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: (a) 31/160 (b)111/120​

Answer 1

Step-by-step explanation:

Hence, 23/ (2352) has a terminating decimal expansion. As you can see, the denominator is not in the form of 2m × 5n. Hence, 129/ (225775) has a non-terminating decimal expansion. Thus, 6/15 has a terminating decimal expansion.

Answer 2

Step-by-step explanation:

Theorem: Let x=

q

p

be a rational number, such that the prime factorisation of q is of the form 2

n

5

m

, where n, m are non-negative integers. Then, x has a decimal expansion which terminates.

(i)

3125

13

Factorise the denominator, we get

3125=5×5×5×5×5=5

5

So, denominator is in form of 5

m

so,

3125

13

is terminating.

(ii)

8

17

Factorise the denominator, we get

8=2×2×2=2

3

So, denominator is in form of 2

n

so,

8

17

is terminating.