Question

Without actually dividing find which of the following are terminating decimals 3/25

Answer 1

Answer :-

p/q is a terminating decimal ,if p and q are co-prime and q = $2^{n}\times 5^{m}$ where n ,m are positive integers.

Check co-prime :-

Since 3 and 25 have no common factors, hence 3 and 25 are co-prime.

Now,

$25=5\times 5\\\\=5^{2}$

Denominator = $5^{2}=1\times5^{2}=2^{0}\times5^{2}$

Denominator is of the form $2^{m}5^{n}$,where m = 0 and n = 2.

∴ 3/25 is a terminating decimal.