Which Rational Numbers Have Terminating Decimal Expansions?

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: Which of the following rational numbers have terminating decimals?

(i) 16/25    (ii) 5/18    (iii) 2/21    (iv) 7/250

Important Rule

A rational number has a terminating decimal expansion if, in its lowest form, the denominator has only the prime factors 2 and/or 5.

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(i) 16/25

25 = 5²

Denominator has only the prime factor 5.

∴ 16/25 has a terminating decimal.

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(ii) 5/18

18 = 2 × 3²

Denominator contains prime factor 3 (other than 2 and 5).

∴ 5/18 has a non-terminating repeating decimal.

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(iii) 2/21

21 = 3 × 7

Denominator contains primes other than 2 and 5.

∴ 2/21 has a non-terminating repeating decimal.

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(iv) 7/250

250 = 2 × 5³

Denominator has only prime factors 2 and 5.

∴ 7/250 has a terminating decimal.

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Final Answer

✔ Rational numbers with terminating decimals:
(i) 16/25 and (iv) 7/250

Conclusion

Thus, among the given rational numbers, 16/25 and 7/250 have terminating decimal expansions.