Objective 3.1A
Vocabulary to Review
standard form [1.1B]
place value [1.1B]
New Vocabulary
decimal notation
decimal
whole-number part
decimal point
decimal part
Discuss the Concepts
1. Name the first seven place values to the left of the decimal point. Name the first five place values to the
right of the decimal point.
2. What is the purpose of a decimal point in a number?
3. Name three situations in which decimals are used.
Concept Check
1. Why is the fraction
13
100
equivalent to the decimal 0.13?
2. When writing a number in standard form, when is it necessary to use the digit 0?
Objective 3.1B
Vocabulary to Review
rounding [1.1D]
Discuss the Concepts
Explain how to round a decimal to the nearest hundredth.
Optional Student Activity
Bring some newspapers to class. Arrange the students in small groups. Have students find and list
situations in which decimals are used. Also ask them to determine whether the decimals they find are exact
or approximations. For example, large numbers (such as 3.2 billion) used for describing the balance of
trade or the national debt, are approximations, whereas numbers used to describe business transactions,
such as the exchange rate or stock dividends, are exact.
Objective 3.2A
Vocabulary to Review
addend [1.2A]
sum [1.2A]
Discuss the Concepts
When we add decimals using a vertical format, why must the decimal points be aligned?
Concept Check
Place plus signs between three of the numbers below so that the sum is 19.24.
0.12
3.45
6.78
9.01
2.34
3.45 + 6.78 + 9.01 = 19.24
Optional Student Activity
The sum of six different positive numbers is 11. Four of the six numbers are 4, 3, 2, and 1. Find the other
two numbers.
This problem has a number of possible solutions. For example, the answer could be 0.2 and 0.8, 0.7 and
0.3, or 0.6 and 0.4.
Objective 3.3A
Vocabulary to Review
minuend [1.3A]
subtrahend [1.3A]
difference [1.3A]
Discuss the Concepts
Explain how to subtract 2.6357 from 4.79. Why is 4.79 rewritten as 4.7900 before the subtraction is
performed?
Optional Student Activity
Find the pattern in each of the following lists of numbers. Then name the next three numbers in the list.
1. -0.379, 0.329, 0.279, 0.229, . . . 0.179, 0.129, 0.079
2. -1.684, 1.574, 1.464, 1.354, . . . 1.244, 1.134, 1.024
3. -9.5, 8.75, 8, 7.25, . . . 6.5, 5.75, 5
Objective 3.3B
Optional Student Activity
As of this writing, the biggest hole ever in the ozone layer was 4.63 million square miles, recorded in 1998.
In 1999, the hole was 3.86 million square miles. (Source: World Meteorological Organization) What is the
difference between these two measurements? 0.77 million square miles
Note: According to the World Meteorological Organization, we are working toward recovery of the ozone
level. Ask students to find current data and then determine the difference between the 1998 measurement
and the current one.
Objective 3.4A
Vocabulary to Review
product [1.4A]
power of 10 [1.6A]
Discuss the Concepts
1. Explain how to place the decimal point in a product when multiplying decimals.
2. How do you determine how many places to move the decimal point in a number being multiplied by a
power of 10 that is written in exponential notation?
Concept Check
Light travels at a speed of 1.86 * 105 miles per second. Write the speed of light, expressing the number in
standard form. 186,000 miles per second
Optional Student Activity
Provide an example of multiplying tenths by hundredths using fractions. Rewrite the example using
decimals in place of the fractions. Show that the results are the same.
Optional Student Activity
Each ◊ in the problem below represents one of the digits 2, 3, 4, 5, 6, 7, 8, and 9. The digits 0 and 1 are
provided for you. Fill in the remaining digits.
.
 .
.927 * .63 = .58401
.01
Objective 3.4B
Optional Student Activity
Light from the star Alpha Centauri takes 4.3 years to reach Earth. Light travels 1.86 3 105 miles per second.
(See the Concept Check for Objective 3.4A.) How far is Alpha Centauri from Earth? Round to the nearest
trillion.
25,000,000,000,000 miles
Answers to Writing Exercises
135. When a number is multiplied by 10, 100, 1000, 10,000, etc., the decimal point is moved as many
places to the right as there are zeros in the multiple of 10. For example, the decimal point in a number
multiplied by 1000 would be moved three places to the right.
136. Add the number of decimal places in each of the numbers being multiplied. The number of decimal
places in the product is equal to this sum.
Objective 3.5A
Vocabulary to Review
divisor [1.5A]
dividend [1.5A]
quotient [1.5A]
power of 10 [1.6A]
Discuss the Concepts
Explain how to divide a number by a power of 10.
Concept Check
Which of the following examples have the same quotient?
a.
15 180
b.
1.5 1.8
c.
1.5 18
d.
0.15 18
e.
0.15 1.8
a, c, and e have the same quotient.
Concept Check
Simplify:
2, 400, 000  0.0000063
0.00009  480
350
Optional Student Activity
Light travels at a speed of 1.86 * 105 miles per second. (See the Concept Check for Objective 3.4A.) How
long would it take light to travel 1.86 million miles? 10 seconds
Objective 3.5B
Optional Student Activity
You use a telephone credit card that charges $.08 for the first minute and $.14 for each additional minute
and then adds a $.50 service charge for using the credit card. If the bill is $6.60, how long did you talk?
44 minutes
Answers to Writing Exercises
115. When a number is divided by 10, 100, 1000, 10,000, etc., the decimal point is moved as many places
to the left as there are zeros in the power of 10. For example, the decimal point in a number divided
by 1000 would be moved three places to the left.
116. To calculate a batting average, divide the number of hits by the number of times at bat. Round to the
nearest thousandth. Nomar Garciaparra’s batting average = 190 ÷ 532 ≈ 0.357
117. To determine where a decimal point is placed in a quotient, first move the decimal point in the divisor
to make it a whole number. Then move the decimal point in the dividend the same number of places
to the right. The decimal point in the quotient lines up vertically with the decimal point in the dividend.
Objective 3.6A
Vocabulary to Review
numerator [2.2A]
denominator [2.2A]
Discuss the Concepts
1. Explain how to write a proper fraction as a decimal.
2. Explain how to write a mixed number as a decimal.
Concept Check
49
Round
to the nearest tenth.
50
Explain why it is incorrect to write the answer as 1.
1.0 indicates that the decimal has been rounded to the nearest tenth; 1 does not.
Optional Student Activity
Stock prices used to be written as mixed numbers rather than as decimals. The table below shows the
stock prices on August 28, 2003, of four companies on the New York Stock Exchange. Convert each price
to a decimal. Discuss the advantage or disadvantage of switching from using fractions to using decimals.
Company
Choice Hotels
Fairmont Hotels
Four Seasons
Trump Hotels
Stock Price
32 3/10
26 7/20
47 ¾
1 4/5
$32.30, $26.35, $47.75, $1.80
Objective 3.6B
Vocabulary to Review
place value [1.1B]
Discuss the Concepts
Explain how to write a decimal as a fraction.
Objective 3.6C
Discuss the Concepts
Given both a fraction and a decimal, how can you determine which is the larger number?
Concept Check
Which of the following is true?
a.
b.
c.
137
 0.456666667 False
300
137
,0.45666666 False
300
137
.0.45666666 True
300
Optional Student Activity
1 2 3
4
Convert
,
,
and
to decimals. Describe the pattern.
9 9 9
9
5 7
8
Use the pattern to convert
,
and
to decimals.
9 9
9
1
2
 0.111...,  0.222...,
9
9
3
 0.333...,
9
and
4
 0.444....
9
The pattern is a decimal with a repeating digit that is the same as the numerator of the original
fraction.
5
7
 0.555...,  0.777...,
9
9
and
8
 0.888...
9
Answers to Writing Exercises
75. A terminating decimal ends, or stops. For example, 3.25 and 9.762104 are terminating decimals. A
repeating decimal never ends. One or more digits to the right of the decimal point repeat without end.
The decimals in the Optional Student Activity for Objective 3.6C are examples of repeating decimals:
0.111 . . . , 0.222 . . . , 0.333 . . . , 0.444 . . . , etc.
A nonrepeating decimal never ends, nor does it have any digits to the right of the decimal point that
repeat. For example, 1.20200200020000200000 . . . is a nonrepeating decimal.
Answers to Focus on Problem Solving—Relevant Information
1
a. The amount of change is asked for.
b. No. We need to know the cost of the strawberries.
c. No.
2
a. The length of the original board is asked for.
b. No. We need to know the length of the other piece.
c. No.
3
a. The number of miles driven per day is asked for.
b. No. We are given only the total number of miles driven. We need the number of days the car is
rented.
c. Yes. Only the total number of miles driven can be used to answer the question.
4
a. We are asked for the number of lots available for sale.
b. Yes.
c. Yes. We do not need the price of the land.
5
a. We are asked for the checking account balance.
b. No. We don’t know the balance before writing the checks and making the deposit.
c. No.
Answers to Projects and Group Activities—Fractions as Terminating or
Repeating Decimals
1
a. Terminating
b. Terminating
c. Repeating
d. Repeating
e. Terminating
f. Repeating
g. Repeating
h. Terminating
i. Repeating
j. Repeating
k. Repeating
l. Terminating
m. Repeating
n. -Terminating
2. Answers will vary.