Question

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

• A. terminating decimal
• B. non-terminating decimal
• C. non-terminating repeating decimal
• D. non-terminating non - repeating decimal

Answer 1

The correct option is A

terminating decimal

The given number is $\frac{23}{8}$

We know a rational number is expressed in simplest form $\frac{p}{q}$ and if $q$ can be expressed as

$2^m\times 5^n$, 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 $2\times 2\times 2$

Or, 8 = $2^m{.5}^n$, where m = 3 and n = 0

Since $q$ can be expressed in the form of $2^m{.5}^n$, we can say $\frac{23}{8}$ is a terminating decimal.