Question

After how many places the decimal expansion of 13/40 will terminate?

Answer 1

Remember that
`40 = 2\cdot 2\cdot 10`.

So, dividing by 40 means dividing by 10, then by 2, then by 2 again.

So, we can go like this: let's divide by 10 first

`13 / 10 = 1.3`

Then, we divide by 2:

`1.3 / 2 = 0.65`

And by 2 again:

`0.65 / 2 = 0.325`

So, the decimal expansion ends after 3 digits.