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.

 (**)  Changing from base b to 10  (*PDF*) (**)  Changing from base 10 to b  (*PDF*) (**)  Changing from base 2 to 4  (*PDF*) (**)  Changing from base 2 to 8  (*PDF*) (**)  Changing from base 3 to 9  (*PDF*) (**)  Adding 2 numbers in a different base  (*PDF*) (***) Changing from a base 10 decimal/fraction to a base b decimal  (*PDF*) (***) Changing from a base b decimal to a base 10 decimal/fraction  (*PDF*) (***) Multiplying 2 numbers in a different base  (*PDF*) (***)  Finding the remainder when nb is divided by (b-1)  (*PDF*)