1. Multiplying and Dividing Decimals

3. Example 1: Multiplying Decimals
0 decimal places 2 
2 decimal places
1.02
0 + 2 = 2 decimal places.
B. (0.4)(3.75)
3.75
2 decimal places
 0.4
1 decimal place
1.500
2 + 1 = 3 decimal places
or 1.5

4. Check It Out!
Multiply.
A. 3.1(0.28)
3.1
1 decimal place 
2 decimal places
0.868
1 + 2 = 3 decimal places
B. (0.4)(2.53)
0.4
1 decimal place
X 2.53
2 decimal places
1.012
1 + 2 = 3 decimal places

5. You will travel about 10.75 miles.
Word Problem
Multiplying Decimals
RAFTING
You travel downstream in a raft at a rate of 4.3 miles per hour. How far will you travel in 2.5 hours?
To find how far you travel in the rafting problem above, substitute the given values into the distance formula: distance rate time. = • d rt = =
2.5 •
4.3
1 decimal place
215  + =
10.75
860
2 decimal places
ANSWER
You will travel about miles.

6. WP Cont…
Multiplying Decimals
CHECK A number’s leading digit is its leftmost nonzero digit. To check for reasonableness, round each factor to its leading digit and multiply.
2.5 •
4.3 3 4 12 =

7. More Practice 
Find the product. Check that the answer is reasonable.
2.1 •
7.39 1.
ANSWER
15.519
5.07 •
19.62 2.
ANSWER
0.04 •
1.13 3.
ANSWER
0.0452 8 •
0.85 4.
ANSWER
6.8

9. When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places represents the number of zeros after the 1 in the power of 10.
1.32
0.4
1.32
0.4 10
13.2 4 = =
1 decimal place
1 zero

10. To find some quotients, you may need to use zeros as placeholders.
Strategy
Using Zeros as Placeholders
To find some quotients, you may need to use zeros as placeholders.
Placeholder in Dividend
Placeholder in Quotient 6 ÷
1.2
0.0126 ÷
1.8
6.0
1.2
0.0126
1.8
126
0.007
0.126 18 60 5 12

11. Example 2: Dividing Decimals
Find ÷ Estimate the reasonableness of your answer.
0.24 )0.384
0.24 has two decimal places so multiple both numbers by 100 to make the divisor an integer. 1 .6
24 )38.4
Then divide as a whole number.
- 24
0.384 ÷ 0.24 = 1.6
Estimate: 40 ÷ 20 = 2 14 4
– 144
The answer is reasonable.

12. Find 0.65 ÷ 0.25. Estimate the reasonableness of your answer.
Check It Out!
Find 0.65 ÷ Estimate the reasonableness of your answer.
0.25 )0.65
0.25 has two decimal places so multiple both numbers by 100 to make the divisor an integer. 2 .6
25 )65.0
Then divide as a whole number.
- 50 15
– n 0
The answer is reasonable.
0.65 ÷ 0.25 = 2.6
Estimate: 60 ÷ 20 = 3

13. Example 3: Evaluating Expressions with Rational Numbers
Evaluate the expression for the given value of the variable.
5.25
for n = 0.15 n
5.25 n
0.15 =
Substitute 0.15 for n.
0.15 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.
0.15 )5.25 35
15 )525
When n = 0.15, = 35.
5.25 n
- 525

14. 3.60 for n = 0.12 n 3.60 = Substitute 0.12 for n. n 0.12
Check It Out!
Evaluate the expression for the given value of the variable.
3.60
for n = 0.12 n
3.60 n
0.12 =
Substitute 0.12 for n.
0.12 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.
0.12 )3.60 30
12 )360
When n = 0.12, = 30.
3.60 n
- 360

15. More Practice 
Find the quotient. Check that the answer is reasonable. 5.
0.04 ÷
1.6
ANSWER 40 6.
0.79 ÷
0.632
ANSWER
0.8 7.
0.65 ÷ 13
ANSWER 20 8.
4.5 ÷
4.365
ANSWER
0.97 9.
0.3744 ÷
1.56
ANSWER
0.24
10.
2.7 ÷
0.0108
ANSWER
0.004

16. Lesson Quiz
Find the product or quotient. Check that the answer is reasonable.
1.5 –  ) (
2.3 1.
ANSWER
3.45 2.
9.6 – 
0.64
ANSWER
6.144 –
5.35 – ) (
2.5 3. ÷
ANSWER
2.14 ÷ –
3.9
5.2 4. b.
2.1
ANSWER
0.75 –