+1855 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.\overline{0121}_3 = 0.01210121 \dots,
which is repeating.
When \frac{1}{288} is expressed in base 25, is it terminating or repeating?
+1950 Let's convert the each number in the fraction to base 25.
One always stays the same, so converting 288 to base 25, we have
This means that
Now, we do base division. We get that
As you can see, 1/288 in base 25 is repeating.
So repeating is our answer.
Thanks! :)
