Multiplying Decimals

1
Multiplying Decimals

• I can multiply decimals

2
To Multiply

• You do not line up the factors by the decimal.
• Instead, place the number with more digits on
  top.
• Line up the other number underneath, at the
  right.
• Multiply
• Count the number of decimal places (from the
  right) in each factor.
• Use the total number of decimal places in your
  two factors to place the decimal in your product.

3
Multiply Decimals

• Step 1 --- Ignore the decimal
• Step 2 --- Rewrite the problem
• Step 3 --- Multiply the problem
• Step 4 --- Underline all numbers to the right of
  decimal(s) in original problem
• Step 5 --- Move decimal that many places left in
  your answer

4
Steps 1 2

• Ignore decimals and rewrite the problem

• 4 . 5 6
• X 0 . 3 9
• 4 5 6
• x 3 9

5
Step 3

• Multiply problem without decimals
• 4 5 6
• x 3 9
• 4 1 0 4
• 1 3 6 8 0
• 1 7 7 8 4

6
Step 4

• Underline numbers to the right of decimals in
  original problem
• 4. 5 6
• x 0. 3 9
• ---------------

( 4 places)
7
Step 5

• Move decimal that many places left in answer
• 4 5 6
• x 3 9
• 4 1 0 4
• 1 3 6 8 0
• 1 7 7 8 4 ( 4 places)

8
Multiplying Decimals

• I can multiply decimals

9
Multiplying Decimals
You can use graph paper to model decimal
multiplication. Here is a model of the product
of 0.7 and 0.3.
0.7
0.3
1
Because 21 of the 100 squares are shaded, 0.7 ?
0.3
0.21.
1
Multiplying Decimals
Words
Multiply decimals as you would
whole numbers. Then place the decimal point in
the product. The number of decimal places in the
product is equal to the sum of the number of
decimal places in the factors.
0.7 ? 0.3 0.21
Numbers
10
Multiplying Decimals
5.82
2 decimal places
0.41
2 decimal places
5 8 2
2 3 2 80

4 decimal places
2.3 8 6 2
1
2
3
4
11
Example 5.63 x 3.7
1
2
4
5.63
two
x
3.7
one
1
1
1
4
39
1
0
9
8
16

1
3
8
0
2
.
three
12
Multiplying Decimals
6.45
2 decimal places
18
0 decimal places
5160
6450

116.10
2 decimal places
ANSWER
6.45 ? 18 116.1
Because 6 ? 20 120, the product is reasonable.
13
Multiplying Decimals
1.273
6.45
3 decimal places
2 decimal places
0.06
18
2 decimal places
0 decimal places
5160
7638
0.0
5 decimal places
645

116.10
2 decimal places
ANSWER
ANSWER
6.45 ? 18 116.1
1.273 ? 0.06 0.07638
CHECK
Because 6 ? 20 120, the product is reasonable.
Because 1 ? 0.06 0.06, the product is
reasonable.
14
Multiplying Decimals to Find Area
Central Park Central Park is a rectangular park
about 2.5 miles long and about 0.5 mile wide.
What is the area of Central Park?
SOLUTION
A l w
Write formula for area of a rectangle.
l w
2.5
(0.5)
Substitute 2.5 for l and 0.5 for w.
1.25
Multiply.
ANSWER
The area of Central Park is about 1.25 square
miles.
15
Showdown

• .31 x .7
• .217
• .9 x .03
• .027

• 2 x .006
• .012
• .66 x 2.52
• 1.6632