Question

EXERCISE 1.4 1. Without actually performing the long division, state whether the following ration numbers will have a terminating decimal expansion or a non-terminating repeating decim expansion: 13 17 64 15 (iv) 3125 8 455 1600 29 6 (v) (vi) 23 2352 (vii) 129 2257 75 (VIII 343 15 35 77 (ix) ( x) 50 210​

Answer 1

Answer:

Let x=pqx=pq be a rational number, such that the prime factorization of qq is of the form 2n×5m2n×5m, where n,mn,m are non-negative integers. Then xx has a decimal expansion which terminates.

Steps:

(i) 133125133125

The denominator is of the form 55.55.

Hence, the decimal expansion of 133125133125is terminating.

(ii) 178178

The denominator is of the form 23.23.

Hence, the decimal expansion of 178178 is terminating.

(iii) 6445564455

455=5×7×13455=5×7×13

Since the denominator is not in the form 2m×5n,2m×5n, and it also contains 77 and 1313 as its factors, its decimal expansion will be non-terminating repeating.

(iv) 151600151600

1600=26×521600=26×52

The denominator is of the form 2m×5n.