MULTIPLYING BY POWERS OF TEN

LESSON READ-THROUGH
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
 

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:

Master the ideas from this section
by practicing the exercise at the bottom of this page.


When you're done practicing, move on to:
Changing Decimals to Fractions

 
 

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 [beautiful math coming... please be patient] $\,631\times 10^3\,$ as $\,631000\,$, not [beautiful math coming... please be patient] $\,631{,}000\,$.

Multiply:
    
(an even number, please)