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

$13 \div 10 = 1.3$

Then, we divide by 2:

$1.3 \div 2 = 0.65$

And by 2 again:

$0.65 \div 2 = 0.325$

So, the decimal expansion ends after 3 digits.