Multiply and Divide Decimals by 10, 100, and 1000
(powers of ten)
This is a complete lesson with a video & exercises showing, first of all, the common shortcut for multiplying & dividing decimals by powers of ten: you move the decimal point as many steps as there are zeros in the number 10, 100, 1000 etc.
Then, I also show where this shortcut originates, using place value charts. In reality, the decimal point moving is sort of an illusion, and instead, the digits of the number move within the place value chart. This explanation can really help students to understand the reason behind the "trick" of moving the decimal point.
The lesson below explains the shortcut in more detail, plus has different kinds of exercises, word problems, and even a fun riddle for students.
Remember?
When you multiply whole numbers by 10, 100, 1000, and so on (powers of
ten), you can simply “tag” as many zeros on the product as there are in the factor
10, 100, 1000 etc.
There is a similar shortcut for multiplying decimal numbers by numbers such as 10, 100, and 1000: 

Move the decimal point one step to the right (10 has one zero). 

Move the decimal point two steps to the right (100 has two zeros). The number 265. is 265 (as shown above). 

1000 means we move the point three steps. Write a zero at the end of 0.37 so that the decimal point can “jump over to” that place. 
1. Multiply.
a. 10 × 0.04 = ________ b. 100 × 0.04 = ________ c. 1000 × 0.04 = ________ 
d. 10 × 0.56 = ________ e. 100 × 0.56 = ________ f. 1000 × 0.56 = ________ 
g. 10 × 0.048 = ________ h. 100 × 0.048 = ________ i. 1000 × 0.048 = _______ 
Another helpful shortcut! Since 100 × 2 = 200, obviously the answer to 100 × 2.105 will be a little more than 200. Hence, you can just write the digits 2105 and put the decimal point so that the answer is 200something: 210.5. 
2. Let's practice some more.
a. 100 × 5.439 = ________ b. 100 × 4.03 = ________ 
c. 1000 × 3.06 = ________ d. 100 × 30.54 = ________ 
e. 30.73 × 10 = ________ f. 93.103 × 100 = _______ 
 
10^{5} = 100,000 has five zeros. Again, write additional zeros so that the decimal point can “jump over to” those places. 
3. Now let's practice using powers of ten.
a. 10^{2} × 0.007 = _____________ 10^{3} × 2.01 = _____________ 10^{5} × 4.1 = ______________ 
b. 10^{5} × 41.59 = _____________ 3.06 × 10^{4} = ______________ 0.046 × 10^{6} = _____________ 
The shortcut for division by 10, 100 and 1000 (powers of ten) is similar. Can you guess it? Move the decimal point to the ( left / right ) for as many places (steps) as there are _________________________ in the factor 10, 100, or 1000. 

Move the decimal point two steps to the ____________. You need to write zeros in front of the number. 

Move the decimal point four steps to the ____________. You need to write zeros in front of the number. 
4. Divide.
a. 0.4 ÷ 10 = ________ 0.4 ÷ 100 = ________ 4.4 ÷ 100 = ________ 
b. 15.4 ÷ 100 = ________ 21.03 ÷ 10 = ________ 0.39 ÷ 10 = ________ 
c. 5.6 ÷ 10 = ________ 34.9 ÷ 100 = ________ 230 ÷ 1000 = ________ 
5. Now let's practice using powers of ten.
a. 0.7 ÷ 10^{2} = _____________ 45.3 ÷ 10^{3} = _____________ 568 ÷ 10^{5} = _____________ 
b. 2.1 ÷ 10^{4} = _____________ 4,500 ÷ 10^{6} = _____________ 9.13 ÷ 10^{3} = _____________ 






The similar shortcut for division works because division is the opposite operation of multiplication—it “undoes” multiplication. If we move the decimal point to the right when multiplying by 10, 100, 1000 and so on, then it is quite natural that the rule for division would work the “opposite” way. 
Fractions vs. division. If we move the decimal point to solve 6 ÷ 100, we get:
Let’s write 6 ÷ 100 using the fraction line: it is 6/100 or 6 hundredths, which is written 0.06 as a decimal. Therefore, in this case you do not need the “shortcut,” but you can just think of fractions and decimals. These kinds of “connections” make mathematics so neat! 
6. Divide. Think of fractions to decimals, or use the shortcut. Compare the problems in each box!







7. A 10lb sack of nuts costs
$72.
How much does one pound cost?
8. Find the price of 100 pingpong balls if one ping pong ball costs $0.89.
Thinking more about fractions and decimals If we divide any whole number by 1,000, the answer will have thousandths or three decimal digits. This makes it easy to divide whole numbers by 1,000: simply copy the dividend as your answer (without the commas), and then make it have three decimal digits: Examples:
Notice in the last two cases, we can simplify the results: 41.300 to 41.3 and 8.000 to 8. 
9. Divide whole numbers by 1000. Simplify the final answer by dropping any ending decimal zeros.











Similarly:
Examples:

10. Divide whole numbers by 10 and 100.











11. Find onetenth of...
a. $8
b. $25.50
c. $126
12. Find onehundredth of...
a. $78
b. $4
c. $390
13. A pair of shoes that cost $29 was discounted by 3/10 of its price. What is the new price?(Hint: First find 1/10 of the price.)
14. Find the discounted price:
a. A bike that costs $126 is discounted by 2/10 of its price.
b. A $45 cell phone is discounted by 5/100 of its price.
(Hint:
First find 1/100 of the price.)
15. Onehundredth of a certain number
is 0.03. What is the number?
16. Which vacuum cleaner ends up being cheaper?
Model A, with the initial price $86.90, is discounted by 3/10 of its price.
Model B costs $75 now, but you will get a discount
of 1/4 of its price.
An important tip In the problem ____ ×
3.09 = 309, the number 3 becomes 300,
so obviously The same works with division, too. In the problem
7,209 ÷
_____ =
7.209, the missing divisor Of course, in some problems it will be easier to think in terms of “moving the decimal point.” 
17. It is time for some final practice. Find the missing numbers. Match the letter of each problem with the right answer in the boxes, and solve the riddle. There are two sets of boxes. The first boxes belong to the first set of exercises, and the latter boxes belong to the latter set.
Why didn’t 7 understand what 3.14 was talking about?
E ____ × 0.04 = 40 D ____ × 9.381 = 938.1 H 1,000 × 4.20 = D ____ × 7.31 = 731 T ____ × 0.075 = 0.75 
I 10 × 3.55 = ______ N 100 × ______ = 4.2 S 1,000 × ______ = 355 E ____ × 60.15 = 60,150 
4,200  1000  100  35.5  100  0.042  10  0.355  1000  1000  
’ 
T _____ ÷ 100 = 0.42 P _____ ÷ 10 = 2.3 N _____ ÷ 1000 = 4.2

S 0.31 ÷ _____ = 0.031 O 4,360 ÷ _____ = 4.36 I 304.5 ÷ _____ = 3.045 
230  100  10  23  1000  4.2  4,200  42  
I also offer free worksheets:
Worksheets for multiplying decimals by powers of ten
Worksheets for dividing decimals by powers of ten
.
This lesson is taken from Maria Miller's book Math Mammoth Decimals 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
Math Mammoth Decimals 2
A selfteaching worktext for 5th6th grade that covers the four operations with decimals up to three decimal digits, concentrating on decimal multiplication and division. The book also covers place value, comparing, rounding, addition and subtraction of decimals. There are a lot of mental math problems.
Download ($6.25). Also available as a printed copy.