How many nonnegative integers less than 1 million contain the digit 2?

The number of all nonnegative integers less than 1 million is \(10^6\) because there are ten possible digits at each of the 6 positions). Before you object that this includes numbers like 000010 and 002222 and excludes numbers like 1, 15 or 2098, consider that if we treat a leading 0 as signifying lack of any digit, then it starts to make sense. A number like 000010 is simply 10 and 002222 is 2222, while 2098 is itself. Then we can represent all nonnegative integers below 1 million as having six digits each (from 000000 to 999999) and the calculation makes sense.

We subtract from it the number of all integers that do NOT contain 2, which is \(9^6\) (nine possible digits (remember, 2 is excluded) at each of the 6 positions) and get:

\[10^6 - 9^6 = 468559\]