Question

which one of the following has a terminating decimal expansion?

(a) 5/64
(b) 8/9
(c) 14/15
(d) 1/12​

Answer 1

Answer:

b. 8/9

Step-by-step explanation:

Decimal expansion of 8/9 = 0.888888888. So 8/9 has terminating expansion

Answer 2

Denominator of the fraction which can be expressed as $\sf{ 2^m \times 5^n }$ will be a terminating decimal and hence a rational number.

$\sf{\\}$

From the given options, look at option (a)

The denominator part that is 64 can be written as

$\sf{ 64 = 2^6 \times 5^0 }$ which is in the form of $\sf{ 2^m \times 5^n }$

Hence, Option (a) $\sf{ \dfrac{5}{64} }$ will have a terminating decimal expansion.