posted by jason on .
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.
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.
Thank you very much, I completely understand your explanation now.