Question

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

(i) $\frac{23}{8}$ (ii) $\frac{125}{441}$ (iii) $\frac{35}{50}$ (iv) $\frac{77}{210}$ (v) $\frac{129}{2^2\times 5^7\times 7^{17}}$

Answer 1

$1)$ Denominator is $8$,so the rational has a non-terminating decimal expansion

$2)$Denominator is a multiple of $3,7$ so the rational number has a terminating decimal expansion

$3)\frac{35}{50}=\frac{7}{10}$ Denominator is $10$,so the rational has a non-terminating decimal expansion

$4)\frac{77}{210}=\frac{11}{30}$ Denominator is a multiple of $3$,so the rational has a terminating decimal expansion

$5)$ Denominator is a multiple of $7$,so the rational has a terminating decimal expansion