Decimals

CHAPTER
3
Decimals

NASCAR
The National Association for Stock Car Auto Racing
(NASCAR) claims as many as 75 million fans responsible for
over $2.5 billion in licensed product sales annually. The
NASCAR season begins in February in Daytona, and runs
through late November before finishing at the Homestead-
Miami Speedway. The Daytona 500 is regarded by many as the
most important and prestigious race on the NASCAR calendar,
carrying by far the largest purse, with the winner receiving
over $1.5 million. The event serves as the final event of Speedweeks
and is sometimes referred to as “The Great American
Race” or the “Super Bowl of Stock Car Racing.” It is also the
series’ first race of the year; this phenomenon is virtually
unique in sports, which tend to have championships or other
major events at the end of the season rather than the start. The
Daytona 500 is 500 miles (804.7 km) long and is run on a 2.5mile
tri-oval track. How many laps would that be?
The 2009 champion, Matt Kenseth, posted an average
speed of 132.816 miles per hour on his way to claiming the
first prize of nearly $1.54 million. Since 1995, U.S. television
ratings for the Daytona 500 have been the highest for any auto
race of the year, surpassing the traditional leader, the Indianapolis
500, which in turn greatly surpasses the Daytona 500
LEARNING OUTCOMES
3-1 Decimals and the Place-Value System
1. Read and write decimals.
2. Round decimals.
3-2 Operations with Decimals
1. Add and subtract decimals.
2. Multiply decimals.
3. Divide decimals.
in in-track attendance and international viewing. According to
Nielsen Media Research, the 2009 Daytona 500 had a 9.2 rating,
which translated to 10.516 million households and 15.954
million viewers. With a total U.S. population of over 308
million—that means 0.052 or at least 1 out of 20 people
watched the Daytona 500—a lot of committed NASCAR fans!
The final race of the NASCAR season is the Ford 400 at
the 1.5 mile oval Homestead-Miami Speedway. How many
laps would that be? A shorter track like this often leads to
more action during the race. From 2001 to 2008, a typical
Homestead race had 17.8 lead changes, 8.6 cautions for 45.5
laps, and an average green-flag run of 23.1 laps. But while
Denny Hamlin may have won the 2009 season-ending Ford
400 at Homestead-Miami Speedway, Jimmie Johnson claimed
the larger prize, winning his fourth consecutive NASCAR
Sprint Cup Championship—the only four-peat in the modern
era. In fact, during the 2009 season, Johnson held a lead in a
race for 2,839.97 miles, nearly twice that of his nearest competitor.
For the year, he totaled nearly $7.34 million in winnings.
Congratulations, Jimmie, and here’s to another great
NASCAR season!
3-3 Decimal and Fraction Conversions
1. Convert a decimal to a fraction.
2. Convert a fraction to a decimal.

3-1 DECIMALS AND THE PLACE-VALUE SYSTEM
Decimal system: a place-value number system
based on 10.
DID YOU
KNOW?
Some countries, such as France,
Mexico, and South Africa, use a
comma instead of a dot to separate
the whole-number part of a number
from the decimal part. They use a
space to separate groups of three,
called the periods, in the wholenumber
part.
15,396.7 is written as 15 396,7
82 CHAPTER 3
Hundred millions
(100,000,000)
Millions Thousands Units
T en millions
(10,000,000)
Millions
(1,000,000)
Hundred thousands
(100,000)
FIGURE 3-2
Place-Value Chart for Decimals
Decimal point: the notation that separates the
whole-number part of a number from the
decimal part.
Whole-number part: the digits to the left of the
decimal point.
Decimal part: the digits to the right of the
decimal point.
T en thousands
(10,000)
LEARNING OUTCOMES
1 Read and write decimals.
2 Round decimals.
Decimals are another way to write fractions. We use decimals in some form or another every
day—even our money system is based on decimals. Calculators use decimals, and decimals are
the basis of percentages, interest, markups, and markdowns.
1 Read and write decimals.
Our money system, which is based on the dollar, uses the decimal system. In the decimal system,
as you move right to left from one digit to the next, the place value of the digit increases by
10 times (multiply by 10). As you move left to right from one digit to the next, the place value of
the digit gets 10 times smaller (divide by 10). The place value of the digit to the right of the ones
place is 1 divided by 10.
There are several ways of indicating 1 divided by 10. In the decimal system, we write 1
divided by 10 as 0.1.
FIGURE 3-1
1 whole divided into 10 parts.
The shaded part is 0.1.
How much is 0.1? How much is 1 divided by 10? It is one part of a 10-part whole (Figure 3-1). We
read 0.1 as one-tenth. Using decimal notation, we can extend our place-value chart to the right of
the ones place and express quantities that are not whole numbers. When extending to the right of the
ones place, a period called a decimal point separates the whole-number part from the decimal
part.
The names of the places to the right of the decimal are tenths, hundredths, thousandths, and
so on. These place names are similar to the place names for whole numbers, but they all end in
ths. In Figure 3-2, we show the place names for the digits in the number 2,315.627432.
Thousands
(1,000)
Hundreds
(100)
HOW TO
T ens
(10)
Ones
(1)
2 3 1 5
Decimal point
T enths
0.1
Read or write a decimal
Hundredths
0.01
Thousandths
0.001
T en-thousandths
0.0001
Hundred-thousandths
0.00001
Millionths
0.000001
. 6 2 7 4 3 2
T en-millionths
0.0000001
Hundred-millionths
0.00000001
Read 3.12.
1. Read or write the whole-number part (to the left of the decimal point) Three
as you would read or write a whole number.
2. Use the word and for the decimal point. and
3. Read or write the decimal part (to the right of the decimal point) twelve
as you would read or write a whole number.
4. Read or write the place name of the rightmost digit. hundredths

EXAMPLE 1 Write the word name for these decimals: (a) 3.6, (b) 0.209,
(c) $234.93.
(a) three and six-tenths 3 is the whole-number part; 6 is the decimal part.
(b) two hundred nine thousandths The whole-number part, 0, is not written.
(c) two hundred thirty-four dollars and The whole-number part is dollars. The decimal
ninety-three cents part is cents.
TIP
Informal Use of the Word Point
Informally, the decimal point is sometimes read as point. Thus, 3.6 is read three point six. The
decimal 0.209 can be read as zero point two zero nine. This informal process is often used in
communication to ensure that numbers are not miscommunicated. However, without hearing
the place value, it is more difficult to get a sense of the size of the number.
TIP
Reading Decimals as Money Amounts
When reading decimal numbers that represent money amounts:
Read whole numbers as dollars.
Decimal amounts are read as cents. In the number $234.93, the decimal part is read ninetythree
cents rather than ninety-three hundredths of a dollar. Because 1 cent is one hundredth
of a dollar, the words cent and hundredth have the same meaning.
STOP
AND CHECK
1. Write 5.8 in words. 2. Write 0.721 in words.
3. Recent statistics show that France had 789.48 cellular
phones for each 1,000 people. Express the number of
phones in words.
5. Write three thousand five hundred forty-eight
ten-thousandths as a number.
2 Round decimals.
As with whole numbers, we often need only an approximate amount. The process for rounding
decimals is similar to rounding whole numbers.
HOW TO
4. Recent statistics show that Italy had 1,341.466 cellular
phones for each 1,000 people. Express the number of
phones in words.
6. Write four dollars and eighty-seven cents as a number.
Round to a specified decimal place
Round to hundredths:
17.3754
1. Find the digit in the specified place. 17.3754
2. Look at the next digit to the right. 17.3754
(a) If this digit is less than 5, eliminate it and all
digits to its right.
(b) If this digit is 5 or more, add 1 to the digit in the 17.38
specified place, and eliminate all digits to its right.
DECIMALS
83

When Do I Round?
In making a series of calculations,
only round the result of
the final calculation.
When making estimates, round
the numbers of the problem
before calculations are made.
TIP
STOP AND CHECK
1. Round 14.342 to the nearest tenth. 2. Round 48.7965 to the nearest hundredth.
3. Round $768.57 to the nearest dollar.
3-1 SECTION EXERCISES
SKILL BUILDERS
Write the word name for the decimal.
84 CHAPTER 3
4. Round $54.834 to the nearest cent.
1. 0.582 2. 0.21 3. 1.0009 4. 2.83 5. 782.07
Write the number that represents the decimal.
6. Thirty-five hundredths 7. Three hundred twelve
thousandths
Round to the nearest dollar.
8. Sixty and twenty-eight
thousandths
10. $493.91 11. $785.03 12. $19.80
Round to the nearest cent.
Round to the nearest tenth.
EXAMPLE 2 Round the number to the specified place: (a) $193.48 to the nearest
dollar, (b) $28.465 to the nearest cent.
(a) $193.48 Rounding to the nearest dollar means rounding to the ones place. The
digit in the ones place is 3.
$193.48 The digit to the right of 3 is 4. Because 4 is less than 5, step 2a applies;
eliminate 4 and all digits to its right.
$193
$193.48 rounded to the nearest dollar is $193.
(b) $28.465 Rounding to the nearest cent means rounding to the nearest hundredth.
The digit in the hundredths place is 6.
$28.465 The digit to the right of 6 is 5. Because 5 is 5 or more, step 2b applies.
$28.47
$28.465 rounded to the nearest cent is $28.47.
13. $0.5239 14. $21.09734 15. $32,048.87219
16. 42.3784 17. 17.03752 18. 4.293
9. Five and three hundredths

APPLICATIONS
19. Tel-Sales, Inc., a prepaid phone card company in Oklahoma
City, sells phone cards for $19.89. Write the card cost in
words.
21. GameStop ® reported a quarterly gross margin of 839.18
dollars in millions of dollars. Write the reported gross
margin in millions of dollars in words.
3-2 OPERATIONS WITH DECIMALS
LEARNING OUTCOMES
1 Add and subtract decimals.
2 Multiply decimals.
3 Divide decimals.
1 Add and subtract decimals.
20. Destiny Telecom of Oakland, California, introduced a Braille
prepaid phone card that costs fourteen dollars and seventy
cents. Write the digits to show Destiny’s sales figure.
22. Gannett Company reported a quarterly income before tax of
negative five thousand, three hundred eighty seven and
twenty-four hundredths dollars in millions of dollars. Write
the reported gross margin in millions of dollars in words.
Some math skills are used more often than others. Adding and subtracting decimal numbers are
regularly used in transactions involving money. To increase your awareness of the use of decimals,
refer to your paycheck stub, grocery store receipt, fast-food ticket, odometer on your car,
bills you receive each month, and checking account statement balance.
HOW TO
Add or subtract decimals
1. Write the numbers in a vertical column, aligning digits
according to their place values.
2. Attach extra zeros to the right end of each decimal
number so that each number has the same quantity of
digits to the right of the decimal point. It is also acceptable
to assume blank places to be zero.
3. Add or subtract as though the numbers are whole numbers.
4. Place the decimal point in the sum or difference to align with
the decimal point in the addends or subtrahend and minuend.
TIP
Add 32 + 2.55 + 8.85 + 0.625.
32
2.55
8.85
0.625
44.025
Unwritten Decimals
When we write whole numbers using numerals, we usually omit the decimal point; the decimal
point is understood to be at the end of the whole number. Therefore, any whole number, such as
32, can be written without a decimal (32) or with a decimal (32.).
TIP
Aligning Decimals in Addition or Subtraction
A common mistake in adding decimals is to misalign the digits or decimal points.
32
2.55
8.85
0.625
44.025
CORRECT
All digits and decimal
points are aligned
correctly.
32
2.55
8.85
0.625
1.797
INCORRECT
;
;
not aligned correctly
not aligned correctly
DECIMALS
85

Decimals and the Calculator
When a number containing a
decimal is entered into a calculator,
use the decimal key • . 53.8
would be entered as 53 • 8.
TIP
STOP AND CHECK
86 CHAPTER 3
EXAMPLE 1 Subtract 26.3 - 15.84.
2 6 5
.3
12
0
10
- 1 5.8 4
1 0.4 6
2 Multiply decimals.
Write the numbers so that the digits align according to their place values.
Subtract the numbers, regrouping as you would in whole-number subtraction.
The difference of 26.3 and 15.84 is 10.46.
1. Add: 67 + 4.38 + 0.291 2. Add: 57.5 + 13.4 + 5.238
3. Subtract: 17.53 - 12.17
5. Garza Humada purchased a shirt for $18.97 and paid with a
$20 bill. What was his change?
4. Subtract: 542.83 - 219.593
6. The stock of FedEx Corporation had a high for the day of
$120.01 and a low of $95.79, closing at $117.58. By how
much did the stock price change during the day?
Suppose you want to calculate the amount of tip to add to a restaurant bill. A typical tip in the
United States is 20 cents per dollar, which is 0.20 or 0.2 per dollar. To calculate the tip on a bill
of $28.73 we multiply 28.73 * 0.2.
We multiply decimals as though they are whole numbers. Then we place the decimal point
according to the quantity of digits in the decimal parts of the factors.
HOW TO
Multiply decimals
1. Multiply the decimal numbers as though they are whole
numbers.
2. Count the digits in the decimal parts of both decimal
numbers.
3. Place the decimal point in the product so that there are
as many digits in its decimal part as there are digits you
counted in step 2. If necessary, attach zeros on the left
end of the product so that you can place the decimal
point accurately.
EXAMPLE 2 Multiply
2.35
* 0.015
1175
235
0.03525
two decimal places
three decimal places
five decimal places.
The product of 2.35 and 0.015 is 0.03525.
2.35 * 0.015.
Multiply 3.5 * 0.3
3.5 one place
* 0.3 one place
1.0 5 two places
One 0 is attached on the left to accurately place the
decimal point.

STOP AND CHECK
Multiply.
1. 4.35 * 0.27
3. 5.32 * 15
TIP
Zero to the Left of the Decimal Point
The zero to the left of the decimal point in the preceding example is not necessary, but it helps
to make the decimal point visible.
0.03525 has the same value as .03525.
HOW TO
Multiply by place-value numbers such as 10, 100, and 1,000
1. Determine the number of zeros in the multiplier.
2. Move the decimal in the multiplicand to the right the same number of places as there are
zeros in the multiplier. Insert zeros as necessary.
EXAMPLE 3 Multiply 36.56 by (a) 10, (b) 100, and (c) 1,000.
(a) 36.56(10) = 365.6
Move the decimal one place to the right.
(b) 36.56(100) = 3,656 Move the decimal two places to the right.
(c) 36.56(1,000) = 36,560 Move the decimal three places to the right. Insert a zero to
have enough places.
EXAMPLE 4 Find the amount of tip you would pay on a restaurant bill of
$28.73 if you tip 20 cents on the dollar (0.20, or 0.2) for the bill.
What You Know What You Are Looking For Solution Plan
Restaurant bill: $28.73
Rate of tip: 0.2 (20 cents on
the dollar) of the bill
Solution
28.73 * .2 = Q 5.746
Conclusion
5. A dinner for 500 guests costs $27.42 per person. What is
the total cost of the dinner?
Amount of tip Amount of tip = restaurant
bill * rate of tip
Amount of tip = 28.73 * 0.2
Round to the nearest cent.
The tip is $5.75 when rounded to the nearest cent.
TIP
Round Money Amount to Cents
When working with money, we often round answers to the nearest cent. In the preceding example
$5.746 is rounded to $5.75.
2. 7.03 * 0.035
4. $8.31 * 4
6. Tromane Mohaned purchased 1,000 shares of IBM stock at
a price of $94.05. How much did the stock cost?
DECIMALS
87

88 CHAPTER 3
3 Divide decimals.
Division of decimals has many uses in the business world. A common use is to determine how
much one item costs if the cost of several items is known. Also, to compare the best buy of similar
products that are packaged differently, we find the cost per common unit. A 12-ounce package
and a 1-pound package of bacon can be compared by finding the cost per ounce of each package.
HOW TO
EXAMPLE 5 Divide 5.95 by 17.
0.35
175.95
5 1
85
85
0
Place a decimal point for the quotient directly above the decimal point in the
dividend.
The quotient of 5.95 and 17 is 0.35.
Divide a decimal by a whole number
1. Place a decimal point for the quotient directly
above the decimal point in the dividend.
2. Divide as though the decimal numbers are whole
numbers.
3. If the division does not come out evenly, attach
zeros as necessary and carry the division one
place past the desired place of the quotient.
4. Round to the desired place.
Divide . 95.2 by 14.
1495.2
6.8
1495.2
84
11 2
11 2
0
EXAMPLE 6 Find the quotient of 37.4 , 24 to the nearest hundredth.
1.558
2437.400
24
13 4
12 0
1 40
1 20
200
192
8
rounds to 1.56 Carry the division to the thousandths place, and then round
to hundredths. Attach two zeros to the right of 4 in the
dividend.
The quotient is 1.56 to the nearest hundredth.
HOW TO
Divide by place-value numbers such as 10, 100, and 1,000
1. Determine the number of zeros in the divisor.
2. Move the decimal in the dividend to the left the same number of places as there are zeros in
the divisor. Insert zeros as necessary.
EXAMPLE 7 Divide 23.71 by (a) 10, (b) 100, and (c) 1,000.
(a) 23.71 , 10 = 2.371
Move the decimal one place to the left.
(b) 23.71 , 100 = 0.2371 Move the decimal two places to the left. It is preferred
to write a zero in front of the decimal point.
(c) 23.71 , 1,000 = 0.02371 Move the decimal three places to the left. Insert a zero to
have enough places.

DID YOU
KNOW?
Moving the decimal in the divisor
and dividend as shown in the HOW
TO box is the same as multiplying
both the divisor and the dividend by
10 or a multiple of 10.
If the divisor is a decimal rather than a whole number, we use an important fact: Multiplying
both the divisor and the dividend by the same factor does not change the quotient.
We can see this by writing a division as a fraction.
10
5
100
50
10 , 5 = 10
5
* 10
10
* 10
10
= 100
50
= 1,000
500
= 2
= 2
= 2
We’ve multiplied both the divisor and the dividend by a factor of 10, and then by a factor of 10
again. The quotient is always 2.
HOW TO
Divide by a decimal
1. Change the divisor to a whole number by moving the
decimal point to the right, counting the places as you go.
Use a caret ( ^ ) to show the new position of the decimal
point.
2. Move the decimal point in the dividend to the right as
many places as you moved the decimal point in the
divisor.
3. Place the decimal point for the quotient directly above
the new decimal point in the dividend.
4. Divide as you would divide by a whole number. Carry
the division one place past the desired place of the quotient.
Round to the desired place.
Divide 3.4776 by 0.72.
0.72 ^ 3.47 76
0.72 ^ 3.47 ^ 76
.
0.72 ^ 3.47 ^ 76
4. 83
0.72 ^ 3.47 ^ 76
2 88
59 7
57 6
2 16
2 16
0
EXAMPLE 8 Find the quotient of 59.9 , 0.39 to the nearest hundredth.
0.3959.90 39
^
5,990
^
.
395,990
^
153.589
395,990.000
3 9
2 09
1 95
140
117
23 0
19 5
3 50
3 12
380
351
29
Move the decimal point two places to the right in
both the divisor and the dividend.
Place the decimal point for the quotient directly
above the new decimal point in the dividend.
L 153.59 (rounded) Divide, carrying out the division to the thousandths
place. Add three zeros to the right of the decimal
point.
The quotient is 153.59 to the nearest hundredth.
DECIMALS
89

A calculator does NOT have a
“divided into” key. The only division
key that a calculator has is a “divided
by” key. To be sure that you enter a
division correctly using a calculator,
read the division problem using the
words divided by. 0.3959.9 is read
59.9 is divided by 0.39.
Unit price or unit cost: price for 1 unit of a
product.
STOP AND CHECK
Divide.
1. 100.80 , 15
90 CHAPTER 3
TIP
Symbol for Approximate Number
When numbers are rounded they become approximate numbers. A symbol that is often used to
show approximate numbers is L.
EXAMPLE 9 Alicia Toliver is comparing the price of bacon to find the better
buy. A 12-oz package costs $2.49 and a 16-oz package costs $2.99. Which package has the
cheaper cost per ounce (often called unit price)?
What You Know What You Are Looking For Solution Plan
Price for 12-oz Cost per ounce for each
package = $2.49 package
Price for 16-oz Which package has the
package = $2.99 cheaper price per ounce?
Solution
Price per ounce = 2.49 , 12 = Q 0.2075 12-oz package
Price per ounce = 2.99 , 16 = Q 0.186875 16-oz package
Rounding to the nearest cent, $0.2075 rounds to $0.21 and $0.186875 rounds to $0.19.
$0.19 is less than $0.21.
Conclusion
The 16-oz package of bacon has the cheaper unit price.
2. 358.26 , 21
Cost of 12-oz package
Price per ounce =
12
Cost of 16-oz package
Price per ounce =
16
Compare the prices per ounce.
3. Round the quotient to tenths: 12.97 , 3.8 4. Round the quotient to hundredths: 103.07 , 5.9
5. Gwen Hilton’s gross weekly pay is $716.32 and her hourly
pay is $19.36. How many hours did she work in the week?
3-2 SECTION EXERCISES
SKILL BUILDERS
Add.
DID YOU
KNOW?
59.9 .39 Q
153.5897436
A single zero before the decimal
point does not have to be entered.
0.39 is entered as .39
Ending zeros on the right of the
decimal do not have to be entered.
0.20 is entered as .2
1. 6.005 + 0.03 + 924 + 3.9 2. 82 + 5,000.1 + 101.703
6. The Denver Post reported that Wal-Mart would sell 42-inch
Hitachi plasma televisions in a 4-day online special for
$1,198 each. If Wal-Mart had paid $648,000,000 for a
million units, how much did each unit cost Wal-Mart?

3. $21.13 + $42.78 + $16.39 4. $203.87 + $1,986.65 + $3,047.38
Subtract.
5. 407.96 - 298.39
6. 500.7 from 8,097.125 7. $468.39 - $223.54
8. $21.65 - $15.96
9. $52,982.97 - $45,712.49
10. $38,517 - $21,837.46
Multiply.
11. 19.7 12. 0.0321 * 10
13. 73.7 * 0.02
14. 43.7 * 1.23
15. 5.03 * 0.073
16. 642 * $12.98
Divide and round to the nearest hundredth if necessary.
17. 123.72 , 12
18. 35589.06
19. 0.350.0084
20. 1,482.97 , 1.7
APPLICATIONS
21. Kathy Mowers purchased items costing $14.97, $28.14,
$19.52, and $23.18. How much do her purchases total?
22. Jim Roznowski submitted a travel claim for meals,
$138.42; hotel, $549.78; and airfare, $381.50. Total his
expenses.
DECIMALS
91

23. Joe Gallegos purchased a calculator for $12.48 and paid
with a $20 bill. How much change did he get?
25. Laura Voight earns $8.43 per hour as a telemarketing
employee. One week she worked 28 hours. What was her
gross pay before any deductions?
27. Calculate the cost of 1,000 gallons of gasoline if it costs
$2.47 per gallon.
29. All the employees in your department are splitting the cost
of a celebratory lunch, catered at a cost of $142.14. If your
department has 23 employees, will each employee be able
to pay an equal share? How should the catering cost be
divided?
3-3 DECIMAL AND FRACTION CONVERSIONS
92 CHAPTER 3
LEARNING OUTCOMES
1 Convert a decimal to a fraction.
2 Convert a fraction to a decimal.
1 Convert a decimal to a fraction.
24. Martisha Jones purchased a jacket for $49.95 and a shirt for
$18.50. She paid with a $100 bill. How much change did
she receive?
26. Cassie James works a 26-hour week at a part-time job
while attending classes at Southwest Tennessee Community
College. Her weekly gross pay is $213.46. What is her
hourly rate of pay?
28. A buyer purchased 2,000 umbrellas for $4.62 each. What is
the total cost?
30. AT&T offers a prepaid phone card for $5. The card
provides 20 minutes of long-distance phone service. Find
the cost per minute.
Decimals represent parts of a whole, just as fractions can. We can write a decimal as a fraction,
or a fraction as a decimal.
HOW TO
Convert a decimal to a fraction
1. Find the denominator: Write 1 followed
by as many zeros as there are places to the
right of the decimal point.
2. Find the numerator: Use the digits without
the decimal point.
3. Reduce to lowest terms and write as a
whole or mixed number if appropriate.
Write 0.8 as a fraction.
Denominator = 10
8
10
4
5

STOP AND CHECK
EXAMPLE 1 Change 0.38 to a fraction.
0.38 = 38
100
38
100
= 19
50
0.38 written as a fraction is 19
50 .
2 Convert a fraction to a decimal.
The digits without the decimal point form the numerator.
There are two places to the right of the decimal point, so the
denominator is 1 followed by two zeros.
Reduce the fraction to lowest terms.
EXAMPLE 2 Change 2.43 to a mixed number.
2.43 = 2 43
100
2.43 is 2 as a mixed number.
43
100
Write as a fraction or mixed number, and write in simplest form.
The whole-number part of the decimal stays as the wholenumber
part of the mixed number.
1. 0.7 2. 0.32 3. 2.087 4. 23.41 5. 0.07
Fractions indicate division. Therefore, to write a fraction as a decimal, perform the division.
Divide the numerator by the denominator, as you would divide decimals.
HOW TO
EXAMPLE 3 1
Change to a decimal number.
0.25
41.00
8
20
20
1
The decimal equivalent of 4 is 0.25.
Write a fraction as a decimal
1. Write the numerator as the dividend and the denominator as the divisor.
2. Divide the numerator by the denominator. Carry the division as many decimal places as
necessary or desirable.
3. For repeating decimals:
(a) Write the remainder as the numerator of a fraction and the divisor as the denominator.
or
(b) Carry the division one place past the desired place and round.
4
Divide the numerator by the denominator, adding zeros to the
right of the decimal point as needed.
DECIMALS
93

Terminating decimal: a quotient that has no
remainder.
Nonterminating or repeating decimal: a
quotient that never comes out evenly. The digits
will eventually start to repeat.
The two versions of answers in Example
4 are called the exact and
approximated decimal equivalents.
3 is the exact decimal equivalent.
An exact decimal equivalent
is not rounded.
0.66 2
DID YOU
KNOW?
0.67 is an approximate decimal
equivalent. An approximate decimal
equivalent is rounded.
2
Other approximate equivalents of 3
are 0.667 and 0.6667.
STOP AND CHECK
94 CHAPTER 3
TIP
Divide by Which Number?
An aid to help remember which number in the fraction is the divisor: Divide by the bottom
number. Both by and bottom start with the letter b.
1
In the preceding example, was converted to a decimal by dividing by 4, the bottom number.
4
When the division comes out even (there is no remainder), we say the division terminates,
and the quotient is called a terminating decimal. If, however, the division never comes out even
(there is always a remainder), we call the number a nonterminating or repeating decimal. If the
quotient is a repeating decimal, either write the remainder as a fraction or round to a specified
place.
EXAMPLE 4 2
Write 3 as a decimal number in hundredths (a) with the remainder
expressed as a fraction and (b) with the decimal rounded to hundredths.
(a) 0.66 3
32.00
1 8
20
18
2
(b)
2
3
EXAMPLE 5 Write 3 as a decimal.
1
1
3
4
3 1
4
2 2
= 0.66 3 or 3 L 0.67.
= 3.25
2
is 3.25 as a decimal number.
Change to decimal numbers. Round to hundredths if necessary.
0.666 L 0.67
32.000
1 8
20
18
20
18
2
4
The whole-number part of the mixed number stays as the wholenumber
part of the decimal number.
3
7
5
4
4
1. 2. 3. 4. 7
5. 8
5
8
12
5
7
3-3 SECTION EXERCISES
SKILL BUILDERS
Write as a fraction or mixed number and write in simplest form.
1. 0.6 2. 0.58 3. 0.625

4. 0.1875 5. 7.3125 6. 28.875
Change to a decimal. Round to hundredths if necessary.
7. 8. 9. 7
7
3
10
8
12
10. 11. 12. 21 11
7
1
2
16
8
12
DECIMALS
95

SUMMARY CHAPTER 3
Learning Outcomes
Section 3-1
1 Read and write decimals. (p. 82)
2 Round
decimals. (p. 83)
Section 3-2
1 Add and subtract decimals. (p. 85)
2 Multiply
decimals. (p. 86)
96 CHAPTER 3
What to Remember with Examples
Read or write a decimal.
1. Read or write the whole number part (to the left of the decimal point) as you would read or
write a whole number.
2. Use the word and for the decimal point.
3. Read or write the decimal part (to the right of the decimal point) as you would read or write
a whole number.
4. Read or write the place of the rightmost digit.
Write the decimal in words.
0.3869 is read three thousand, eight-hundred sixty-nine ten-thousandths.
Round to a specified decimal place.
1. Find the digit in the specified place.
2. Look at the next digit to the right.
(a) If this digit is less than 5, eliminate it and all digits to its right.
(b) If this digit is 5 or more, add 1 to the digit in the specified place, and eliminate all digits
to its right.
Round to the specified place.
37.357 rounded to the nearest tenth is 37.4.
3.4819 rounded to the first digit is 3.
1. Write the numbers in a vertical column, aligning digits according to their places.
2. Attach extra zeros to the right end of each decimal number so that each number has the same
quantity of digits to the right of the decimal point (optional). It is also acceptable to assume
blank spaces to be zero.
3. Add or subtract as though the numbers are whole numbers.
4. Place the decimal point in the sum or difference to align with the decimal point in the
addends or subtrahend and minuend.
Add: 32.68 + 3.31 + 49 Subtract: 24.7 - 18.25
32.68
3.31
+ 49.
84.99
24.70
- 1 8.2 5
6.4 5
Multiply decimals.
1. Multiply the decimal numbers as though they are whole numbers.
2. Count the digits in the decimal parts of both decimal numbers.
3. Place the decimal point in the product so that there are as many digits in its decimal part as
there are digits you counted in step 2. If necessary, attach zeros on the left end of the product
so that you can place the decimal point accurately.
Multiply: 36.48 * 2.52 Multiply: 2.03 * 0.036
36.48
2.03
* 2.52
* 0.0 36
72 96
1 2 18
18 24 0
6 0 9
72 96
91.92 96
0.07 3 08

3 Divide
decimals. (p. 88)
Multiply by place-value numbers such as 10, 100, and 1,000.
1. Determine the number of zeros in the multiplier.
2. Move the decimal in the multiplicand to the right the same number of places as there are
zeros in the multiplier. Insert zeros as necessary.
Multiply: 4.52(1,000)
4.52(1,000) = 4,520
Divide a decimal by a whole number.
Divide: 58.5 , 45
1.3
4558.5
45
13 5
13 5
0
Divide: 4.52 , 100
4.52 , 100 = 0.0452
Move the decimal three places to the right. Insert a zero to have
enough places.
1. Place a decimal point for the quotient directly above the decimal point in the dividend.
2. Divide as though the decimal numbers are whole numbers.
3. If the division does not come out evenly, attach zeros as necessary and carry the division one
place past the desired place of the quotient.
4. Round to the desired place.
Divide by place-value numbers such as 10, 100, and 1,000.
1. Determine the number of zeros in the divisor.
2. Move the decimal in the dividend to the left the same number of places as there are zeros in
the divisor. Insert zeros as necessary.
Divide by a decimal.
Move the decimal two places to the left. Insert a zero to have
enough places. It is preferred to write a zero in front of the
decimal.
1. Change the divisor to a whole number by moving the decimal point to the right, counting the
places as you go. Use a caret (
^
) to show the new position of the decimal point.
2. Move the decimal point in the dividend to the right as many places as you moved the decimal
point in the divisor.
3. Place the decimal point for the quotient directly above the new decimal point in the dividend.
4. Divide as you would divide by a whole number. Carry the division one place past the desired
place of the quotient. Round to the desired place.
Divide: 0.770 , 3.5
Divide: 0.485 , 0.24
Round to the nearest tenth.
0. 22
3.5
^
0.7
^
70
7 0
70
70
0
2 . 02 = 2.0 rounded
0.24 ^ 0.48 ^ 50
48
50
48
2
DECIMALS
97

Section 3-3
1 Convert a decimal to a fraction.
(p. 92)
2 Convert
a fraction to a decimal.
(p. 93)
98 CHAPTER 3
1. Find the denominator: Write 1 followed by as many zeros as there are places to the right of
the decimal point.
2. Find the numerator: Use the digits without the decimal point.
3. Reduce to lowest terms and write as a whole or mixed number if appropriate.
Write each decimal as a fraction in lowest terms.
0.05 = 5
100
, 5
5
= 1
20
Write each fraction as a decimal.
5
8
0.584 = 584
1,000
, 8
8
= 73
125
1. Write the numerator as the dividend and the denominator as the divisor.
2. Divide the numerator by the denominator. Carry the division as many decimal places as necessary
or desirable.
3. For repeating decimals:
(a) Write the remainder as the numerator of a fraction and the divisor as the denominator.
or
(b) Carry the division one place past the desired place and round.
0.625
= 85.000
4 8
0.166 L 0.17 (Rounded to hundredths)
1
= 61.000
6
6
20 40
16
36
40 40
40
36
4

NAME DATE
EXERCISES SET A
Write the word name for the decimal.
1. 0.5 2. 0.108 3. 0.00275 4. 17.8
5. 128.23 6. 500.0007
Round to the specified place.
CHAPTER 3
7. 0.1345 (nearest thousandth) 8. 384.73 (nearest ten) 9. 1,745.376 (nearest hundred) 10. $175.24 (nearest dollar)
Add.
11. 0.3 + 0.05 + 0.266 + 0.63
12. 78.87 + 54 + 32.9569 + 0.0043
13. $5.13 + $8.96 + $14.73
14. $283.17 + $58.73 + $96.92
Subtract.
15. 500.05 - 123.31
16. 125.35 - 67.8975
17. 423 - 287.4
18. 482.073 - 62.97
Multiply.
19. 27.63 20. 6.42 21. 75.84 22. 27.58 * 10
* 7
* 7.8
* 0.28
DECIMALS
99

Divide. Round to hundredths if necessary.
23. 34291.48
Write as fractions or mixed numbers in simplest form.
100 CHAPTER 3
24. 2.894.546 25. 296.36 , 0.19
1,5 59 .789 L 1,559.79
0.19 296.36 000
26. 41,285 , 0.68
27. 0.55 28. 191.82
Write as decimals. Round to hundredths if necessary.
29. 17
20
31. A shopper purchased a cake pan for $8.95, a bath mat for
$9.59, and a bottle of shampoo for $2.39. Find the total cost
of the purchases.
33. Four tires that retailed for $486.95 are on sale for $397.99. By
how much are the tires reduced?
35. What is the cost of 5.5 pounds of chicken breasts if they cost
$3.49 per pound?
30. 13
16
32. Leon Treadwell’s checking account had a balance of $196.82
before he wrote checks for $21.75 and $82.46. What was his
balance after he wrote the checks?
34. If 100 gallons of gasoline cost $142.90, what is the cost per
gallon?
36. A. G. Edwards is purchasing 100 cell phones for $189.95.
How much is the total purchase?

NAME DATE
EXERCISES SET B CHAPTER 3
Write the word name for the decimal.
1. 0.27 2. 0.013 3. 0.120704 4. 3.04
5. 3,000.003 6. 184.271
Round to the specified place.
7. 384.72 (nearest tenth) 8. 1,745.376 (nearest
hundredth)
Add.
9. 32.57 (nearest whole
number)
11. 31.005 + 5.36 + 0.708 + 4.16 12. 9.004 + 0.07 + 723 + 8.7
13. $7.19 + $5.78 + $21.96 14. $596.16 + $47.35 + $72.58
Subtract.
15. 815.01 - 335.6
Multiply.
10. $5.333 (nearest cent)
16. 404.04 - 135.8716 17. 807.38 - 529.79 18. 5,003.02 - 689.23
19. 3 84
20. 0.0015
21. 73.41
22. 1.394 * 100
* 3.51
* 6.003
* 15
DECIMALS
101

Divide. Round to the nearest hundredth if division does not terminate.
23. 27365.04
24. 7485.486
25. 923.19 , 0.541
26. 363.45 , 2.5
Write as fractions or mixed numbers in simplest form.
27.
Write as decimals. Round to hundredths if necessary.
29. 1
20
31. Rob McNab ordered 18.3 square meters of carpet for his halls,
123.5 square meters for the bedrooms, 28.7 square meters for
the family room, and 12.9 square meters for the playroom.
Find the total amount of carpet he ordered.
33. Ernie Jones worked 37.5 hours at the rate of $14.80 per hour.
Calculate his earnings.
35. If two lengths of metal sheeting measuring 12.5 inches and
15.36 inches are cut from a roll of metal measuring 240
inches, how much remains on the roll?
102 CHAPTER 3
28. 17.5
30. 3 7
20
32. Janet Morris weighed 149.3 pounds before she began a
weight-loss program. After eight weeks she weighed 129.7
pounds. How much did she lose?
34. If sugar costs $2.87 for 80 ounces, what is the cost per ounce,
rounded to the nearest cent?
36. If 1,000 gallons of gasoline cost $1,589, what is the cost of
45 gallons?

NAME DATE
PRACTICE TEST CHAPTER 3
1. Round 42.876 to tenths.
Perform the indicated operation.
5. 39.17 - 15.078
7. 0.387 + 3.17 + 17 + 204.3
9. 324
* 1.38
11. 128 - 38.18
2. Round 30.5375 to one nonzero digit.
3. Write the word name for 24.1007. 4. Write the number for three and twenty-eight thousandths.
6. 27.418 * 100
8. 28.34 , 50 (nearest hundredth)
10. 0.138 , 10
12. 17.75
* 0.325
DECIMALS
103

13. 2.347 + 0.178 + 3.5 + 28.341
17. A patient’s chart showed a temperature reading of 101.2 degrees
Fahrenheit at 3 P.M. and 99.5 degrees Fahrenheit at 10 P.M.
What was the drop in temperature?
19. Stephen Lewis owns 100 shares of PepsiCo at $47.40; 50
shares of Alcoa at $27.19; and 200 shares of McDonald’s at
$24.72. What is the total stock value?
EXCEL
104 CHAPTER 3
14. 91.25 , 12.5
15. 317.24 - 138 16. 374.17 * 100
18. Eastman Kodak’s stock changed from $26.14 a share to
$22.15 a share. Peter Carp owned 2,000 shares of stock. By
how much did his stock decrease?
20. What is the average price per share of the 350 shares of stock
held by Stephen Lewis if the total value is $11,043.50?

CRITICAL THINKING CHAPTER 3
1. Explain why numbers are aligned on the decimal point when they are
added or subtracted.
3. Explain the process of changing a fraction to a decimal number.
Identify the error and describe what caused the error. Then work the example correctly.
5
5. Change to a decimal number.
12
2.4
512.0
10
2 0
5
= 2.4
12
4.3 7
* 2.1
4 3 7
8 7 4
9.1 7 7
Challenge Problem
2. Describe the process for placing the decimal point in the product of
two decimal numbers.
4. Explain the process of changing a decimal number to a fraction.
6. Add: 3.72 + 6 + 12.5 + 82.63
3.72
6
12.5
82.63
87.66
7. Multiply: 4.37 * 2.1 8. Divide: 18.27 , 54. Round to tenths.
4.37
2.95 L 3.0
* 2.1
4 37
87 4
91.77
18.27 54.00 00
36 54
17 460
16 443
1 0170
9135
1035
Net income for Hershey Foods for the third quarter is $143,600,000 or $1.09 a share. This is compared with net income of $123,100,000 or $0.89 a share for
the same quarter a year ago. What was the increase or decrease in the number of shares of stock?
DECIMALS
105

3-1 Pricing Stock Shares
106 CHAPTER 3
CASE STUDIES
Shantell recognized the stationery, and looked forward to another of her Aunt Mildred’s letters. Inside,
though, were a number of documents along with a short note. The note read: “Shantell, your Uncle
William and I are so proud of you. You are the first female college graduate in our family. Your parents
would have been so proud as well. Please accept these stocks as a gift towards the fulfillment of starting
your new business. Cash them in or keep them for later, it’s up to you! With love, Aunt Millie.” Shantell
didn’t know how to react. Finishing college had been very difficult for her financially. Having to work
two jobs meant little time for studying, and a nonexistent social life. But this she never expected. With
dreams of opening her own floral shop, any money would be a godsend. She opened each certificate and
found the following information: Alcoa—35 shares at 15 3/8; Coca Cola—150 shares at 24 5/8; IBM—
80 shares at 40 11/16; and AT&T—50 shares at 35 1/8.
1. Shantell knew the certificates were old, because stocks do not trade using fractions anymore. What
would the stock prices be for each company if they were converted from fractions to decimals?
2. Using your answers with decimals from Exercise 1, find the total value of each company’s stock.
What is the total value from all four companies?
3. Shantell couldn’t believe her eyes. The total she came up with was over $9,000! Suddenly, though, she realized that the amounts she
used could not possibly be the current stock prices. After 30 minutes on-line, she was confident she had the current prices: Alcoa: 35
shares at $34.19; Coca Cola: 150 shares at $48.05; IBM: 80 shares at $95.03; and AT&T: 50 shares at $38.88. Using the current prices,
what would be the total value of each company’s stock? What would be the total value for all of the stocks? Given the answer, would you
cash the stocks in now or hold on to them to see if they increased in value?
3-2 JK Manufacturing Demographics
Carl has just started his new job as a human resource management assistant for JK Manufacturing. His
first project is to gather demographic information on the personnel at their three locations in El Paso, San
Diego, and Chicago. Carl studied some of the demographics collected by the Bureau of Labor Statistics
(www.stats.bls.gov) in one of his human resource classes and decided to collect similar data. Primarily, he
wants to know the gender, level of education, and ethnic/racial backgrounds of JK Manufacturing’s workforce.
He designs a survey using categories he found at the Bureau of Labor Statistics web site.
Employees at each of the locations completed Carl’s survey, and reported the following information:
El Paso: 140 women, 310 men; 95 had a bachelor’s degree or higher, 124 had some college or an associate’s degree, 200 were high school
graduates, and the rest had less than a high school diploma; 200 employees were white non-Hispanic, 200 were Hispanic or Latino, 20 were
black or African American, 15 were Asian, and the rest were “other.”
San Diego: 525 women, 375 men; 150 had a bachelor’s degree or higher, 95 had some college or an associate’s degree, 500 were high school
graduates, and the rest had less than a high school diploma; 600 employees were Hispanic or Latino, 200 were black or African American, 50
were white non-Hispanic, 25 were Asian, and the rest were “other.”
Chicago: 75 women, 100 men; 20 had a bachelor’s degree or higher, 75 had some college or an associate’s degree, 75 were high school graduates,
and the rest had less than a high school diploma; 100 employees were white non-Hispanic, 50 were black or African American, 25 were
Hispanic or Latino, there were no Asians or “other” at the facility.
1. Carl’s supervisor asked him to summarize the information and convert the raw data to a decimal part of the total for each location. Carl
designed the following chart to organize the data. To complete the chart, write a fraction with the number of employees in each category
as the numerator and the total number of employees in each city as the denominator. Then convert the fraction to a decimal rounded to
the nearest hundredth. Enter the decimal in the chart. To check your calculations, the total of the decimal equivalents for each city should
equal 1 or close to 1 because of rounding discrepancies.

Gender El Paso San Diego Chicago
Men 310 375 100
Women 140 525 75
Total 450 900 175
Education El Paso San Diego Chicago
Bachelor’s degree or higher 95 150 20
Some college or an associate’s degree 124 95 75
High School (HS) graduate 200 500 75
Less than a HS diploma 31 155 5
Total 450 900 175
Race/Ethnicity El Paso San Diego Chicago
White/non-Hispanic 200 50 100
Black/African American 20 200 50
Hispanic/Latino 200 600 25
Asian 15 25
Other 15 25
Total 450 900 175
DECIMALS
107