Question

Without actually performing the long division, state whether the following rational
numbers will have a terminating decimal expansion or a non-terminating repeating
decimal expansion:
(i) 13/3125 (ii) 17/8 (iii) 64/455
(iv) 15/1600

Answer 1

Step-by-step explanation:

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Answer 2

: Required Answer

➝ Note

If the denominator has only factors of 2 and 5 or in the form of 2m ×5n then it has terminating decimal expansion.

If the denominator has factors other than 2 and 5 then it has a non-terminating decimal expansion.

(i) 13/3125

Factorizing the denominator, we get,

3125 = 5 × 5 × 5 = 55

Since, the denominator has only 5 as its factor, 13/3125 has a terminating decimal expansion.

(ii) 17/8

Factorizing the denominator, we get,

8 = 2×2×2 = 23

Since, the denominator has only 2 as its factor, 17/8 has a terminating decimal expansion.

(iii) 64/455

Factorizing the denominator, we get,

455 = 5×7×13

Since, the denominator is not in the form of 2m × 5n, thus 64/455 has a non-terminating decimal expansion.

(iv) 15/ 1600

Factorizing the denominator, we get,

1600 = 2652

Since, the denominator is in the form of 2m × 5n, thus 15/1600 has a terminating decimal expansion.