+1216 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?
+1950 First, let's convert 1/288 into base 25 form.
We get that (BD)25=(11×251)+(13×250)=(288)10
This means that 128810=1BD25
Doing base division, we have that
1BD25=0.¯0.02468ACEGIKN
So when 1/288 is in base 25, the decimal is repeating.
So repeating is our answer.
Thanks! :)
