Question

Which of the following numbers has non-terminating repeating decimal expansion?

पर्याय

• `11/640`

• `7/120`

• `1/125`

• `3/250`

Answer 1

`bb(7/120)`

Explanation:

The decimal expansion of a rational number is either terminating or non-terminating repeating.

A rational number has a terminating decimal expansion if its denominator in simplest form has only 2 and/or 5 as prime factors i.e., the denominator is of the form 2^m × 5ⁿ, where m, n are whole numbers.

It has a non-terminating repeating decimal expansion if its denominator contains any prime factor other than 2 or 5.

Now, let’s analyse each option’s denominator factorisation:

(a) `11/640`

Denominator: 640 = 2⁷ × 5¹ only 2 and 5 → Terminating decimal.

(b) `7/120`

Denominator: 120 = 2³ × 3 × 5 contains 3 → Non-terminating repeating decimal.

(c) `1/125`

Denominator: 125 = 5³ only 5 → Terminating decimal.

(d) `3/250`

Denominator: 250 = 2 × 5³ only 2 and 5 → Terminating decimal.

Since 120 has a prime factor 3 in the denominator apart from 2 and 5, `7/120` will have a non-terminating repeating decimal expansion, unlike the other options which are terminating decimals because their denominators include only 2 and/or 5 as prime factors.