How many two digit numbers are there in base 5. I really don't understand how to figure this out. I know it's been asked already, but I still don't understand it.

Answer 1

The digits of a base 10 number goes from 0 to 9. The first digit of a two digit number (any base) cannot be zero, otherwise the number will become a 1-digit number.

So in base 10, there are 9 choices for the first digit, and 10 choices for the second, for a total of 9*10 numbers.

For a number in base 5, we have up to 5 different digits, namely 0,1,2,3,4. The digit 5, 6, ... do not exist in a number to base 5.

So the number of choices for the first digit, excluding zero, is 5-1=4. The number of choices for the second digit is 5.

So there is a total of 4*5 =20 two digit base 5 numbers, namely
10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31.....34, 40, 41, 42, 43, 44.
(Remember digits 5 and above do not exist in base 5, just like we have no digit for 10 and above for base 10).

If this is still not clear, please post.

Answer 2

Mathmate-
Thank you very much, I completely understand your explanation now.