Question

Which of the following rational numbers have terminating decimal?

(i) $\frac{16}{225}$
(ii) $\frac{5}{18}$
(iii) $\frac{2}{21}$
(iv) $\frac{7}{250}$

(a) (i) and (ii)
(b) (ii) and (iii)
(c) (i) and (iii)
(d) (i) and (iv)

Answer 1

(i) We have,

Theorem states:

Let be a rational number, such that the prime factorization of q is not of the form, where m and n are non-negative integers.

Then, x has a decimal expression which does not have terminating decimal.

(ii) We have,

Theorem states:

Let be a rational number, such that the prime factorization of q is not of the form, where m and n are non-negative integers.

Then, x has a decimal expression which does not have terminating decimal.

(iii) We have,

Theorem states:

Let be a rational number, such that the prime factorization of q is not of the form, where m and n are non-negative integers.

Then, x has a decimal expression which does not have terminating decimal.

(iv) We have,

Theorem states:

Let be a rational number, such that the prime factorization of q is of the form, where m and n are non-negative integers.

Then, x has a decimal expression which terminates after k places of decimals, where k is the larger of m and n.

Then, x has a decimal expression which will have terminating decimal after 3 places of decimal.

Hence the (iv) option will have terminating decimal expansion.

There is no correct option.