This document provides examples and explanations for multiplying and dividing whole numbers and decimals by powers of ten. It explains that when multiplying, the digits stay the same and zeros are added to the end. When dividing, the digits move in the opposite direction to become smaller. A grid is suggested to help visualize moving the digits. Several examples are provided for students to practice multiplying and dividing whole numbers and decimals by 10, 100, and 1,000.

1. Sara Shiel

2. Revision
 Can you remember the rules you used for
- multiplying by 10,100 or 1,000?
- dividing by 10,100 or 1,000?
Do you have two different rules?
Isn’t it the same thing really? Lets have a look!

3. Multiplying Whole Numbers
 What is 34 x 100?
3400 – we keep the digits together and add two
zeros, right?
Really what’s happening?
Thousand Hundreds Tens Units
s
3 4
3 4 0
34 x 10
3 4 0 0 34x 100

4.  Now try the examples below using a grid like the one
on the previous page to help you
 345 x 10 =
 55 x 1,000 =
 867 x 100 =
 ____ x 100 = 78900
 676 x ____ = 676000

5. Dividing Whole Numbers
No prizes here for guessing what happens this time!
What is 34500/ 10?
Tens of Thousand Hundreds Tens Units
Thousand s
s
3 4 5 0 0
3 4 5 0
That’s correct, the digits all move the other way… Think
about which way will make them smaller..

6.  Now try some examples. Estimating first will always
help
3700/10 =
67800/100 =
3454/10 =
5675/1000 =
What happens with the last couple of examples? If you
are using your grid, these are no different to any of the
other examples…

7. Multiplying Decimals
 What will happen when we divide a decimal by a
power of ten?

8.  Now some final examples
 345.22 x 100 =
 7676.234 x 10 =
 2628.987987 x 100 =
 56709100 =
 72349010 =
 67687.98100 =
 676799.7978100 =