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Section 3.4
Dividing Decimals
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Divide a Decimal by a Whole Number
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Example
Divide.
a.
b. 124.18 ÷ 4
c. 0.24 ÷ 3
6 14.28
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Solution Strategy
a. 6 14.28−12
22−18
48−48
0
2.384 124.18
−124
−418
−1620
−200
31.045b. 3 0.24
−240
.08c.
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Divide a Decimal by a Power of 10
Dividing a Decimal by a Power of 10 such as 10, 100, 1000 . . .
Move the decimal point in the dividend to the left the same number of places as there are zeros in the power of 10. Insert zeros, as necessary.
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Divide a Decimal by a Power of 10
Dividing a Decimal by a Power of 10 such as 0.1, 0.01, 0.001 . . .
Move the decimal point in the dividend to the right the same number of places as there are place values in the decimal power of 10. Insert zeros as necessary.
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Example
d. 13,000 ÷ 0.001
Divide.
b. 58.73 ÷ 1000
c.
100 15.306a.
3.724
0.01
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Solution Strategy
= 0.15306
= 0.05873
= 372.4
= 13,000,000d. 13,000 ÷ 0.001
Divide.
b. 58.73 ÷ 1000
100 15.306
3.724
0.01c.
a.
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Divide a Decimal or a Whole Number by a Decimal
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Example
Divide.
b.
c.
0.59 32.686a.
1.4 17.675
6.4 34.24 Round to the nearest tenth.
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Solution StrategyDivide.
a.
b. 14 176.750−14
36−28
87−84
35−28
70−70
0
12.625
59 3268.6−295
318−295
236−236
0
55.45.4c.
64 342.40−320
224−192
320−320
0
5.35
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Estimate When Dividing Decimals
Steps for Estimating Dividing Decimals
Step 1. Round each number to the specified place.
Step 2. Divide the rounded dividend by the rounded divisor.
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Example
Divide 86.7 ÷ 8.5
Then estimate the quotient by rounding the dividend and divisor to one nonzero digit.
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Solution Strategy
Then estimate the quotient by rounding the dividend and divisor to one nonzero digit.
85 867.0−85
170−170
0
10.2
10 100−100
0
10
Divide 86.7 ÷ 8.5
86.7 ÷ 8.5
100 ÷ 10
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Example Apply your knowledge
You are a clerk at The Time and Again boutique. This morning you made sales of $213.37, $143.77, and $89.62. What is the average of your morning sales?