Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form.
i. ii.
iii. iv.
v. vi.
(i)
∵ denominator is of the form, 2n × 5m,
where n = 3 and m = 2.
∴ it is terminating in nature.
ii.
∵ denominator is of the form, 2n × 5m,
125 = 5 × 5 × 5.
where n = 0 and m = 3.
∴ it is terminating in nature.
iii.
∵ denominator is of the form, 2n × 5m,
800 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5
where n = 5 and m = 2.
∴ it is terminating in nature.
iv.
∵ denominator is of the form, 2n × 5m,
1600 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5
where n = 6 and m = 2.
∴ it is terminating in nature.
v.
∵ denominator is of the form, 2n × 5m,
320 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5
where n = 6 and m = 1.
∴ it is terminating in nature.
vi.
∵ denominator is of the form, 2n × 5m,
3125 = 5 × 5 × 5 × 5 × 5
where n = 0 and m = 5.
∴ it is terminating in nature.