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

## (i) (ii) (iii) (iv)

## (v) (vi) (vii) (viii)

## (ix) (x)

**Solution:**

According to Theorem, any given rational number of the form **where p and q are co-prime**, has a terminating decimal expansion if q is of the form , where m and n are non-negative integers.

## (i)

Therefore, denominator is of the form , where m=5 and n=0.

It means rational number has a **terminating** decimal expansion.

**(ii) **

Therefore, denominator is of the form , where m=0 and n=3.

It means rational number has a **terminating** decimal expansion.

**(iii) **

Therefore, denominator is not of the form , where m and n are non-negative integers.

It means rational number has a **non-terminating repeating** decimal expansion.

**(iv) **

Therefore, denominator is of the form , where m=1 and n=6.

It means rational number has a **terminating** decimal expansion.

**(v) **

Therefore, denominator is not of the form , where m and n are non-negative integers.

It means rational number has **non-terminating repeating** decimal expansion.

## (vi)

Therefore, denominator is of the form , where m=2 and n=3 are non-negative integers.

It means rational number has **terminating** decimal expansion.

## (vii)

Therefore, denominator is not of the form , where m and n are non-negative integers.

It means rational number has **non-terminating repeating** decimal expansion.

**(viii) **

Therefore, denominator is of the form , where m=1 and n=0.

It means rational number has **terminating** decimal expansion.

## (ix)

Therefore, denominator is of the form , where m=1 and n=1..

It means rational number has **terminating decimal** expansion.

**(x) **

Therefore, denominator is not of the form , where m and n are non-negative integers.

It means rational number has **non-terminating repeating** decimal expansion.