When we see numbers in everyday life, we always see numbers that are composed of the digits 0 through 9. This is base 10. For instance, take the number 1234. When you see this number you see:
(10)3 x 1 + (10)2 x 2 + (10)1 x 3 + (10)0 x 4
This is how you manipulate numbers in base 10. If you were in a different base, 'b', then the highest digit in the base is 'b' - 1, and any numbers would be represented by the following:
(b)n x a + ... + (b)1 x a' + (b)0 x a''. where a, a', and a'' represent different digits.
The lowest base is of course 2, since the only numbers you can have are 0 and 1.
In number sense, we see problems that deal with bases and there are many methods we can use.