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

Answer:

Solve the equation using balancing method:

2

− 2 = 26

Answer 2

$\huge\bf\fbox\red{Answer:-}$

(i) 13/3125

=> Factorizing the denominator,

we get,

=> 3125 = 5 × 5 × 5 = 5^{5}

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 = 2^{3}

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 = 2^{6}5^{2}

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