 or 5. So, the number is non- terminating.

(ii) $\frac{7}{100}$
Denominator is 100 = 2×2×5×5 = $2^2$×$5^2$.
Hence, denominator doesn't have any factor other than 2 or 5. So, the number is terminating.