What does each column represent?

We can express the values of the columns of the numbers we use as **exponents**. You will already be familiar with this concept from decimal number, where we often refer to the columns as tens, hundreds and thousands.

Exponents use **powers** to represent numbers. For example 10^{2} means 10 raised to the second power or 10 multiplied by itself 2 times. This gives us (10 x 10) or 100.

10^{5} is (10 x 10 x 10 x 10 x 10) or 100000.

How, then, do we use exponents to represent the columns in numbers? From right to left the columns are 1s, 10s, 100s, etc. We have seen that 10^{2} is 100. 10^{1} is simply 10. What about the 1s column?

To work this out we can use an example. What is 10^{3} x 10^{2}? If we expand this we get (10 x 10 x 10) x (10 x 10). This is simply (10 x 10 x 10 x 10 x 10) or 10^{5}.

So 10^{3} x 10^{2} is the same as 10^{3+2} or 10^{5}.

What then is 10^{3} x 10^{0}? It is 10^{3+0} or simply 10^{3}.

What number can we use to multiply 10^{3} and get 10^{3}? The answer is 1. Therefore 10^{0} is 1.

**Next: Base 10**