+1932 When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
0.¯01213=0.01210121…,
which is repeating.
When $\frac{1}{288}$ is expressed in base $25,$ is it terminating or repeating?
+1953 First, let's convert 1/288 into base 25 form.
We get that
This means that
Doing base division, we have that
So when is in base 25, the decimal is repeating.
So repeating is our answer.
Thanks! :)
