The fraction 17/40 has a terminating decimal expansion. How many digits does it have after the decimal point?

In lowest terms the denominator is $40=2^3\times 5^1$. Multiplying top and bottom by $5^2$ balances the primes: 17/40 = 425/1000 = 0.425, which has 3 decimal places. The rule is that the number of places equals the LARGER of the two indices — here max(3, 1) = 3. Using the smaller index gives 1, and adding them gives 4.