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Prealgebra 2e

5.1 Decimals

Prealgebra 2e5.1 Decimals
  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. 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
    11. Chapter 11
  17. Index

Learning Objectives

By the end of this section, you will be able to:

  • Name decimals
  • Write decimals
  • Convert decimals to fractions or mixed numbers
  • Locate decimals on the number line
  • Order decimals
  • Round decimals
Be Prepared 5.1

Before you get started, take this readiness quiz.

Name the number 4,926,0154,926,015 in words.
If you missed this problem, review Example 1.4.

Be Prepared 5.2

Round 748748 to the nearest ten.
If you missed this problem, review Example 1.9.

Be Prepared 5.3

Locate 310310 on a number line.
If you missed this problem, review Example 4.16.

Name Decimals

You probably already know quite a bit about decimals based on your experience with money. Suppose you buy a sandwich and a bottle of water for lunch. If the sandwich costs $3.45$3.45, the bottle of water costs $1.25$1.25, and the total sales tax is $0.33$0.33, what is the total cost of your lunch?

A vertical addition problem is shown. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.

The total is $5.03.$5.03. Suppose you pay with a $5$5 bill and 33 pennies. Should you wait for change? No, $5$5 and 33 pennies is the same as $5.03.$5.03.

Because 100 pennies=$1,100 pennies=$1, each penny is worth 11001100 of a dollar. We write the value of one penny as $0.01,$0.01, since 0.01=1100.0.01=1100.

Writing a number with a decimal is known as decimal notation. It is a way of showing parts of a whole when the whole is a power of ten. In other words, decimals are another way of writing fractions whose denominators are powers of ten. Just as the counting numbers are based on powers of ten, decimals are based on powers of ten. Table 5.1 shows the counting numbers.

Counting number Name
11 One
10=1010=10 Ten
10·10=10010·10=100 One hundred
10·10·10=100010·10·10=1000 One thousand
10·10·10·10=10,00010·10·10·10=10,000 Ten thousand
Table 5.1

How are decimals related to fractions? Table 5.2 shows the relation.

Decimal Fraction Name
0.10.1 110110 One tenth
0.010.01 11001100 One hundredth
0.0010.001 11,00011,000 One thousandth
0.00010.0001 110,000110,000 One ten-thousandth
Table 5.2

When we name a whole number, the name corresponds to the place value based on the powers of ten. In Whole Numbers, we learned to read 10,00010,000 as ten thousand. Likewise, the names of the decimal places correspond to their fraction values. Notice how the place value names in Figure 5.2 relate to the names of the fractions from Table 5.2.

A chart is shown labeled “Place Value”. There are 12 columns. The columns are labeled, from left to right, Hundred thousands, Ten thousands, Thousands, Hundreds, Tens, Ones, Decimal Point, Tenths, Hundredths, Thousandths, Ten-thousandths, Hundred-thousandths.
Figure 5.2 This chart illustrates place values to the left and right of the decimal point.

Notice two important facts shown in Figure 5.2.

  • The “th” at the end of the name means the number is a fraction. “One thousand” is a number larger than one, but “one thousandth” is a number smaller than one.
  • The tenths place is the first place to the right of the decimal, but the tens place is two places to the left of the decimal.

Remember that $5.03$5.03 lunch? We read $5.03$5.03 as five dollars and three cents. Naming decimals (those that don’t represent money) is done in a similar way. We read the number 5.035.03 as five and three hundredths.

We sometimes need to translate a number written in decimal notation into words. As shown in Figure 5.3, we write the amount on a check in both words and numbers.

An image of a check is shown. The check is made out to Jane Doe. It shows the number $152.65 and says in words, “One hundred fifty two and 65 over 100 dollars.”
Figure 5.3 When we write a check, we write the amount as a decimal number as well as in words. The bank looks at the check to make sure both numbers match. This helps prevent errors.
Let’s try naming a decimal, such as 15.68.
We start by naming the number to the left of the decimal. fifteen______
We use the word “and” to indicate the decimal point. fifteen and_____
Then we name the number to the right of the decimal point as if it were a whole number. fifteen and sixty-eight_____
Last, name the decimal place of the last digit. fifteen and sixty-eight hundredths

The number 15.6815.68 is read fifteen and sixty-eight hundredths.

How To

Name a decimal number.

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

Example 5.1

Name each decimal: 4.34.3 2.452.45 0.0090.009 −15.571.−15.571.

Try It 5.1

Name each decimal:

6.76.7 19.5819.58 0.0180.018 −2.053−2.053

Try It 5.2

Name each decimal:

5.85.8 3.573.57 0.0050.005 −13.461−13.461

Write Decimals

Now we will translate the name of a decimal number into decimal notation. We will reverse the procedure we just used.

Let’s start by writing the number six and seventeen hundredths:

six and seventeen hundredths
The word and tells us to place a decimal point. ___.___
The word before and is the whole number; write it to the left of the decimal point. 6._____
The decimal part is seventeen hundredths.
Mark two places to the right of the decimal point for hundredths.
6._ _
Write the numerals for seventeen in the places marked. 6.17

Example 5.2

Write fourteen and thirty-seven hundredths as a decimal.

Try It 5.3

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

Try It 5.4

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

How To

Write a decimal number from its name.

  1. Step 1. Look for the word “and”—it locates the decimal point.
  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.
    • 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.
  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.

The second bullet in Step 2 is needed for decimals that have no whole number part, like ‘nine thousandths’. We recognize them by the words that indicate the place value after the decimal – such as ‘tenths’ or ‘hundredths.’ Since there is no whole number, there is no ‘and.’ We start by placing a zero to the left of the decimal and continue by filling in the numbers to the right, as we did above.

Example 5.3

Write twenty-four thousandths as a decimal.

Try It 5.5

Write as a decimal: fifty-eight thousandths.

Try It 5.6

Write as a decimal: sixty-seven thousandths.

Before we move on to our next objective, think about money again. We know that $1$1 is the same as $1.00.$1.00. The way we write $1(or$1.00)$1(or$1.00) depends on the context. In the same way, integers can be written as decimals with as many zeros as needed to the right of the decimal.

5=5.0−2=−2.05=5.00−2=−2.005=5.000−2=−2.0005=5.0−2=−2.05=5.00−2=−2.005=5.000−2=−2.000
and so on…and so on…

Convert Decimals to Fractions or Mixed Numbers

We often need to rewrite decimals as fractions or mixed numbers. Let’s go back to our lunch order to see how we can convert decimal numbers to fractions. We know that $5.03$5.03 means 55 dollars and 33 cents. Since there are 100100 cents in one dollar, 33 cents means 31003100 of a dollar, so 0.03=3100.0.03=3100.

We convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal 0.03,0.03, the 33 is in the hundredths place, so 100100 is the denominator of the fraction equivalent to 0.03.0.03.

0.03=31000.03=3100

For our $5.03$5.03 lunch, we can write the decimal 5.035.03 as a mixed number.

5.03=531005.03=53100

Notice that when the number to the left of the decimal is zero, we get a proper fraction. When the number to the left of the decimal is not zero, we get a mixed number.

How To

Convert a decimal number to a fraction or mixed number.

  1. Step 1. Look at the number to the left of the decimal.
    • If it is zero, the decimal converts to a proper fraction.
    • If it is not zero, the decimal converts to a mixed number.
      • Write the whole number.
  2. Step 2. Determine the place value of the final digit.
  3. Step 3. Write the fraction.
    • numerator—the ‘numbers’ to the right of the decimal point
    • denominator—the place value corresponding to the final digit
  4. Step 4. Simplify the fraction, if possible.

Example 5.4

Write each of the following decimal numbers as a fraction or a mixed number:

4.094.09 3.73.7 −0.286−0.286

Try It 5.7

Write as a fraction or mixed number. Simplify the answer if possible.

5.35.3 6.076.07 −0.234−0.234

Try It 5.8

Write as a fraction or mixed number. Simplify the answer if possible.

8.78.7 1.031.03 −0.024−0.024

Locate Decimals on the Number Line

Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.

Example 5.5

Locate 0.40.4 on a number line.

Try It 5.9

Locate 0.60.6 on a number line.

Try It 5.10

Locate 0.90.9 on a number line.

Example 5.6

Locate −0.74−0.74 on a number line.

Try It 5.11

Locate −0.63−0.63 on a number line.

Try It 5.12

Locate −0.25−0.25 on a number line.

Order Decimals

Which is larger, 0.040.04 or 0.40?0.40?

If you think of this as money, you know that $0.40$0.40 (forty cents) is greater than $0.04$0.04 (four cents). So,

0.40>0.040.40>0.04

In previous chapters, we used the number line to order numbers.

a<bais less thanbwhenais to the left ofbon the number linea>bais greater thanbwhenais to the right ofbon the number linea<bais less thanbwhenais to the left ofbon the number linea>bais greater thanbwhenais to the right ofbon the number line

Where are 0.040.04 and 0.400.40 located on the number line?

A number line is shown with 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 labeled. There is a red dot between 0.0 and 0.1 labeled as 0.04. There is another red dot at 0.4.

We see that 0.400.40 is to the right of 0.04.0.04. So we know 0.40>0.04.0.40>0.04.

How does 0.310.31 compare to 0.308?0.308? This doesn’t translate into money to make the comparison easy. But if we convert 0.310.31 and 0.3080.308 to fractions, we can tell which is larger.

0.310.31 0.3080.308
Convert to fractions. 3110031100 30810003081000
We need a common denominator to compare them. . 3081000 3081000
31010003101000 30810003081000

Because 310>308,310>308, we know that 3101000>3081000.3101000>3081000. Therefore, 0.31>0.308.0.31>0.308.

Notice what we did in converting 0.310.31 to a fraction—we started with the fraction 3110031100 and ended with the equivalent fraction 3101000.3101000. Converting 31010003101000 back to a decimal gives 0.310.0.310. So 0.310.31 is equivalent to 0.310.0.310. Writing zeros at the end of a decimal does not change its value.

31100=3101000and0.31=0.31031100=3101000and0.31=0.310

If two decimals have the same value, they are said to be equivalent decimals.

0.31=0.3100.31=0.310

We say 0.310.31 and 0.3100.310 are equivalent decimals.

Equivalent Decimals

Two decimals are equivalent decimals if they convert to equivalent fractions.

Remember, writing zeros at the end of a decimal does not change its value.

How To

Order decimals.

  1. Step 1. Check to see if both numbers have the same number of decimal places. If not, write zeros at the end of the one with fewer digits to make them match.
  2. Step 2. Compare the numbers to the right of the decimal point as if they were whole numbers.
  3. Step 3. Order the numbers using the appropriate inequality sign.

Example 5.7

Order the following decimals using <or>:<or>:

  1. 0.64__0.60.64__0.6
  2. 0.83__0.8030.83__0.803
Try It 5.13

Order each of the following pairs of numbers, using <or>:<or>:

0.42__0.40.42__0.4 0.76__0.7060.76__0.706

Try It 5.14

Order each of the following pairs of numbers, using <or>:<or>:

0.1__0.180.1__0.18 0.305__0.350.305__0.35

When we order negative decimals, it is important to remember how to order negative integers. Recall that larger numbers are to the right on the number line. For example, because −2−2 lies to the right of −3−3 on the number line, we know that −2>−3.−2>−3. Similarly, smaller numbers lie to the left on the number line. For example, because −9−9 lies to the left of −6−6 on the number line, we know that −9<−6.−9<−6.

A number line is shown with integers from negative 10 to 0. Blue dots are placed on negative nine and negative six. Red dots are placed at negative two and negative three.

If we zoomed in on the interval between 00 and −1,−1, we would see in the same way that −0.2>−0.3and−0.9<−0.6.−0.2>−0.3and−0.9<−0.6.

Example 5.8

Use <or><or> to order. −0.1__−0.8.−0.1__−0.8.

Try It 5.15

Order each of the following pairs of numbers, using <or>:<or>:

−0.3___−0.5−0.3___−0.5

Try It 5.16

Order each of the following pairs of numbers, using <or>:<or>:

−0.6___−0.7−0.6___−0.7

Round Decimals

In the United States, gasoline prices are usually written with the decimal part as thousandths of a dollar. For example, a gas station might post the price of unleaded gas at $3.279$3.279 per gallon. But if you were to buy exactly one gallon of gas at this price, you would pay $3.28$3.28, because the final price would be rounded to the nearest cent. In Whole Numbers, we saw that we round numbers to get an approximate value when the exact value is not needed. Suppose we wanted to round $2.72$2.72 to the nearest dollar. Is it closer to $2$2 or to $3?$3? What if we wanted to round $2.72$2.72 to the nearest ten cents; is it closer to $2.70$2.70 or to $2.80?$2.80? The number lines in Figure 5.4 can help us answer those questions.

In part a, a number line is shown with 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 3. There is a dot between 2.7 and 2.8 labeled as 2.72.  In part b, a number line is shown with 2.70, 2.71, 2.72, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, 2.79, and 2.80. There is a dot at 2.72.
Figure 5.4 We see that 2.722.72 is closer to 33 than to 2.2. So, 2.722.72 rounded to the nearest whole number is 3.3.
We see that 2.722.72 is closer to 2.702.70 than 2.80.2.80. So we say that 2.722.72 rounded to the nearest tenth is 2.7.2.7.

Can we round decimals without number lines? Yes! We use a method based on the one we used to round whole numbers.

How To

Round a decimal.

  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 given place value.
  3. Step 3. Is this digit greater than or equal to 5?5?
    • Yes - add 11 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, removing all digits to the right of the given place value.

Example 5.9

Round 18.37918.379 to the nearest hundredth.

Try It 5.17

Round to the nearest hundredth: 1.047.1.047.

Try It 5.18

Round to the nearest hundredth: 9.173.9.173.

Example 5.10

Round 18.37918.379 to the nearest tenth whole number.

Try It 5.19

Round 6.5826.582 to the nearest hundredth tenth whole number.

Try It 5.20

Round 15.217515.2175 to the nearest thousandth hundredth tenth.

Section 5.1 Exercises

Practice Makes Perfect

Name Decimals

In the following exercises, name each decimal.

1.

5.55.5

2.

7.87.8

3.

5.015.01

4.

14.0214.02

5.

8.718.71

6.

2.642.64

7.

0.0020.002

8.

0.0050.005

9.

0.3810.381

10.

0.4790.479

11.

−17.9−17.9

12.

−31.4−31.4

Write Decimals

In the following exercises, translate the name into a decimal number.

13.

Eight and three hundredths

14.

Nine and seven hundredths

15.

Twenty-nine and eighty-one hundredths

16.

Sixty-one and seventy-four hundredths

17.

Seven tenths

18.

Six tenths

19.

One thousandth

20.

Nine thousandths

21.

Twenty-nine thousandths

22.

Thirty-five thousandths

23.

Negative eleven and nine ten-thousandths

24.

Negative fifty-nine and two ten-thousandths

25.

Thirteen and three hundred ninety-five ten thousandths

26.

Thirty and two hundred seventy-nine thousandths

Convert Decimals to Fractions or Mixed Numbers

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

27.

1.991.99

28.

5.835.83

29.

15.715.7

30.

18.118.1

31.

0.2390.239

32.

0.3730.373

33.

0.130.13

34.

0.190.19

35.

0.0110.011

36.

0.0490.049

37.

−0.00007−0.00007

38.

−0.00003−0.00003

39.

6.46.4

40.

5.25.2

41.

7.057.05

42.

9.049.04

43.

4.0064.006

44.

2.0082.008

45.

10.2510.25

46.

12.7512.75

47.

1.3241.324

48.

2.4822.482

49.

14.12514.125

50.

20.37520.375

Locate Decimals on the Number Line

In the following exercises, locate each number on a number line.

51.

0.80.8

52.

0.30.3

53.

−0.2−0.2

54.

−0.9−0.9

55.

3.13.1

56.

2.72.7

57.

−2.5−2.5

58.

−1.6−1.6

Order Decimals

In the following exercises, order each of the following pairs of numbers, using <or>.<or>.

59.

0.9__0.60.9__0.6

60.

0.7__0.80.7__0.8

61.

0.37__0.630.37__0.63

62.

0.86__0.690.86__0.69

63.

0.6__0.590.6__0.59

64.

0.27__0.30.27__0.3

65.

0.91__0.9010.91__0.901

66.

0.415__0.410.415__0.41

67.

−0.5__−0.3−0.5__−0.3

68.

−0.1_−0.4−0.1_−0.4

69.

−0.62_−0.619−0.62_−0.619

70.

−7.31_−7.3−7.31_−7.3

Round Decimals

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

71.

0.670.67

72.

0.490.49

73.

2.842.84

74.

4.634.63

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

75.

0.8450.845

76.

0.7610.761

77.

5.79325.7932

78.

3.62843.6284

79.

0.2990.299

80.

0.6970.697

81.

4.0984.098

82.

7.0967.096

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

83.

5.7815.781

84.

1.6381.638

85.

63.47963.479

86.

84.28184.281

Everyday Math

87.

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

dollar

thousand dollars

ten thousand dollars.

88.

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

dollar

thousand dollars

ten thousand dollars.

89.

Sales Tax Hyo Jin lives in San Diego. She bought a refrigerator for $1624.99$1624.99 and when the clerk calculated the sales tax it came out to exactly $142.186625.$142.186625. Round the sales tax to the nearest penny dollar.

90.

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

Writing Exercises

91.

How does your knowledge of money help you learn about decimals?

92.

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

93.

Jim ran a 100-meter100-meter race in 12.32 seconds.12.32 seconds. Tim ran the same race in 12.3 seconds.12.3 seconds. Who had the faster time, Jim or Tim? How do you know?

94.

Gerry saw a sign advertising postcards marked for sale at 10for0.99¢.”10for0.99¢.” What is wrong with the advertised price?

Self Check

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

.

If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Whom can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

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