Solution:

A decimal expansion is called a terminating decimal expansion if it has a finite number of digits after the decimal point.

We need to check which of the given fractions have a terminating decimal expansion.

a) 8/225

We can simplify the fraction 8/225 by dividing both the numerator and denominator by their HCF, which is 1.

8/225 = (8 ÷ 1)/(225 ÷ 1) = 8/225

The denominator of the simplified fraction is not divisible by any prime other than 3 or 5, so the decimal expansion of 8/225 will be non-terminating.

b) 5/18

We can simplify the fraction 5/18 by dividing both the numerator and denominator by their HCF, which is 1.

5/18 = (5 ÷ 1)/(18 ÷ 1) = 5/18

The denominator of the simplified fraction is not divisible by any prime other than 2 or 5, so the decimal expansion of 5/18 will be non-terminating.

c) 11/21

We can simplify the fraction 11/21 by dividing both the numerator and denominator by their HCF, which is 1.

11/21 = (11 ÷ 1)/(21 ÷ 1) = 11/21

The denominator of the simplified fraction is not divisible by any prime other than 3 or 7, so the decimal expansion of 11/21 will be non-terminating.

d) 21/150

We can simplify the fraction 21/150 by dividing both the numerator and denominator by their HCF, which is 3.

21/150 = (21 ÷ 3)/(150 ÷ 3) = 7/50

The denominator of the simplified fraction is divisible by only the primes 2 and 5, so the decimal expansion of 7/50 will be terminating.

Therefore, the only fraction among the given options that has a terminating decimal expansion is 21/150.