+380 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 $19,$ is it terminating or repeating?
+1950 First, let's convert the numbers in to base 19.
We have
(F3)19=(15×191)+(3×190)=(288)10
This means that 128810=1F319
Doing some base division, we have
1F319=¯0.014F9AE6
Thus, it is a repeating decimal.
So our answer is repeating.
Thanks! :)
