Question

Which of the following will have or terminating decimal expansion?
A) 13/81
B) 23/30
C) 123/8
D) 112/441

Answer 1

Answer:

$\frac{123}{8}$

Step-by-step explanation:

because to be a terminating decimal the denominator must be in the form of $\frac{x}{2^{n} * 5^{m} }$

hence here 8 is 2³×$5^{0}$

Answer 2

123/8 is having terminated decimal expansion.

Option C is correct.

Given:

• A) 13/81
• B) 23/30
• C) 123/8
• D) 112/441

To find:

• Which of the above will have terminating decimal expansion?

Solution:

Concept to be used:

A rational number p/q,where p.and q are co-prime numbers and q≠0 is having terminating decimal expansion if denominator $\bf q = {2}^{n} {5}^{m}$, where n and m are non-negative integers.

Option A): 13/81

13 and 81 are co-prime.

Write prime factors of 81.

$81 = 3 \times 3 \times 3 \times 3$

or

$81 = {3}^{4}$

It is not in the form explained above.

Thus,

13/81 is having non-terminating decimal expansion.

Option B):23/30

23 and 30 are co-prime.

$30 = 2 \times 3 \times 5$

It is not in the form explained above.

Thus,

23/30 is having non-terminating decimal expansion.

Option C) 123/8

123 and 8 are co-prime numbers.

Prime factors of 8;

$8 = 2 \times 2 \times 2$

or

$8 = {2}^{3} \times {5}^{0}$

Because

$\bf {a}^{0} = 1$

Here denominator of rational number is in the form explained above.

Thus,

123/8 is having terminated decimal expansion.

Option D)112/441 is having non-terminating decimal expansion .

Thus,

123/8 is having terminated decimal expansion.

Option C is correct.

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