Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion: 23/8 , Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion: 23/8

A. non-terminating non – repeating decimal

B. non-terminating repeating decimal

C. non-terminating decimal

D. terminating decimal

Correct Answer :

D. terminating decimal

Explanation

The given number is 23/8

We know a rational number is expressed in simplest form p/q and if q can be expressed as

×, then it is a terminating decimal

Clearly, 2 and 5 are not the factors of 23

8 can be expressed in terms of its primes as 2×2×2

Or, 8 =., where m = 3 and n = 0

Since q can be expressed in the form of., we can say 23/8 is a terminating decimal.