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3-4 Multiplying Decimals
Learn to multiply decimals by whole
numbers and by decimals.
3-4 Multiplying Decimals
Additional Example 1: Science Application
Something that weighs 1 lb on Earth weighs
0.17 lb on the Moon. How much would a 4 lb
dumbbell weigh on the Moon?
4  0.17
17
 4
68
Multiply 4 by 0.17, since 1 pound on
Earth is 0.17 pound on the Moon.
Multiply as you would with whole
numbers.
3-4 Multiplying Decimals
Additional Example 1 Continued
Something that weighs 1 lb on Earth weighs
0.17 lb on the Moon. How much would a 4 lb
dumbbell weigh on the Moon?
Place the decimal point by adding the
number of decimal places in the
numbers multiplied.
0.17
 4
0.68
2 decimal places
+ 0 decimal places
2 decimal places
A 4 lb dumbbell on Earth weighs 0.68 lb on the Moon.
3-4 Multiplying Decimals
Check It Out: Example 1
Something that weighs 1 lb on Earth weighs
0.17 lb on the Moon. How much would a 7 lb
dumbbell weigh on the Moon?
7  0.17
17
 7
119
Multiply 7 by 0.17, since 1 pound on
Earth is 0.17 pound on the Moon.
Multiply as you would with whole
numbers.
3-4 Multiplying Decimals
Check It Out: Example 1 Continued
Something that weighs 1 lb on Earth weighs
0.17 lb on the Moon. How much would a 7 lb
dumbbell weigh on the Moon?
Place the decimal point by adding the
number of decimal places in the
numbers multiplied.
0.17
 7
1.19
2 decimal places
+ 0 decimal places
2 decimal places
A 7 lb dumbbell on Earth weighs 1.19 lb on the Moon.
3-4 Multiplying Decimals
Helpful Hint
You can use a decimal grid to model multiplication
of decimals.
3-4 Multiplying Decimals
Additional Example 2A: Multiplying a Decimal by
a Decimal
Find the product.
0.3  0.4
Multiply. Then place the decimal point.
0.3
1 decimal place
 0.4
+ 1 decimal place
0.12
2 decimal places
3-4 Multiplying Decimals
Additional Example 2B: Multiplying a Decimal by
a Decimal
0.07  0.8
0.07  1 = 0.07 Estimate the product. 0.8 is
close to 1.
0.07
 0.8
0.056
Multiply. Then place the
decimal point.
2 decimal places
+ 1 decimal place
3 decimal places; use a
placeholder zero
0.056 is close to the estimate of 0.07. The
answer is reasonable.
3-4 Multiplying Decimals
Additional Example 2C: Multiplying a Decimal by
a Decimal
1.34  2.5
13=3
1.34
 2.5
670
2680
3.350
Estimate the product. Round
each factor to the nearest
whole number.
Multiply. Then place the
decimal point.
2 decimal places
+ 1 decimal place
3 decimal places
3.350 is close to the estimate of 3. The answer
is reasonable.
3-4 Multiplying Decimals
Check It Out: Example 2A
Find the product.
0.5  0.2
Multiply. Then place the decimal point.
0.5
1 decimal place
 0.2
+ 1 decimal place
0.10
2 decimal places
3-4 Multiplying Decimals
Check It Out: Example 2B
0.03  0.9
0.03  1 = 0.03 Estimate the product. 0.9 is
close to 1.
0.03

0.9
0.027
Multiply. Then place the
decimal point.
2 decimal places
+ 1 decimal place
3 decimal places; use a
placeholder zero
0.027 is close to the estimate of 0.03. The
answer is reasonable.
3-4 Multiplying Decimals
Check It Out: Example 2C
3.80  3.3
4  3 = 12
3.80
 3.3
1140
11400
12.540
Estimate the product. Round
each factor to the nearest
whole number.
Multiply. Then place the
decimal point.
2 decimal places
+ 1 decimal places
3 decimal places
12.54 is close to the estimate of 12. The answer
is reasonable.
3-4 Multiplying Decimals
Additional Example 3A: Evaluating Decimal
Expressions
Evaluate 5x for the value of x.
x = 3.062
5x = 5(3.062)
Substitute 3.062 for x.
3.062
3 decimal places
5
+ 0 decimal places
15.310
3 decimal places

Remember!
These notations all mean multiply 3 times x.
3•x
3x
3(x)
3-4 Multiplying Decimals
Additional Example 3B: Evaluating Decimal
Expressions
Evaluate 5x for the value of x.
x = 4.79
5x = 5(4.79)

Substitute 4.79 for x.
4.79
2 decimal places
5
+ 0 decimal places
23.95
2 decimal places
3-4 Multiplying Decimals
Check It Out: Example 3A
Evaluate 5x for the value of x.
x = 2.012
5x = 5(2.012)
Substitute 2.012 for x.
2.012
3 decimal places
5
+ 0 decimal places
10.060
3 decimal places

3-4 Multiplying Decimals
Check It Out: Example 3B
Evaluate 5x for the value of x.
x = 6.22
5x = 5(6.22)
Substitute 6.22 for x.
6.22
2 decimal places
5
+ 0 decimal places
31.10
2 decimal places
