Which of the following is/are terminating decimal(s)?

Terminating decimal is a such decimal that has only a finite number of non-zero digits. That's why if you will write such decimal as a fraction you will have as a denominator 10,100, 1000, etc. Since the fraction can be simplified, you can have in the denominator at the end some product of 2 or 5.

For example:
\(0.4=4/10=2/5\), 5 in the denominator
\(0.25=25/100=1/4\), 4=2*2 in the denominator.

But anyway, if you have terminating decimal you can't have anything other 2 or 5 in prime factorization of denominator. So we have a rule:

The fraction expressed as a decimal will be the terminating decimal if it can be presented as \(\frac{a}{{2^n\cdot 5^m}}\) where \(a\) is an integer, \(m=0,1,2,3..\). , and \(n=0,1,2,3...\) .

Or

if a fraction has in denominator any prime factor different from 2 and 5, such fraction will be infinite decimal.

Now, according to your problem:

I. Has only 2 as prime factor, since \(32=2^5\). Terminating
II. Has 7 as prime factor. Infinite
III. Has only 5 as prime factor. Terminating

The correct answer is B.


Hope this helps!:)