Without actual division, find which of the following rational numbers are terminating decimals. (i) 1380 (ii) 724 (iii) 512 (iv)31375 (v) 16125
For terminating decimals, factors of denominator should be in the form of 2m×5n.
(i) 1380
Here, denominator is 80
80=2×2×2×2×5=24×5
hence denominator doesn't have any factor other than 2 or 5.
So, the number is terminating.
(ii) 724
Denominator is 24.
24=2×2×2×3=23×3
Hence, denominator has factor other than 2 or 5.
So, the number is non-terminating.
(iii) 512
Denominator is 12.
12=2×2×3=22×3
Hence, denominator has factor other than 2 or 5.
So, the number is non-terminating.
(iv) 31375
Denominator is 375.
375=5×5×5×3=53×3
Hence, denominator has factor other than 2 or 5.
So, the number is non-terminating.
(v) 16125
denominator is 125.
125=5×5×5=53
Hence, the denominator doesn't have any factor other than 2 or 5.
So, the number is terminating.