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330	Chapter 4 Decimals

WRITING

107.Explain the difference between ten and one-tenth.

108.“The more digits a number contains, the larger it is.” Is this statement true? Explain.

109.Explain why is it wrong to read 2.103 as “two and one hundred and three thousandths.”

110.SIGNS

a.A sign in front of a fast food restaurant had the cost of a hamburger listed as .99¢. Explain the error.

b.The illustration below shows the unusual notation that some service stations use to express the price of a gallon of gasoline. Explain the error.

REGULAR		UNLEADED		UNLEADED +
2.79	9	2.89	9	2.99	9
	––		––		––
	10		10		10

111. Write a deﬁnition for each of these words.

decade

decathlon

decimal

112.Show that in the decimal numeration system, each

place-value column for the fractional part of a decimal is 101 of the value of the place directly to its left.

REVIEW

113.a. Find the perimeter of the rectangle shown below.

b. Find the area of the rectangle.

3 – ft

2 – ft

114.a. Find the perimeter of the triangle shown below.

b. Find the area of the triangle.

1 – in.

9 2 ––10 in.

1 – in.

Objectives

S E C T I O N 4.2

1Add decimals.

2Subtract decimals.

3Add and subtract signed decimals.

4Estimate sums and differences of decimals.

Adding and Subtracting Decimals

To add or subtract objects, they must be similar. The federal income tax form shown below has a vertical line to make sure that dollars are added to dollars and cents added to cents. In this section, we show how decimal numbers are added and subtracted using this type of vertical form.

5Solve application problems by adding and subtracting decimals.

Department of the Treasury—Internal Revenue Service

Form

	1040EZ		Income Tax Return for Single and
	1040EZ		Joint Filers With No Dependents 2010
Income		1	Wages, salaries, and tips. This should be shown in box 1 of	1	21,056	89
Income			your Form(s) W-2. Attach your Form(s) W-2.	1	21,056	89
Attach			your Form(s) W-2. Attach your Form(s) W-2.


Form(s)		2	Taxable interest. If the total is over $1,500, you cannot use Form 1040EZ.	2	42	06
W-2 here.
Enclose, but		3	Unemployment compensation and Alaska Permanent Fund dividends	3	200	00
do not attach,			(see page 11).	3	200	00
any payment.
any payment.		4	Add lines 1, 2, and 3. This is your adjusted gross income.	4	21,298	95
		4	Add lines 1, 2, and 3. This is your adjusted gross income.	4	21,298	95

1 Add decimals.

Adding decimals is similar to adding whole numbers. We use vertical form and stack the decimals with their corresponding place values and decimal points lined up. Then we add the digits in each column, working from right to left, making sure that

4.2 Adding and Subtracting Decimals

331

hundredths are added to hundredths, tenths are added to tenths, ones are added to ones, and so on. We write the decimal point in the sum so that it lines up with the decimal points in the addends. For example, to ﬁnd 4.21 1.23 2.45, we proceed as follows:

Ones column

Tenths column

Hundredths column

Vertical form	4 . 2		1
	1	. 2	3
	2	. 4 5
	7	. 8	9

The sum is 7.89.

The numbers that are being added, 4.21, 1.23, and 2.45 are called addends.

Write the decimal point in the sum directly under the decimal points in the addends.

Sum of the hundredths digits: Think 1 3 5 9 Sum of the tenths digits: Think 2 2 4 8 Sum of the ones digits: Think 4 1 2 7

In this example, each addend had two decimal places, tenths and hundredths. If the number of decimal places in the addends are different, we can insert additional zeros so that the number of decimal places match.

Adding Decimals

To add decimal numbers:

1.Write the numbers in vertical form with the decimal points lined up.

2.Add the numbers as you would add whole numbers, from right to left.

3.Write the decimal point in the result from Step 2 directly below the decimal points in the addends.

Like whole number addition, if the sum of the digits in any place-value column is greater than 9, we must carry.

EXAMPLE 1 Add: 31.913 5.6 68 16.78

Strategy We will write the addition in vertical form so that the corresponding place values and decimal points of the addends are lined up. Then we will add the digits, column by column, working from right to left.

WHY We can only add digits with the same place value.

Solution To make the column additions easier, we will write two zeros after the 6 in the addend 5.6 and one zero after the 8 in the addend 16.78. Since whole numbers have an “understood” decimal point immediately to the right of their ones digit, we can write the addend 68 as 68.000 to help line up the columns.

31 . 913

5 . 600 Insert two zeros after the 6.

68 . 000 Insert a decimal point and three zeros: 68 68.000.

16 . 780 Insert a zero after the 8.

Line up the decimal points.

Self Check 1

Add: 41.07 35 67.888 4.1

Now Try Problem 19

Now we add, right to left, as we would whole numbers, writing the sum from each column below the horizontal bar.

332	Chapter 4 Decimals

2 2
31.913	Carry a 2	(shown in blue) to the ones column.
5.600	Carry a 2	(shown in green) to the tens column.
68.000

16.780

122.293

Write the decimal point in the result directly below the decimal points in the addends.

The sum is 122.293.

Success Tip In Example 1, the digits in each place-value column were added from top to bottom. To check the answer, we can instead add from bottom to top. Adding down or adding up should give the same result. If it does not, an error has been made and you should re-add.

	122.293
	122.293
First add	31.913
First add	5.600	To check,
top to	5.600	To check,
bottom	68.000	add
bottom	68.000	bottom
	16.780	bottom
	16.780	to top
	122.293
	122.293

Using Your CALCULATOR Adding Decimals

The bar graph on the right shows the number of grams of ﬁber in a standard serving of each of several foods. It is believed that men can signiﬁcantly cut their risk of heart attack by eating at least 25 grams of ﬁber a day. Does this diet meet or exceed the 25-gram requirement?

	15
		12.75
of fiber	10
of fiber					7.3
Grams	5			3.5
	3.1			3.5
	3.1
			0.9		1.1
			0.9
	1	Bran	Lettuce	1	Spaghetti Kidney
	Grapefruit cereal			Apple	beans

To ﬁnd the total ﬁber intake, we add the ﬁber content of each of the foods. We can use a calculator to add the decimals.

3.1

12.75

3.5

1.1

7.3

28.65

On some calculators, the ENTER key is pressed to ﬁnd the sum.

Since 28.65 25, this diet exceeds the daily ﬁber requirement of 25 grams.

2 Subtract decimals.

Subtracting decimals is similar to subtracting whole numbers. We use vertical form and stack the decimals with their corresponding place values and decimal points lined up so that we subtract similar objects—hundredths from hundredths, tenths from tenths, ones from ones, and so on. We write the decimal point in the difference so that

4.2 Adding and Subtracting Decimals

333

it lines up with the decimal points in the minuend and subtrahend. For example, to ﬁnd 8.59 1.27, we proceed as follows:

Ones column

Tenths column

Hundredths column

Vertical form	8	. 5	9
	1	. 2	7
	7	. 3	2

The difference is 7.32.

8.59 is the minuend and 1.27 is the subtrahend.

Write the decimal point in the difference directly under the decimal points in the minuend and subtrahend.

Difference of the hundredths digits: Think 9 7 2 Difference of the tenths digits: Think 5 2 3 Difference of the ones digits: Think 8 1 7

Subtracting Decimals

To subtract decimal numbers:

1.Write the numbers in vertical form with the decimal points lined up.

2.Subtract the numbers as you would subtract whole numbers from right to left.

3.Write the decimal point in the result from Step 2 directly below the decimal points in the minued and the subtrahend.

As with whole numbers, if the subtraction of the digits in any place-value column requires that we subtract a larger digit from a smaller digit, we must borrow or regroup.

EXAMPLE 2 Subtract: 279.6 138.7

Strategy As we prepare to subtract in each column, we will compare the digit in the subtrahend (bottom number) to the digit directly above it in the minuend (top number).

WHY If a digit in the subtrahend is greater than the digit directly above it in the minuend, we must borrow (regroup) to subtract in that column.

Solution Since 7 in the tenths column of 138.7 is greater than 6 in the tenths column of 279.6, we cannot immediately subtract in that column because 6 7 is not a whole number. To subtract in the tenths column, we must regroup by borrowing as shown below.

8 16

279.6To subtract in the tenths column, borrow 1 one in the form of 10 tenths

138.7 from the ones column. Add 10 to the 6 in the tenths column to get 16

140.9(shown in blue).

Recall from Section 1.3 that subtraction can be checked by addition. If a subtraction is done correctly, the sum of the difference and the subtrahend will equal the minuend: Difference subtrahend minuend.

Check:

140.9Difference

138.7 Subtrahend

279.6Minuend

Since the sum of the difference and the subtrahend is the minuend, the subtraction is correct.

Some subtractions require borrowing from two (or more) place-value columns.

Self Check 2

Subtract: 382.5 227.1

Now Try Problem 27

334	Chapter 4 Decimals

Self Check 3

Subtract 27.122 from 29.7.

Now Try Problem 31

EXAMPLE 3 Subtract 13.059 from 15.4.

Strategy We will translate the sentence to mathematical symbols and then perform the subtraction. As we prepare to subtract in each column, we will compare the digit in the subtrahend (bottom number) to the digit directly above it in the minuend (top number).

WHY If a digit in the subtrahend is greater than the digit directly above it in the minuend, we must borrow (regroup) to subtract in that column.

Solution Since 13.059 is the number to be subtracted, it is the subtrahend.

Subtract 13.059 from 15.4

15.4 13.059

To ﬁnd the difference, we write the subtraction in vertical form. To help with the column subtractions, we write two zeros to the right of 15.4 so that both numbers have three decimal places.

15 . 400 Insert two zeros after the 4 so that the decimal places match.

13 . 059

Line up the decimal points.

Since 9 in the thousandths column of 13.059 is greater than 0 in the thousandths column of 15.400, we cannot immediately subtract. It is not possible to borrow from the digit 0 in the hundredths column of 15.400. We can, however, borrow from the digit 4 in the tenths column of 15.400.

	3 10
15	. 400	Borrow 1 tenth in the form of 10 hundredths from 4 in the tenths column.
13	. 059	Add 10 to 0 in the hundredths column to get 10 (shown in blue).

Now we complete the two-column borrowing process by borrowing from the 10 in the hundredths column.Then we subtract, column-by-column, from the right to the left to ﬁnd the difference.

	9
15	3 10 10
15	. 4 0 0	Borrow 1 hundredth in the form of 10 thousandths from 10 in the
13	. 0 5 9	hundredths column. Add 10 to 0 in the thousandths column to
2	. 3 4 1	get 10 (shown in green).
2	. 3 4 1

When 13.059 is subtracted from 15.4, the difference is 2.341.

Check:

1 1

2.341 Since the sum of the difference and the subtrahend13.059 is the minuend, the subtraction is correct.

15.400

Using Your CALCULATOR Subtracting Decimals

A giant weather balloon is made of a ﬂexible rubberized material that has an uninﬂated thickness of 0.011 inch. When the balloon is inﬂated with helium, the thickness becomes 0.0018 inch. To ﬁnd the change in thickness, we need to subtract. We can use a calculator to subtract the decimals.

.011

.0018

0.0092

On some calculators, the ENTER key is pressed to ﬁnd the difference.

After the balloon is inﬂated, the rubberized material loses 0.0092 inch in thickness.

EXAMPLE 5

4.2 Adding and Subtracting Decimals

335

3 Add and subtract signed decimals.

To add signed decimals, we use the same rules that we used for adding integers.

Adding Two Decimals That Have the Same (Like) Signs

1.To add two positive decimals, add them as usual. The ﬁnal answer is positive.

2.To add two negative decimals, add their absolute values and make the ﬁnal answer negative.

Adding Two Decimals That Have Different (Unlike) Signs

To add a positive decimal and a negative decimal, subtract the smaller absolute value from the larger.

1.If the positive decimal has the larger absolute value, the ﬁnal answer is positive.

2.If the negative decimal has the larger absolute value, make the ﬁnal answer negative.

EXAMPLE 4 Add: 6.1 ( 4.7)

Strategy We will use the rule for adding two decimals that have the same sign.

WHY Both addends, 6.1 and 4.7, are negative.

Solution Find the absolute values: 0 6.1 0 6.1 and 0 4.7 0 4.7.

6.1 ( 4.7)	10.8 Add the absolute values, 6.1 and 4.7, to		6.1
			6.1
		get 10.8. Then make the ﬁnal answer	4.7
		get 10.8. Then make the ﬁnal answer	4.7
		negative.	10.8
			10.8

Self Check 4

Add: 5.04 ( 2.32)

Now Try Problem 35

Add: 5.35 ( 12.9)

Strategy We will use the rule for adding two integers that have different signs.

WHY One addend is positive and the other is negative.

Solution Find the absolute values: 0 5.35 0 5.35 and 0 12.9 0 12.9.

5.35 ( 12.9) 7.55	Subtract the smaller absolute value from	8 10
		8 10
	the larger: 12.9 5.35 7.55. Since the	12.9 0
	the larger: 12.9 5.35 7.55. Since the	5.3 5
	negative number, 12.9, has the larger	5.3 5
	negative number, 12.9, has the larger	7.5 5
	absolute value, make the ﬁnal answer
	negative.
	negative.

The rule for subtraction that was introduced in Section 2.3 can be used with signed decimals: To subtract two decimals, add the ﬁrst decimal to the opposite of the decimal to be subtracted.

Self Check 5

Add: 21.4 16.75

Now Try Problem 39

EXAMPLE 6 Subtract: 35.6 5.9

Strategy We will apply the rule for subtraction: Add the ﬁrst decimal to the opposite of the decimal to be subtracted.

WHY It is easy to make an error when subtracting signed decimals. We will probably be more accurate if we write the subtraction as addition of the opposite.

Self Check 6

Subtract: 1.18 2.88

Now Try Problem 43

Perform the addition.

Add the opposite of 10.7.

Perform the addition.

EXAMPLE 8

336	Chapter 4 Decimals

Self Check 7

Subtract: 2.56 ( 4.4)

Now Try Problem 47

Self Check 8

Evaluate: 4.9 ( 1.2 5.6)

Now Try Problem 51

Solution The number to be subtracted is 5.9. Subtracting 5.9 is the same as adding its opposite, 5.9.

Change the subtraction to addition.



35.6 5.9 35.6 ( 5.9) 41.5		Use the rule for adding	1 1
35.6 5.9 35.6 ( 5.9) 41.5		Use the rule for adding	1 1
		two decimals with the	35.6
		two decimals with the	5.9
	Change the number being	same sign. Make the	5.9
	Change the number being	same sign. Make the	41.5
	subtracted to its opposite.	ﬁnal answer negative.
	subtracted to its opposite.	ﬁnal answer negative.

EXAMPLE 7 Subtract: 8.37 ( 16.2)

Strategy We will apply the rule for subtraction: Add the ﬁrst decimal to the opposite of the decimal to be subtracted.

WHY It is easy to make an error when subtracting signed decimals. We will probably be more accurate if we write the subtraction as addition of the opposite.

Solution The number to be subtracted is 16.2. Subtracting 16.2 is the same as adding its opposite, 16.2.

	Add . . .	Use the rule for adding
		two decimals with
		two decimals with
8.37 ( 16.2) 8.37 16.2 7.83		different signs. Since
		16.2 has the larger


		absolute value, the ﬁnal
	. . . the opposite	absolute value, the ﬁnal
	. . . the opposite	answer is positive.
		answer is positive.

Evaluate: 12.2 ( 14.5 3.8)

Strategy We will perform the operation within the parentheses ﬁrst.

WHY This is the ﬁrst step of the order of operations rule.

Solution We perform the addition within the grouping symbols ﬁrst.

12.2 ( 14.5 3.8) 12.2 ( 10.7)

12.2 10.7

1.5

5 1 10

16.2 0

8. 3 7

7. 8 3

3 15

14. 5

3. 8

10.7

1 12

12. 210. 7 1. 5

4 Estimate sums and differences of decimals.

Estimation can be used to check the reasonableness of an answer to a decimal addition or subtraction.There are several ways to estimate, but the objective is the same: Simplify the numbers in the problem so that the calculations can be made easily and quickly.

Self Check 9		EXAMPLE 9
		EXAMPLE 9

a.Estimate by rounding the

addends to the nearest ten: a. Estimate by rounding the addends to the nearest ten: 261.76 432.94

526.93 284.03

b.Estimate using front-end rounding: 512.33 36.47

Now Try Problems 55 and 57

b. Estimate using front-end rounding: 381.77 57.01

Strategy We will use rounding to approximate each addend, minuend, and subtrahend. Then we will ﬁnd the sum or difference of the approximations.

WHY Rounding produces numbers that contain many 0’s. Such numbers are easier to add or subtract.

EXAMPLE 11

4.2 Adding and Subtracting Decimals

337

Solution

261.76260 Round to the nearest ten.

432.94	430	Round to the nearest ten.
432.94	430	Round to the nearest ten.
	690

The estimate is 690. If we compute 261.76 432.94, the sum is 694.7. We can see that the estimate is close; it’s just 4.7 less than 694.7.

We use front-end rounding. Each number is rounded to its largest place value.

381.77400 Round to the nearest hundred.

57.01	60	Round to the nearest ten.
57.01	60	Round to the nearest ten.
	340

The estimate is 340. If we compute 381.77 57.01, the difference is 324.76. We can see that the estimate is close; it’s 15.24 more than 324.76.

5Solve application problems by adding and subtracting decimals.

To make a proﬁt, a merchant must sell an item for more than she paid for it. The price at which the merchant sells the product, called the retail price, is the sum of what the item cost the merchant plus the markup.

Retail price cost markup

EXAMPLE 10	Pricing Find the retail price of a Rubik’s Cube if a game

store owner buys them for $8.95 each and then marks them up $4.25 to sell in her store.

Analyze

	• Rubik’s Cubes cost the store owner $8.95 each.					Given		Presazzi/Dreamstime.com
	• She marks up the price $4.25.					Given		Presazzi/Dreamstime.com
	• What is the retail price of a Rubik’s Cube?					Find		Andrea
								Andrea
Form We translate the words of the problem to numbers and symbols.

	The retail price		is equal to	the cost	plus		the markup.
	The retail price			8.95			4.25
Solve Use vertical form to perform decimal addition:
1		1
8.95
4.25
13.20
State The retail price of a Rubik’s Cube is $13.20.

Check We can estimate to check the result. If we use $9 to approximate the cost of a Rubik’s Cube to the store owner and $4 to be the approximate markup, then the retail price is about $9 $4 $13. The result, $13.20, seems reasonable.

Kitchen Sinks One model of kitchen sink is made of 18-gauge stainless steel that is 0.0500 inch thick. Another, less expensive, model is made from 20-gauge stainless steel that is 0.0375 inch thick. How much thicker is the 18-gauge?

Self Check 10

PRICING Find the retail price of a wool coat if a clothing outlet buys them for $109.95 each and then marks them up $99.95 to sell in its stores.

Now Try Problem 91

EXAMPLE 12

Conditioning Programs

338	Chapter 4 Decimals

Self Check 11

ALUMINUM How much thicker is 16-gauge aluminum that is 0.0508 inch thick than 22-gauge aluminum that is 0.0253 inch thick?

Now Try Problem 97

Analyze

• The18-gauge stainless steel is
0.0500 inch thick.	Given
• The 20-gauge stainless steel is
0.0375 inch thick.	Given	Image copyright V. J. Matthew, 2009. Used under
• How much thicker is the 18-gauge		license from Shutterstock.com
• How much thicker is the 18-gauge
stainless steel?	Find

Form Phrases such as how much older, how much longer, and, in this case, how much thicker, indicate subtraction. We translate the words of the problem to numbers and symbols.

How much	is equal to	the thickness of the	minus	the thickness of the
thicker		18-gauge stainless steel		20-gauge stainless steel.

How much		0.0500		0.0375
thicker

Solve Use vertical form to perform subtraction:

4 10 10

0.050 0

0.03 7 5

0.012 5

State The 18-gauge stainless steel is 0.0125 inch thicker than the 20-gauge.

Check We can add to check the subtraction:

1 1

0.0125 Difference

0.0375 Subtrahend

0.0500 Minuend

The result checks.

Self Check 12

WRESTLING A 195.5-pound wrestler had to lose 6.5 pounds to make his weight class. After the weigh-in, he gained back 3.7 pounds. What did he weigh then?

Now Try Problem 103

Sometimes more than one operation is needed to solve a problem involving decimals.

A 350-pound football player lost 15.7 pounds during the ﬁrst week of practice. During the second week, he gained 4.9 pounds. Find his weight after the ﬁrst two weeks of practice.

Analyze

• The football player’s beginning weight was 350 pounds.		Given
• The ﬁrst week he lost 15.7 pounds.		Given
•	The second week he gained 4.9 pounds.	Given
•	What was his weight after two weeks of practice?	Find

Form The word lost indicates subtraction. The word gained indicates addition. We translate the words of the problem to numbers and symbols.

The player’s weight after	is equal to	his beginning	minus	the ﬁrst-week	plus	the second-week
two weeks of practice		weight		weight loss		weight gain.


The player’s weight after		350		15.7		4.9
two weeks of practice

4.2 Adding and Subtracting Decimals

339

Solve To evaluate 350 15.7 4.9, we work from left to right and perform the subtraction ﬁrst, then the addition.

4 10 10

3 5 0. 0 Write the whole number 350 as 350.0 and use a two-column1 5 .7 borrowing process to subtract in the tenths column.

3 3 4 .3 This is the player’s weight after one week of practice.

Next, we add the 4.9-pound gain to the previous result to ﬁnd the player’s weight after two weeks of practice.

334.34.9

339.2

State The player’s weight was 339.2 pounds after two weeks of practice.

Check We can estimate to check the result. The player lost about 16 pounds the ﬁrst week and then gained back about 5 pounds the second week, for a net loss of 11 pounds. If we subtract the approximate 11 pound loss from his beginning weight, we get 350 11 339 pounds. The result, 339.2 pounds, seems reasonable.

ANSWERS TO SELF CHECKS
ANSWERS TO SELF CHECKS
1.	148.058	2.	155.4 3. 2.578	4. 7.36 5. 4.65	6. 4.06 7. 1.84 8. 9.3
9.	a. 810	b.	460 10. $209.90	11. 0.0255 in. 12.	192.7 lb

S E C T I O N 4.2 STUDY SET

VOCABULARY

Fill in the blanks.

1.In the addition problem shown below, label each addend and the sum.

1.72
4.68


2.02


8.42

2. When using the vertical form to add decimals, if the addition of the digits in any one column produces a sum greater than 9, we must .

3.In the subtraction problem shown below, label the minuend, subtrahend, and the difference.

12.9

4.3

8.6

4.If the subtraction of the digits in any place-value column requires that we subtract a larger digit from

a smaller digit, we must or regroup.

5. To see whether the result of an addition is reasonable, we can round the addends and the sum.

6.In application problems, phrases such as how much older, how much longer, and how much thicker

indicate the operation of

CONCEPTS

7.Check the following result. Use addition to determine if 15.2 is the correct difference.

28.7

12.5

15.2

8.Determine whether the sign of each result is positive or negative. You do not have to ﬁnd the sum.

a.7.6 ( 1.8)

b.24.99 29.08

c.133.2 ( 400.43)

9.Fill in the blank: To subtract signed decimals, add the

of the decimal that is being subtracted.

10.Apply the rule for subtraction and ﬁll in the three blanks.

3.6 ( 2.1) 3.6

340	Chapter 4 Decimals

11.Fill in the blanks to rewrite each subtraction as addition of the opposite of the number being subtracted.

a.6.8 1.2 6.8 ( )

b.29.03 ( 13.55) 29.03

c.5.1 7.4 5.1 ( )

12.Fill in the blanks to complete the estimation.

567.7						Round to the nearest ten.
214.3						Round to the nearest ten.


782.0

NOTATION

13.Copy the following addition problem. Insert a decimal point and additional zeros so that the number of decimal places in the addends match.

46.6

15.702

14.Refer to the subtraction problem below. Fill in the

blanks: To subtract in the column, we

borrow 1 tenth in the form of 10 hundredths from the 3 in the column.

2 11

29.3 1

25.16

GUIDED PRACTICE

Add. See Objective 1.
15.	32.5	16.	16.3
	7.4		3.5
17.	3.04	18.	2.11
	4.12		5.04
	1.43		2.72

Add. See Example 1.

19.36.821 7.3 42 15.44

20.46.228 5.6 39 19.37

21.27.471 6.4 157 12.12

22.52.763 9.1 128 11.84

Subtract. See Objective 2.
23.	6.83	24.	9.47
	3.52		5.06
25.	8.97	26.	7.56
	6.22		2.33
Subtract. See Example 2.
27.	495.4	28.	977.6
	153.7		345.8

29.	878.1	30.	767.2
	174.6		614.7

Perform the indicated operation. See Example 3.

31.Subtract 11.065 from 18.3.

32.Subtract 15.041 from 17.8.

33.Subtract 23.037 from 66.9.

34.Subtract 31.089 from 75.6.

Add. See Example 4.
35.	6.3 ( 8.4)		36.	9.2 ( 6.7)
37.	9.5 ( 9.3)		38.	7.3 ( 5.4)
Add. See Example 5.
39.	4.12 ( 18.8)		40.	7.24 ( 19.7)
41.	6.45 ( 12.6)		42.	8.81 ( 14.9)
Subtract. See Example 6.
43.	62.8	3.9	44.	56.1	8.6
45.	42.5	2.8	46.	93.2	3.9
Subtract. See Example 7.
47.	4.49	( 11.3)	48.	5.76	( 13.6)
49.	6.78	( 24.6)	50.	8.51	( 27.4)

Evaluate each expression. See Example 8.

51.11.1 ( 14.4 7.8)

52.12.3 ( 13.6 7.9)

53.16.4 ( 18.9 5.9)

54.15.5 ( 19.8 5.7)

Estimate each sum by rounding the addends to the nearest ten.

See Example 9.

55. 510.65 279.19

56. 424.08 169.04

Estimate each difference by using front-end rounding.

See Example 9.

57. 671.01 88.35 58. 447.23 36.16

TRY IT YOURSELF

Perform the indicated operations.
59.	45.6 34.7	60.	19.04 2.4
61.	9.5 7.1	62.	7.08 14.3
63.	46.09 ( 7.8)	64.	34.7 ( 30.1)
65.	21.88	66.	19.05
	33.12		31.95

67.30.03 ( 17.88)

68.143.3 ( 64.01)

69.645 9.90005 0.12 3.02002

70.505.0103 23 0.989 12.0704

71.Subtract 23.81 from 24.

72.	Subtract 5.9 from 7.001.
73.	(3.4 6.6) 7.3	74. 3.4 (6.6 7.3)

75.247.9 40 0.56

76.0.0053 1.78 6

77.	78.1	78.	202.234
	7.81		19.34
79.	7.8 ( 6.5)	80.	5.78 ( 33.1)

81.16 (67.2 6.27)

82.43 (0.032 0.045)

83.Find the sum of two and forty-three hundredths and ﬁve and six tenths.

84.Find the difference of nineteen hundredths and six thousandths.

85.	0 14.1 6.9 0 8	86.	15	0 2.3 ( 2.4) 0
87.	5 0.023	88.	30	11.98
89.	2.002 ( 4.6)	90.	0.005 ( 8)

APPLICATIONS

91.RETAILING Find the retail price of each appliance listed in the following table if a department store purchases them for the given costs and then marks them up as shown.

			Retail
Appliance	Cost	Markup	price

Refrigerator	$610.80	$205.00
Washing machine	$389.50	$155.50
Dryer	$363.99	$167.50

92.PRICING Find the retail price of a Kenneth Cole two-button suit if a men’s clothing outlet buys them for $210.95 each and then marks them up $144.95 to sell in its stores.

93.OFFSHORE DRILLING A company needs to construct a pipeline from an offshore oil well to a reﬁnery located on the coast. Company engineers have come up with two plans for consideration, as shown. Use the information in the illustration to complete the table that is shown in the next column.

2.32mi

Refinery

1.74 mi

2.90 mi

Oil well

Design 1

Design 2

	4.2 Adding and Subtracting Decimals		341

	Pipe	Pipe	Total
	underwater	underground	pipe
	(mi)	(mi)	(mi)

Design 1
Design 2

94.DRIVING DIRECTIONS Find the total distance of the trip using the information in the MapQuest printout shown below.

START	1: Start out going EAST on SUNKIST AVE.	0.0 mi
	2: Turn LEFT onto MERCED AVE.	0.4 mi
	3: Turn Right onto PUENTE AVE.	0.3 mi
10	4: Merge onto I-10 W toward LOS ANGELES.	2.2 mi
WEST
SOUTH605	5: Merge onto I-605 S.	10.6 mi
5	6: Merge onto I-5 S toward SANTA ANA.	14.9 mi
SOUTH
110 A	7: Take the HARBOR BLVD exit, EXIT 110A.	0.3 mi
EXIT	7: Take the HARBOR BLVD exit, EXIT 110A.	0.3 mi
	8: Turn RIGHT onto S HARBOR BLVD.	0.1 mi
END	9: End at 1313 S Harbor Blvd Anaheim, CA.

Total Distance: ? miles	®

95.PIPE (PVC) Find the outside diameter of the plastic sprinkler pipe shown below if the thickness of the pipe wall is 0.218 inch and the inside diameter is 1.939 inches.

Outside diameter

Inside diameter

96.pH SCALE The pH scale shown below is used to measure the strength of acids and bases in chemistry. Find the difference in pH readings between

a.bleach and stomach acid.

b.ammonia and coffee.

c.blood and coffee.

Strong acid							Neutral					Strong base
0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Stomach acid				Coffee			Blood				Ammonia		Bleach
	1.75			5.01			7.38				12.03		12.7

342	Chapter 4 Decimals

97.RECORD HOLDERS The late Florence GrifﬁthJoyner of the United States holds the women’s world record in the 100-meter sprint: 10.49 seconds. Libby Trickett of Australia holds the women’s world

record in the 100-meter freestyle swim: 52.88 seconds. How much faster did Grifﬁth-Joyner run the 100 meters than Trickett swam it? (Source: The World Almanac and Book of Facts, 2009)

98.WEATHER REPORTS Barometric pressure readings are recorded on the weather map below. In a low-pressure area (L on the map), the weather is often stormy. The weather is usually fair in a highpressure area (H). What is the difference in readings between the areas of highest and lowest pressure?

28.9

L
	29.4
29.4	30.0
29.4

30.329.7

30.7

99.BANKING A businesswoman deposited several checks in her company’s bank account, as shown on the deposit slip below. Find the Subtotal line on the slip by adding the amounts of the checks and total from the reverse side. If the woman wanted to get $25 in cash back from the teller, what should she write as the Total deposit on the slip?

Deposit slip

Cash
Checks (properly endorsed)	116	10
	47	93
Total from reverse side	359	16
Subtotal
Less cash	25	00

Total deposit

100.SPORTS PAGES Decimals are often used in the sports pages of newspapers. Two examples are given below.

a.“German bobsledders set a world record today with a ﬁnal run of 53.03 seconds, ﬁnishing ahead of the Italian team by only fourteen thousandths of a second.” What was the time for the Italian bobsled team?

b.“The women’s ﬁgure skating title was decided by only thirty-three hundredths of a point.” If the winner’s point total was 102.71, what was the second-place ﬁnisher’s total? (Hint: The highest score wins in a ﬁgure skating contest.)

101.Suppose certain portions of a patient’s morning (A.M.) temperature chart were not ﬁlled in. Use the given information to complete the chart below.

(Hint: 98.6°F is considered normal.)

from Campus to Careers

Home Health Aide

Tetra Images/Getty Images

	Patient’s A.M.	Amount
Day of week	temperature	above normal

Monday	99.7°
Tuesday		2.5°
Wednesday	98.6°
Thursday	100.0°
Friday		0.9°

102.QUALITY CONTROL An electronics company has strict speciﬁcations for the silicon chips it uses in its computers. The company only installs chips that are within 0.05 centimeter of the indicated thickness. The table below gives that speciﬁcations for two types of chips. Fill in the blanks to complete the chart.

	Thickness	Acceptable range
	Thickness
Chip type	speciﬁcation	Low	High

A	0.78 cm
B	0.643 cm

103.FLIGHT PATHS Find the added distance a plane must travel to avoid ﬂying through the storm.

		9.65 mi
	14.57 mi	16.18 mi
	14.57 mi	Storm
		Storm
		20.39 mi

104.TELEVISION The following illustration shows the six most-watched television shows of all time (excluding Super Bowl games and the Olympics).

a.What was the combined total audience of all six shows?

b.How many more people watched the last episode of “MASH” than watched the last episode of “Seinfeld”?

c.How many more people would have had to watch the last “Seinfeld” to move it into a tie for ﬁfth place?

(millions)	106	All-Time Largest U.S. TV Audiences
	106
		83.6	80.5	77.4	76.7
				77.4		76.3
Viewing audience

Last	"Dallas:	Last	"The Day	"Roots,"	Last
"MASH," Who Shot "Cheers,"			After,"	Part 8,	"Seinfeld,"
1983	J.R.?" 1980	1994	1983	1977	1999

Source: Nielsen Media Research

105.THE HOME SHOPPING NETWORK The illustration shows a description of a cookware set that was sold on television.

a.Find the difference between the manufacturer’s suggested retail price (MSRP) and the sale price.

b.Including shipping and handling (S & H), how much will the cookware set cost?

Item 229-442

Continental 9-piece

Cookware Set

Stainless steel

MSRP $149.79

HSN Price	$59.85
On Sale	$47.85
S & H	$7.95

106.VEHICLE SPECIFICATIONS Certain dimensions of a compact car are shown. Find the wheelbase of the car.

43.5 in.

40.9 in.

Wheelbase

187.8 in.

4.2 Adding and Subtracting Decimals

343

WRITING

107.Explain why we line up the decimal points and corresponding place-value columns when adding decimals.

108.Explain why we can write additional zeros to the right of a decimal such as 7.89 without affecting its value.

109.Explain what is wrong with the work shown below.

203.56

370.43

204.36

110. Consider the following addition:

23.7

41.9

12.8

78.4

Explain the meaning of the small red 2 written above the ones column.

111.Write a set of instructions that explains the twocolumn borrowing process shown below.

4 10 10

2.650 0

1.3 2 4 6

1.32 5 4

112.Explain why it is easier to add the decimals 0.3 and

0.17than the fractions 103 and 10017 .

REVIEW

Perform the indicated operations.

113.a. 5 12

b.45 125

c.45 125

d.45 125

114.a. 8 6

b.38 16

c.38 16

d.38 16

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