Question

State whether the following rational numbers will have a terminating decimal expansion or non-terminating repeating decimal expansions:

(a) $$\frac{26}{2185}$$

(b) $$\frac{15632}{625}$$

(c) $$\frac{368}{512}$$

(d) $$\frac{15632}{625}$$

Justify your answer.

Answer 1

$${\textbf{Step -1: Find out the values of all numbers given}}{\textbf{.}}$$

$$\text a) \dfrac{{26}}{{2185}} = 0.01189$$$$93135$$

$$\text b)\dfrac{{15632}}{{625}} = 25.0112$$

$$\text c)\dfrac{{368}}{{512}} = 0.71875$$

$$\text d)\dfrac{{15632}}{{625}} = 25.0112$$

$${\textbf{Step -2: State whether they are terminating or non - terminating}}{\textbf{.}}$$

$$\text a) \dfrac{{26}}{{2185}} = {\text{ Non - terminating because the number to be divided has no end result}}{\text{.}}$$

$$\text b) \dfrac{{15632}}{{625}} = {\text{ Terminating because the number being divided has an end value}}{\text{.}}$$

$$\text c) \dfrac{{368}}{{512}} = {\text{Terminating because the number being divided has an end value}}{\text{.}}$$

$$\text d) \dfrac{{15632}}{{625}} = {\text{ Terminating because the number being divided has an end value}}{\text{.}}$$

$${\textbf{Hence, the sequence for nature of numbers are}}$$

$${\textbf{a) Non - terminating , b) Terminating, c) Terminating, d) Terminating}}{\textbf{.}}$$