Which of the following has terminating decimal representation?

Correct option is D

Given:

To determine if a fraction has a terminating decimal representation, we need to check its denominator when the fraction is in its simplest form.

A fraction will have a terminating decimal representation if its denominator has only the prime factors 2 or 5.

Concept Used:

For a mixed fraction  $$a \frac{b}{c}$$​we convert it to an improper fraction as follows:

Improper Fraction =  $$a + \frac{b}{c} = \frac{(a \cdot c) + b}{c}$$​​

Once in improper fraction form, we simplify the denominator to check if it has only 2 and/or 5 as prime factors.

Solution:

Option A: $$4 \frac{1}{9} = \frac{(4 \times 9) + 1}{9} = \frac{37}{9}$$​

Option C: 2 $$\frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}$$​​

The denominator is 3, which is not 2 or 5, so this fraction does not have a terminating decimal representation.

Option D:   $$1 \frac{1}{5} = \frac{(1 \times 5) + 1}{5} = \frac{6}{5}$$​​

The denominator is 5, which is a prime factor of only 2 or 5. Therefore, this fraction has a terminating decimal representation.

Thus, the correct answer is Option D: $$1 \frac{1}{5}.$$​​

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