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  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Use the Language of Algebra
    4. 1.3 Add and Subtract Integers
    5. 1.4 Multiply and Divide Integers
    6. 1.5 Visualize Fractions
    7. 1.6 Add and Subtract Fractions
    8. 1.7 Decimals
    9. 1.8 The Real Numbers
    10. 1.9 Properties of Real Numbers
    11. 1.10 Systems of Measurement
    12. Key Terms
    13. Key Concepts
    14. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations and Inequalities
    1. Introduction
    2. 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 2.2 Solve Equations using the Division and Multiplication Properties of Equality
    4. 2.3 Solve Equations with Variables and Constants on Both Sides
    5. 2.4 Use a General Strategy to Solve Linear Equations
    6. 2.5 Solve Equations with Fractions or Decimals
    7. 2.6 Solve a Formula for a Specific Variable
    8. 2.7 Solve Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Math Models
    1. Introduction
    2. 3.1 Use a Problem-Solving Strategy
    3. 3.2 Solve Percent Applications
    4. 3.3 Solve Mixture Applications
    5. 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
    6. 3.5 Solve Uniform Motion Applications
    7. 3.6 Solve Applications with Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Graphs
    1. Introduction
    2. 4.1 Use the Rectangular Coordinate System
    3. 4.2 Graph Linear Equations in Two Variables
    4. 4.3 Graph with Intercepts
    5. 4.4 Understand Slope of a Line
    6. 4.5 Use the Slope-Intercept Form of an Equation of a Line
    7. 4.6 Find the Equation of a Line
    8. 4.7 Graphs of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Systems of Linear Equations
    1. Introduction
    2. 5.1 Solve Systems of Equations by Graphing
    3. 5.2 Solving Systems of Equations by Substitution
    4. 5.3 Solve Systems of Equations by Elimination
    5. 5.4 Solve Applications with Systems of Equations
    6. 5.5 Solve Mixture Applications with Systems of Equations
    7. 5.6 Graphing Systems of Linear Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Polynomials
    1. Introduction
    2. 6.1 Add and Subtract Polynomials
    3. 6.2 Use Multiplication Properties of Exponents
    4. 6.3 Multiply Polynomials
    5. 6.4 Special Products
    6. 6.5 Divide Monomials
    7. 6.6 Divide Polynomials
    8. 6.7 Integer Exponents and Scientific Notation
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Factoring
    1. Introduction
    2. 7.1 Greatest Common Factor and Factor by Grouping
    3. 7.2 Factor Trinomials of the Form x2+bx+c
    4. 7.3 Factor Trinomials of the Form ax2+bx+c
    5. 7.4 Factor Special Products
    6. 7.5 General Strategy for Factoring Polynomials
    7. 7.6 Quadratic Equations
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Rational Expressions and Equations
    1. Introduction
    2. 8.1 Simplify Rational Expressions
    3. 8.2 Multiply and Divide Rational Expressions
    4. 8.3 Add and Subtract Rational Expressions with a Common Denominator
    5. 8.4 Add and Subtract Rational Expressions with Unlike Denominators
    6. 8.5 Simplify Complex Rational Expressions
    7. 8.6 Solve Rational Equations
    8. 8.7 Solve Proportion and Similar Figure Applications
    9. 8.8 Solve Uniform Motion and Work Applications
    10. 8.9 Use Direct and Inverse Variation
    11. Key Terms
    12. Key Concepts
    13. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Roots and Radicals
    1. Introduction
    2. 9.1 Simplify and Use Square Roots
    3. 9.2 Simplify Square Roots
    4. 9.3 Add and Subtract Square Roots
    5. 9.4 Multiply Square Roots
    6. 9.5 Divide Square Roots
    7. 9.6 Solve Equations with Square Roots
    8. 9.7 Higher Roots
    9. 9.8 Rational Exponents
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Quadratic Equations
    1. Introduction
    2. 10.1 Solve Quadratic Equations Using the Square Root Property
    3. 10.2 Solve Quadratic Equations by Completing the Square
    4. 10.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 10.4 Solve Applications Modeled by Quadratic Equations
    6. 10.5 Graphing Quadratic Equations in Two Variables
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
  13. Index
Be Prepared 1.7

A more thorough introduction to the topics covered in this section can be found in the Prealgebra chapter, Decimals.

Name and Write Decimals

Decimals are another way of writing fractions whose denominators are powers of 10.

0.1=1100.1is “one tenth”0.01=11000.01is “one hundredth”0.001=11,0000.001 is “one thousandth”0.0001=110,0000.0001 is “one ten-thousandth”0.1=1100.1is “one tenth”0.01=11000.01is “one hundredth”0.001=11,0000.001 is “one thousandth”0.0001=110,0000.0001 is “one ten-thousandth”

Notice that “ten thousand” is a number larger than one, but “one ten-thousandth” is a number smaller than one. The “th” at the end of the name tells you that the number is smaller than one.

When we name a whole number, the name corresponds to the place value based on the powers of ten. We read 10,000 as “ten thousand” and 10,000,000 as “ten million.” Likewise, the names of the decimal places correspond to their fraction values. Figure 1.14 shows the names of the place values to the left and right of the decimal point.

A table is shown with the title Place Value. From left to right the row reads “Hundred thousands,” “Ten thousands,” “Thousands,” “Hundreds,” “Tens,” and “Ones.” Then there is a blank cell and below it is a decimal point. To the right of this, the cells read “Tenths,” “Hundredths,” “Thousandths,” “Ten-thousandths,” and “Hundred-thousandths.”
Figure 1.14 Place value of decimal numbers are shown to the left and right of the decimal point.

Example 1.91

How to Name Decimals

Name the decimal 4.3.

Try It 1.181

Name the decimal: 6.7.6.7.

Try It 1.182

Name the decimal: 5.8.5.8.

We summarize the steps needed to name a decimal below.

How To

Name a Decimal.

  1. Step 1. Name the number to the left of the decimal point.
  2. Step 2. Write “and” for the decimal point.
  3. Step 3. Name the “number” part to the right of the decimal point as if it were a whole number.
  4. Step 4. Name the decimal place of the last digit.

Example 1.92

Name the decimal: −15.571.−15.571.

Try It 1.183

Name the decimal: −13.461.−13.461.

Try It 1.184

Name the decimal: −2.053.−2.053.

When we write a check we write both the numerals and the name of the number. Let’s see how to write the decimal from the name.

Example 1.93

How to Write Decimals

Write “fourteen and twenty-four thousandths” as a decimal.

Try It 1.185

Write as a decimal: thirteen and sixty-eight thousandths.

Try It 1.186

Write as a decimal: five and ninety-four thousandths.

We summarize the steps to writing a decimal.

How To

Write a decimal.

  1. Step 1. Look for the word “and”—it locates the decimal point.
    • Place a decimal point under the word “and.” Translate the words before “and” into the whole number and place it to the left of the decimal point.
    • If there is no “and,” write a “0” with a decimal point to its right.
  2. Step 2. Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word.
  3. Step 3. Translate the words after “and” into the number to the right of the decimal point. Write the number in the spaces—putting the final digit in the last place.
  4. Step 4. Fill in zeros for place holders as needed.

Round Decimals

Rounding decimals is very much like rounding whole numbers. We will round decimals with a method based on the one we used to round whole numbers.

Example 1.94

How to Round Decimals

Round 18.379 to the nearest hundredth.

Try It 1.187

Round to the nearest hundredth: 1.047.1.047.

Try It 1.188

Round to the nearest hundredth: 9.173.9.173.

We summarize the steps for rounding a decimal here.


How To

Round Decimals.

  1. Step 1. Locate the given place value and mark it with an arrow.
  2. Step 2. Underline the digit to the right of the place value.
  3. Step 3. Is this digit greater than or equal to 5?
    • Yes—add 1 to the digit in the given place value.
    • No—do not change the digit in the given place value.
  4. Step 4. Rewrite the number, deleting all digits to the right of the rounding digit.

Example 1.95

Round 18.379 to the nearest tenth whole number.

Try It 1.189

Round 6.5826.582 to the nearest hundredth tenth whole number.

Try It 1.190

Round 15.217515.2175 to the nearest thousandth hundredth tenth.

Add and Subtract Decimals

To add or subtract decimals, we line up the decimal points. By lining up the decimal points this way, we can add or subtract the corresponding place values. We then add or subtract the numbers as if they were whole numbers and then place the decimal point in the sum.

How To

Add or Subtract Decimals.

  1. Step 1. Write the numbers so the decimal points line up vertically.
  2. Step 2. Use zeros as place holders, as needed.
  3. Step 3. Add or subtract the numbers as if they were whole numbers. Then place the decimal point in the answer under the decimal points in the given numbers.

Example 1.96

Add: 23.5+41.38.23.5+41.38.

Try It 1.191

Add: 4.8+11.69.4.8+11.69.

Try It 1.192

Add: 5.123+18.47.5.123+18.47.

Example 1.97

Subtract: 2014.65.2014.65.

Try It 1.193

Subtract: 109.58.109.58.

Try It 1.194

Subtract: 5037.42.5037.42.

Multiply and Divide Decimals

Multiplying decimals is very much like multiplying whole numbers—we just have to determine where to place the decimal point. The procedure for multiplying decimals will make sense if we first convert them to fractions and then multiply.

So let’s see what we would get as the product of decimals by converting them to fractions first. We will do two examples side-by-side. Look for a pattern!

.
Convert to fractions. .
Multiply. .
Convert to decimals. .

Notice, in the first example, we multiplied two numbers that each had one digit after the decimal point and the product had two decimal places. In the second example, we multiplied a number with one decimal place by a number with two decimal places and the product had three decimal places.

We multiply the numbers just as we do whole numbers, temporarily ignoring the decimal point. We then count the number of decimal points in the factors and that sum tells us the number of decimal places in the product.

The rules for multiplying positive and negative numbers apply to decimals, too, of course!

When multiplying two numbers,

  • if their signs are the same the product is positive.
  • if their signs are different the product is negative.

When we multiply signed decimals, first we determine the sign of the product and then multiply as if the numbers were both positive. Finally, we write the product with the appropriate sign.

How To

Multiply Decimals.

  1. Step 1. Determine the sign of the product.
  2. Step 2. Write in vertical format, lining up the numbers on the right. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.
  3. Step 3. Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors.
  4. Step 4. Write the product with the appropriate sign.

Example 1.98

Multiply: (−3.9)(4.075).(−3.9)(4.075).

Try It 1.195

Multiply: −4.5(6.107).−4.5(6.107).

Try It 1.196

Multiply: −10.79(8.12).−10.79(8.12).

In many of your other classes, especially in the sciences, you will multiply decimals by powers of 10 (10, 100, 1000, etc.). If you multiply a few products on paper, you may notice a pattern relating the number of zeros in the power of 10 to number of decimal places we move the decimal point to the right to get the product.

How To

Multiply a Decimal by a Power of Ten.

  1. Step 1. Move the decimal point to the right the same number of places as the number of zeros in the power of 10.
  2. Step 2. Add zeros at the end of the number as needed.

Example 1.99

Multiply 5.63 by 10 by 100 by 1,000.

Try It 1.197

Multiply 2.58 by 10 by 100 by 1,000.

Try It 1.198

Multiply 14.2 by 10 by 100 by 1,000.

Just as with multiplication, division of decimals is very much like dividing whole numbers. We just have to figure out where the decimal point must be placed.

To divide decimals, determine what power of 10 to multiply the denominator by to make it a whole number. Then multiply the numerator by that same power of 10.10. Because of the equivalent fractions property, we haven’t changed the value of the fraction! The effect is to move the decimal points in the numerator and denominator the same number of places to the right. For example:

0.80.40.8(10)0.4(10)840.80.40.8(10)0.4(10)84

We use the rules for dividing positive and negative numbers with decimals, too. When dividing signed decimals, first determine the sign of the quotient and then divide as if the numbers were both positive. Finally, write the quotient with the appropriate sign.

We review the notation and vocabulary for division:

adividend÷bdivisor=cquotientbdivisorcquotientadividendadividend÷bdivisor=cquotientbdivisorcquotientadividend

We’ll write the steps to take when dividing decimals, for easy reference.

How To

Divide Decimals.

  1. Step 1. Determine the sign of the quotient.
  2. Step 2. Make the divisor a whole number by “moving” the decimal point all the way to the right. “Move” the decimal point in the dividend the same number of places—adding zeros as needed.
  3. Step 3. Divide. Place the decimal point in the quotient above the decimal point in the dividend.
  4. Step 4. Write the quotient with the appropriate sign.

Example 1.100

Divide: −25.65÷(−0.06).−25.65÷(−0.06).

Try It 1.199

Divide: −23.492÷(−0.04).−23.492÷(−0.04).

Try It 1.200

Divide: −4.11÷(−0.12).−4.11÷(−0.12).

A common application of dividing whole numbers into decimals is when we want to find the price of one item that is sold as part of a multi-pack. For example, suppose a case of 24 water bottles costs $3.99. To find the price of one water bottle, we would divide $3.99 by 24. We show this division in Example 1.101. In calculations with money, we will round the answer to the nearest cent (hundredth).

Example 1.101

Divide: $3.99÷24.$3.99÷24.

Try It 1.201

Divide: $6.99÷36.$6.99÷36.

Try It 1.202

Divide: $4.99÷12.$4.99÷12.

Convert Decimals, Fractions, and Percents

We convert decimals into fractions by identifying the place value of the last (farthest right) digit. In the decimal 0.03 the 3 is in the hundredths place, so 100 is the denominator of the fraction equivalent to 0.03.

00.03=310000.03=3100

Notice, when the number to the left of the decimal is zero, we get a fraction whose numerator is less than its denominator. Fractions like this are called proper fractions.

The steps to take to convert a decimal to a fraction are summarized in the procedure box.

How To

Convert a Decimal to a Proper Fraction.

  1. Step 1. Determine the place value of the final digit.
  2. Step 2. Write the fraction.
    • numerator—the “numbers” to the right of the decimal point
    • denominator—the place value corresponding to the final digit

Example 1.102

Write 0.374 as a fraction.

Try It 1.203

Write 0.234 as a fraction.

Try It 1.204

Write 0.024 as a fraction.

We’ve learned to convert decimals to fractions. Now we will do the reverse—convert fractions to decimals. Remember that the fraction bar means division. So 4545 can be written 4÷54÷5 or 54.54. This leads to the following method for converting a fraction to a decimal.

How To

Convert a Fraction to a Decimal.

To convert a fraction to a decimal, divide the numerator of the fraction by the denominator of the fraction.

Example 1.103

Write 5858 as a decimal.

Try It 1.205

Write 7878 as a decimal.

Try It 1.206

Write 3838 as a decimal.

When we divide, we will not always get a zero remainder. Sometimes the quotient ends up with a decimal that repeats. A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly. A bar is placed over the repeating block of digits to indicate it repeats.

Repeating Decimal

A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly.

A bar is placed over the repeating block of digits to indicate it repeats.

Example 1.104

Write 43224322 as a decimal.

Try It 1.207

Write 27112711 as a decimal.

Try It 1.208

Write 51225122 as a decimal.

Sometimes we may have to simplify expressions with fractions and decimals together.

Example 1.105

Simplify: 78+6.4.78+6.4.

Try It 1.209

Simplify: 38+4.9.38+4.9.

Try It 1.210

Simplify: 5.7+1320.5.7+1320.

A percent is a ratio whose denominator is 100. Percent means per hundred. We use the percent symbol, %, to show percent.

Percent

A percent is a ratio whose denominator is 100.

Since a percent is a ratio, it can easily be expressed as a fraction. Percent means per 100, so the denominator of the fraction is 100. We then change the fraction to a decimal by dividing the numerator by the denominator.

6%6% 78%78% 135%135%
Write as a ratio with denominator 100. 61006100 7810078100 135100135100
Change the fraction to a decimal by dividing the numerator by the denominator. 0.060.06 0.780.78 1.351.35
Table 1.30

Do you see the pattern? To convert a percent number to a decimal number, we move the decimal point two places to the left.

The first part of this figure shows 6% with an arrow drawn from between the 6 and the percentage sign to the space to the left of 6 and then to the space further to the left of that space. Below this, the number 0.06 is given. The second part of this figure shows 78% with an arrow drawn from between the 8 and the percentage sign to the space between the 7 and the 8 and then to the space to the left of the 7. Below this, the number 0.78 is given. The third part of this figure shows 2.7% with an arrow drawn from the decimal point to the space to the left of the 2 and then to the space further to the left of that space. Below this, the number 0.027 is given. The fourth part of this figure shows 135% with an arrow drawn from between the 5 and the percentage sign to the space between 3 and 5 and then to the space between 1 and 3. Below this, the number 1.35 is given.

Example 1.106

Convert each percent to a decimal: 62% 135% 35.7%.

Try It 1.211

Convert each percent to a decimal: 9%9% 87%87% 3.9%.

Try It 1.212

Convert each percent to a decimal: 3% 91% 8.3%.

Converting a decimal to a percent makes sense if we remember the definition of percent and keep place value in mind.

To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is 100, it is easy to change that fraction to a percent.

0.830.83 1.051.05 0.0750.075
Write as a fraction. 8310083100 1510015100 751000751000
The denominator is 100. 105100105100 7.51007.5100
Write the ratio as a percent. 83%83% 105%105% 7.5%7.5%
Table 1.31

Recognize the pattern? To convert a decimal to a percent, we move the decimal point two places to the right and then add the percent sign.

The first part of this figure shows 0.05 with an arrow drawn from the decimal point to the space between 0 and 5 and then to the space after 5. Below this, the number 5% is given. The second part of this figure shows 0.83 with an arrow drawn from the decimal point to the space between 8 and 3 and then to the space after 3. Below this, the number 83% is given. The third part of this figure shows 1.05 with an arrow drawn from the decimal point to the space between 0 and 5 and then to the space after 5. Below this, the number 105% is given. The fourth part of this figure shows 0.075 with an arrow drawn from the decimal point to the space between 0 and 7 and then to the space between 7 and 5. Below this, the number 7.5% is given. The fifth part of this figure shows 0.3 with an arrow drawn from the decimal point to the space after 3 and then to space further to the right of that 3. Below this, the number 30% is given.

Example 1.107

Convert each decimal to a percent: 0.51 1.25 0.093.

Try It 1.213

Convert each decimal to a percent: 0.17 1.75 0.0825.

Try It 1.214

Convert each decimal to a percent: 0.41 2.25 0.0925.

Section 1.7 Exercises

Practice Makes Perfect

Name and Write Decimals

In the following exercises, write as a decimal.

531.

Twenty-nine and eighty-one hundredths

532.

Sixty-one and seventy-four hundredths

533.

Seven tenths

534.

Six tenths

535.

Twenty-nine thousandth

536.

Thirty-five thousandths

537.

Negative eleven and nine ten-thousandths

538.

Negative fifty-nine and two ten-thousandths

In the following exercises, name each decimal.

539.

5.5

540.

14.02

541.

8.71

542.

2.64

543.

0.002

544.

0.479

545.

17.917.9

546.

31.431.4

Round Decimals

In the following exercises, round each number to the nearest tenth.

547.

0.67

548.

0.49

549.

2.84

550.

4.63

In the following exercises, round each number to the nearest hundredth.

551.

0.845

552.

0.761

553.

0.299

554.

0.697

555.

4.098

556.

7.096

In the following exercises, round each number to the nearest hundredth tenth whole number.

557.

5.781

558.

1.6381

559.

63.479

560.

84.28184.281

Add and Subtract Decimals

In the following exercises, add or subtract.

561.

16.92+7.5616.92+7.56

562.

248.2591.29248.2591.29

563.

21.7630.9921.7630.99

564.

38.6+13.6738.6+13.67

565.

−16.5324.38−16.5324.38

566.

−19.4732.58−19.4732.58

567.

−38.69+31.47−38.69+31.47

568.

29.83+19.7629.83+19.76

569.

72.510072.5100

570.

86.210086.2100

571.

15+0.7315+0.73

572.

27+0.8727+0.87

573.

91.95(−10.462)91.95(−10.462)

574.

94.69(−12.678)94.69(−12.678)

575.

55.013.755.013.7

576.

59.084.659.084.6

577.

2.517.42.517.4

578.

3.846.13.846.1

Multiply and Divide Decimals

In the following exercises, multiply.

579.

(0.24)(0.6)(0.24)(0.6)

580.

(0.81)(0.3)(0.81)(0.3)

581.

(5.9)(7.12)(5.9)(7.12)

582.

(2.3)(9.41)(2.3)(9.41)

583.

(−4.3)(2.71)(−4.3)(2.71)

584.

(−8.5)(1.69)(−8.5)(1.69)

585.

(−5.18)(−65.23)(−5.18)(−65.23)

586.

(−9.16)(−68.34)(−9.16)(−68.34)

587.

(0.06)(21.75)(0.06)(21.75)

588.

(0.08)(52.45)(0.08)(52.45)

589.

(9.24)(10)(9.24)(10)

590.

(6.531)(10)(6.531)(10)

591.

(55.2)(1000)(55.2)(1000)

592.

(99.4)(1000)(99.4)(1000)

In the following exercises, divide.

593.

4.75÷254.75÷25

594.

12.04÷4312.04÷43

595.

$117.25÷48$117.25÷48

596.

$109.24÷36$109.24÷36

597.

0.6÷0.20.6÷0.2

598.

0.8÷0.40.8÷0.4

599.

1.44÷(−0.3)1.44÷(−0.3)

600.

1.25÷(−0.5)1.25÷(−0.5)

601.

−1.75÷(−0.05)−1.75÷(−0.05)

602.

−1.15÷(−0.05)−1.15÷(−0.05)

603.

5.2÷2.55.2÷2.5

604.

6.5÷3.256.5÷3.25

605.

11÷0.5511÷0.55

606.

14÷0.3514÷0.35

Convert Decimals, Fractions and Percents

In the following exercises, write each decimal as a fraction.

607.

0.04

608.

0.19

609.

0.52

610.

0.78

611.

1.25

612.

1.35

613.

0.375

614.

0.464

615.

0.095

616.

0.085

In the following exercises, convert each fraction to a decimal.

617.

17201720

618.

13201320

619.

114114

620.

174174

621.

3102531025

622.

2842528425

623.

15111511

624.

18111811

625.

1511115111

626.

2511125111

627.

2.4+582.4+58

628.

3.9+9203.9+920

In the following exercises, convert each percent to a decimal.

629.

1%

630.

2%

631.

63%

632.

71%

633.

150%

634.

250%

635.

21.4%

636.

39.3%

637.

7.8%

638.

6.4%

In the following exercises, convert each decimal to a percent.

639.

0.01

640.

0.03

641.

1.35

642.

1.56

643.

3

644.

4

645.

0.0875

646.

0.0625

647.

2.254

648.

2.317

Everyday Math

649.

Salary Increase Danny got a raise and now makes $58,965.95 a year. Round this number to the nearest dollar thousand dollars ten thousand dollars.

650.

New Car Purchase Selena’s new car cost $23,795.95. Round this number to the nearest dollar thousand dollars ten thousand dollars.

651.

Sales Tax Hyo Jin lives in San Diego. She bought a refrigerator for $1,624.99 and when the clerk calculated the sales tax it came out to exactly $142.186625. Round the sales tax to the nearest penny and dollar.

652.

Sales Tax Jennifer bought a $1,038.99 dining room set for her home in Cincinnati. She calculated the sales tax to be exactly $67.53435. Round the sales tax to the nearest penny and dollar.

653.

Paycheck Annie has two jobs. She gets paid $14.04 per hour for tutoring at City College and $8.75 per hour at a coffee shop. Last week she tutored for 8 hours and worked at the coffee shop for 15 hours. How much did she earn? If she had worked all 23 hours as a tutor instead of working both jobs, how much more would she have earned?

654.

Paycheck Jake has two jobs. He gets paid $7.95 per hour at the college cafeteria and $20.25 at the art gallery. Last week he worked 12 hours at the cafeteria and 5 hours at the art gallery. How much did he earn? If he had worked all 17 hours at the art gallery instead of working both jobs, how much more would he have earned?

Writing Exercises

655.

How does knowing about US money help you learn about decimals?

656.

Explain how you write “three and nine hundredths” as a decimal.

657.

Without solving the problem “44 is 80% of what number” think about what the solution might be. Should it be a number that is greater than 44 or less than 44? Explain your reasoning.

658.

When the Szetos sold their home, the selling price was 500% of what they had paid for the house 30 years ago. Explain what 500% means in this context.

Self Check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has six rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “name and write decimals,” “round decimals,” “add and subtract decimals,” “multiply and divide decimals,” and “convert decimals, fractions and percents.” The rest of the cells are blank.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

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