What is the base in an expression in math?

Answer 1

The base is the number at which you move from one place value to the next. In normal counting, we count in units up to 10, at which point we count in tens and units up to 100 (10x10) at which point we count in hundreds, tens and units up until 1,000 (10x10x10) and so on. Thus normal counting is called base 10.

In base 4, say, you would count in units until you got to 4, then move into counting in 4s and units until you got to 16 (4x4) and then move into counting in 16s 4s and units. Base 4 counting would look like this: 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 100, 101, 102, 103, 110... and so on

21 in base 4 would equal 9 in base 10.

112 in base 4 would equal 22 in base 10.