Question

Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

\[\frac{23}{8}\]

Answer 1

The given number is \[\frac{23}{8}\] Here, \[8 = 2^3\] and 2 is not a factor of 23.

So, the given number is in its simplest form.
Now,

\[8 = 2^3\]   is of the form

\[2^m \times 5^n\]  where m = 3 and n = 0.
So, the given number has a terminating decimal expansion.