3-4 multiplying decimals learn to multiply decimals by whole numbers and by decimals
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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?
Multiply 4 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon.
17 4
68
Multiply as you would with whole numbers.
4 0.17
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?
0.17 40.68
Place the decimal point by adding the number of decimal places in the numbers multiplied.
A 4 lb dumbbell on Earth weighs 0.68 lb on the Moon.
2 decimal places+ 0 decimal places
2 decimal places
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?
Multiply 7 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon.
17 7119
Multiply as you would with whole numbers.
7 0.17
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?
0.17 71.19
Place the decimal point by adding the number of decimal places in the numbers multiplied.
A 7 lb dumbbell on Earth weighs 1.19 lb on the Moon.
2 decimal places+ 0 decimal places
2 decimal places
3-4 Multiplying Decimals
You can use a decimal grid to model multiplication of decimals.
Helpful Hint
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
0.4
1 decimal place
+ 1 decimal place
2 decimal places 0.12
3-4 Multiplying Decimals
Additional Example 2B: Multiplying a Decimal by a Decimal
0.07 0.8
Multiply. Then place the decimal point.
0.07 0.8
2 decimal places + 1 decimal place3 decimal places; use a placeholder zero
0.056
Estimate the product. 0.8 is close to 1.
0.07 1 = 0.07
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
Multiply. Then place the decimal point.
1.34
2.52 decimal places
+ 1 decimal place
3 decimal places
670
Estimate the product. Round each factor to the nearest whole number.
1 3 = 3
3.350 is close to the estimate of 3. The answer is reasonable.
26803.350
3-4 Multiplying Decimals
Check It Out: Example 2A
Find the product.
0.5 0.2
Multiply. Then place the decimal point.
0.5
0.21 decimal place
+ 1 decimal place
2 decimal places 0.10
3-4 Multiplying Decimals
Check It Out: Example 2B
0.03 0.9
Multiply. Then place the decimal point.
0.03
0.92 decimal places
+ 1 decimal place3 decimal places; use a placeholder zero
0.027
Estimate the product. 0.9 is close to 1.
0.03 1 = 0.03
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
Multiply. Then place the decimal point.
3.80
3.32 decimal places
+ 1 decimal places
3 decimal places
1140
Estimate the product. Round each factor to the nearest whole number.
4 3 = 12
12.54 is close to the estimate of 12. The answer is reasonable.
1140012.540
3-4 Multiplying Decimals
Additional Example 3A: Evaluating Decimal Expressions
Evaluate 5x for the value of x.
x = 3.062
3.062
53 decimal places
+ 0 decimal places
3 decimal places15.310
Substitute 3.062 for x. 5x = 5(3.062)
These notations all mean multiply 3 times x.
3 • x 3x 3(x)
Remember!
3-4 Multiplying Decimals
Additional Example 3B: Evaluating Decimal Expressions
Evaluate 5x for the value of x.
x = 4.79
4.79
52 decimal places
+ 0 decimal places
2 decimal places 23.95
Substitute 4.79 for x. 5x = 5(4.79)
3-4 Multiplying Decimals
Check It Out: Example 3A
Evaluate 5x for the value of x.
x = 2.012
2.012
53 decimal places
+ 0 decimal places
3 decimal places 10.060
Substitute 2.012 for x. 5x = 5(2.012)
3-4 Multiplying Decimals
Check It Out: Example 3B
Evaluate 5x for the value of x.
x = 6.22
6.22
52 decimal places
+ 0 decimal places
2 decimal places 31.10
Substitute 6.22 for x. 5x = 5(6.22)