audio read-through Multiplying by Powers of 10

Need some basic practice with place value first? Identifying Place Values

In the base ten number system, it is extremely easy to multiply by powers of ten.

To multiply by   $\,10^1 = 10\,$,   put $\,1\,$ zero at the end of the number:   $237\cdot 10 = 2{,}370\,$

To multiply by $\,10^2 = 100\,$, put $\,2\,$ zeros at the end of the number:   $237\cdot 100 = 23{,}700\,$

To multiply by $\,10^n\,$ (which is $\,1\,$ followed by $\,n\,$ zeroes),
put $\,n\,$ zeros at the end of the number.
For example, $\,237 \cdot 10^7 = 2{,}370{,}000{,}000\,$. (Count the seven zeros after the ‘$\,237\,$’!)

Think about why this is so easy!

When, say, $\,237\,$ is multiplied by $\,10\,$:

Each digit needs to shift into the next-left place value. Putting the zero at the end of the number accomplishes this.

In this exercise, multiplication is denoted in two ways:

Practice

Here, you will practice multiplying by powers of ten. Do not insert commas in your answers for this web exercise. That is, type the answer to $\,631\times 10^3\,$ as $\,631000\,$, not $\,631{,}000\,$.