Question

3. Without actual division, determine which of the following can be represented as terminating or non-terminating repeating decimals.

(d)$\frac{\mathbf{31}}{\mathbf{-}\mathbf{625}}$

Answer 1

Step 1:

For terminating decimals the prime factors of the denominators must not be other than $2$ or $5$ and For non-terminating decimals it can be other than $2$ or $5$.

We have to check the prime factors of the denominators, i.e. 625

$625=5\times 5\times 5\times 5$

So clearly we can see that the denominators does not have any prime factors other than $2$ or $5$,

So this is a terminating decimal.

Answer : Terminating Decimal