Chapter 5 DECIMAL NOTATION

Transcription

1 Name: Instructor: Date: Section: Chapter 5 DECIMAL NOTATION 5.1 Decimal Notation, Order, and Rounding Learning Objectives A Given decimal notation, write a word name. B Convert between decimal notation and fraction notation. C Given a pair of numbers in decimal notation, tell which is larger. D Round decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand. Key Terms Use the terms listed below to complete each statement in Exercises 1 4. Some of the terms will be used more than once. left right zeros decimal places larger smaller 1. To convert from fraction notation to decimal notation when the denominator is 10, 100, 1000, and so on, a) count the number of and b) move the decimal point that number of places to the. Leave off the denominator. 2. To convert from decimal notation to fraction notation, a) count the number of, b) move the decimal point that many places to the, and c) write the answer over a denominator of 1 followed by that number of. 3. To compare two positive numbers in decimal notation, start at the and compare corresponding digits. When two digits differ, the number with the digit is the larger of the two numbers. 4. To compare two negative numbers in decimal notation, start at the and compare corresponding digits. When two digits differ, the number with the digit is the larger of the two numbers. Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 91

2 GUIDED EXAMPLES AND PRACTICE Objective A Given decimal notation, write a word name. Review these examples for Objective A: 1. Write a word name for a) Write a word name for the whole number. Three hundred six b) Write and for the decimal point. Three hundred six and c) Write a word name for the number named to the right of the decimal point, followed by the place value of the last digit. Three hundred six and eight hundred forty-five thousandths A word name for is three hundred six and eight hundred forty-five thousandths. 2. Write a word name for $146.98, as on a check. One hundred forty-six and Practice these exercises: 1. Write a word name for Write a word name for $23.79, as on a check. Objective B Convert between decimal notation and fraction notation. Review these examples for Objective B: 3. Write fraction notation for places move 3 places = Write decimal notation for zeros Move 3 places 5. Write decimal notation for zeros = 5+ 7 = 5 and 7 = = Practice these exercises: 3. Write fraction notation for Write decimal notation for Write decimal notation for Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

3 Name: Instructor: Date: Section: Objective C Given a pair of numbers in decimal notation, tell which is larger. Review these examples for Objective C: 6. Which is larger: 0.01 or 0.009? 0.01 Starting at the left, these digits are the first to differ; 1 is larger than 0. Thus, 0.01 is larger. In symbols, 0.01 > Practice these exercises: 6. Which is larger: 2.08 or 2.11? 7. Which is larger: 2.03 or 2.028? 2.03 Starting at the left, these digits are the first to differ; 2 is smaller than 3. Thus, is larger. In symbols, > Which is larger: 15.2 or 15.23? Objective D Round decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand. Review this example for Objective D: 8. Round to the nearest hundredth Thousandths digit is 4 or lower. Round down. 8. Round to the nearest tenth. ADDITIONAL EXERCISES Objective A Given decimal notation, write a word name. For extra help, see Examples 1 5 on pages of your text and the Section 5.1 lecture Write a word name for the number in each sentence. 1. The Suez Canal is miles long. 2. One meter is equivalent to about yards. Write in words, as on a check. 3. $ $ Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 93

4 Objective B Convert between decimal notation and fraction notation. For extra help, see Examples 6 12 on pages of your text and the Section 5.1 lecture Write each number as a fraction and, if possible, as a mixed numeral. Do not simplify Write decimal notation for each number ,000 Objective C Given a pair of numbers in decimal notation, tell which is larger. For extra help, see Examples on page 305 of your text and the Section 5.1 lecture Which number is larger? , , , , 100 Objective D Round decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand. For extra help, see Examples on page 306 of your text and the Section 5.1 lecture Round to the nearest: 13. Tenth 14. Hundredth 15. Thousandth 16. Round to the nearest one. 94 Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

5 Name: Instructor: Date: Section: Chapter 5 DECIMAL NOTATION 5.2 Addition and Subtraction of Decimals Learning Objectives A Add using decimal notation. B Subtract using decimal notation. C Add and subtract negative decimals. D Combine like terms with decimal coefficients. GUIDED EXAMPLES AND PRACTICE Objective A Add using decimal notation. Review this example for Objective A: 1. Add: Add: Lining up the decimals and writing and extra zero Adding Objective B Subtract using decimal notation. Review this example for Objective B: 2. Subtract: Subtract: Writing an extra zero Subtracting Objective C Add and subtract negative decimals. Review this example for Objective C: 3. Subtract: 6.4 ( 7.9). 6.4 ( 7.9) = Adding the opposite of 7.9 = 1.5 Subtracting absolute values. The answer is positive since 7.9 has the larger absolute value. 3. Add: Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 95

6 Objective D Combine like terms with decimal coefficients. Review this example for Objective D: 4. Combine like terms: 4.3x 2.1y 6.2x+ 4.8 y. 4.3x 2.1y 6.2x+ 4.8y = 4.3x+ ( 2.1y) + ( 6.2x) y Rewriting as addition = 4.3x+ ( 6.2x) + ( 2.1y) y Using the commutative law to rearrange = 1.9x+ 2.7 y Combining like terms 4. Combine like terms: 5.7a+ 3.9b 4.2a 5.6 b. ADDITIONAL EXERCISES Objective A Add using decimal notation. For extra help, see Examples 1 3 on pages of your text and the Section 5.2 lecture Add Objective B Subtract using decimal notation. For extra help, see Examples 4 6 on pages of your text and the Section 5.2 lecture Subtract Objective C Add and subtract negative decimals. For extra help, see Examples 7 10 on pages of your text and the Section 5.2 lecture Add or subtract, as indicated ( 18.7) Objective D Combine like terms with decimal coefficients. For extra help, see Examples on page 313 of your text and the Section 5.2 lecture Combine like terms x+ 5.8x y 19.21y a a y 5.7x 4.3y+ 2.8x 96 Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

7 Name: Instructor: Date: Section: Chapter 5 DECIMAL NOTATION 5.3 Multiplication of Decimals Learning Objectives A Multiply using decimal notation. B Convert from notation like 45.7 million to standard notation and convert between dollars and cents. C Evaluate algebraic expressions using decimal notation. Key Terms Use the terms listed below to complete each statement in Exercises 1 4. The terms will be used more than once. right left 1. To multiply any number by 10, 100, 1000, and so on, a) count the number of zeros, and b) move the decimal point that many places to the. 2. To multiply any number by a tenth, hundredth, or thousandth, and so on, a) count the number of decimal places, and b) move the decimal point that many places to the. 3. To convert from cents to dollars, move the decimal points two places to the and change the sign at the end to a $ sign in front. 4. To convert from dollars to cents, move the decimal point two places to the and change the $ in front to a at the end. GUIDED EXAMPLES AND PRACTICE Objective A Multiply using decimal notation. Review these examples for Objective A: 1. Multiply: (1 decimal place) (2 decimal places) (3 decimal places) Practice these exercises: 1. Multiply: Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 97

8 2. Multiply: = Moving the decimal point 3 places to the left. This requires adding one extra zero. = Multiply: = 3460 Moving the decimal point 2 places to the right and using one zero as a placeholder. 2. Multiply: Multiply: Objective B Convert from notation like 45.7 million to standard notation and convert between dollars and cents. Review these examples for Objective B: 4. Convert 45.7 million to standard notation million = million = ,000,000 6 zeros = 45,700,000 Moving the decimal 6 places to the right 5. Convert $63.42 to cents. $63.42 = $1 We think of $63.42 as dollar or $1 = Substituting 100 for $1: $1 = 100 = 6342 Multiplying Practice these exercises: 4. Convert 6.2 billion to standard notation. 5. Convert $ to cents. 6. Convert 9168 to dollars. 6. Convert 245 to dollars = We think of 9168 as cent or = 9168 $0.01 Substituting $0.01 for 1 : 1 =$0.01 = $91.68 Multiplying Objective C Evaluate algebraic expressions using decimal notation. Review this example for Objective C: 7. Evaluate Prt for P = 100, r = 0.08, and t = 1.5. Prt = 100( 0.08)( 1.5) = 81.5 ( ) = Evaluate lwh for l = 2.7, w = 3.4, and h = Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

9 Name: Instructor: Date: Section: ADDITIONAL EXERCISES Objective A Multiply using decimal notation. For extra help, see Examples 1 12 on pages of your text and the Section 5.3 lecture Multiply ( 0.01) ( 45.1) Objective B Convert from notation like 45.7 million to standard notation and convert between dollars and cents. For extra help, see Examples on page 322 of your text and the Section 5.3 lecture Convert from dollars to cents. 5. $ $0.79 Convert from cents to dollars Convert the number in this sentence to standard notation: The number of real Christmas tress purchased in a recent year was 32.8 million. Objective C Evaluate algebraic expressions using decimal notation. For extra help, see Examples on page 323 of your text and the Section 5.3 lecture Evaluate q( p+ q), for p= 7 and q= AB + B A = B = 2 3, for 4.5 and 1.3 Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 99

10 Find (a) the perimeter and (b) the area of a rectangle with the given dimensions. 12. Length: 12.6 ft, width: 5.4 ft 13. Length: 3.3 m, width: 2.9 m 14. The amount it now takes to equal the value of $1 in 1913 can be estimated by the expression x , where x is the number of years after Estimate how much it took to equal the value of $1 in 1913 in Round to the nearest cent (hundredth). 100 Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

11 Name: Instructor: Date: Section: Chapter 5 DECIMAL NOTATION 5.4 Division of Decimals Learning Objectives A Divide using decimal notation. B Simplify expressions using the rules for order of operations. Key Terms Write the letters A, B, C, and D in the blanks to indicate the order in which operations should be performed when simplifying expressions A. Evaluate all exponential expressions. B. Do all additions and subtractions in order from left to right. C. Do all calculations within grouping symbols. D. Do all multiplications and divisions in order from left to right. GUIDED EXAMPLES AND PRACTICE Objective A Divide using decimal notation. Review these examples for Objective A: 1. Divide: Divide: First we find Since = 3.5, we have = 3.5. Practice these exercises: 1. Divide: Divide: Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 101

12 3. Divide: = = = zeros 3 places to the left to change 1000 to 1 The answer is Divide: ,930 = = = 42, zeros 3 places to the right to change to 1 The answer is 42, Divide: Divide: Objective B Simplify expressions using the rules for order of operations. Review these examples for Objective B: 2 5. Simplify: ( 8 2.4) ( 8 2.4) = Working inside the parentheses = Evaluating the exponential term = Multiplying and dividing in order from left to right = 50.4 Practice these exercises: 5. Simplify: ( ) While on a weekend trip, the Hernandez family drove mi on the first day, mi on the second day, and mi the third day. Find the average distance driven per day. To find the average distance, find the sum of the distances and divide by the number of addends, 3. ( ) 3 = = The average distance is mi. 6. Keisha walked 3.5 mi on Tuesday, 1.2 mi on Wednesday, 2.9 mi on Thursday, and 4 mi on Friday. Find the average distance walked per day. 102 Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

13 Name: Instructor: Date: Section: ADDITIONAL EXERCISES Objective A Divide using decimal notation. For extra help, see Examples 1 9 on pages of your text and the Section 5.4 lecture Divide Objective B Simplify expressions using the rules for order of operations. For extra help, see Examples on pages of your text and the Section 5.4 lecture Simplify ( ) ( ) [ ( 3 3.6) 0.3] 8. Marco earned $25.50 in tips on Monday, $21.40 on Tuesday, $24.75 on Wednesday, $35 on Thursday, and $42.90 on Friday. Find the average amount earned in tips per day during this period. Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 103

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15 Name: Instructor: Date: Section: Chapter 5 DECIMAL NOTATION 5.5 Using Fraction Notation with Decimal Notation Learning Objectives A Use division to convert fraction notation to decimal notation. B Round numbers named by repeating decimals. C Convert certain fractions to decimal notation by using equivalent fractions. D Simplify expressions that contain both fraction and decimal notation. GUIDED EXAMPLES AND PRACTICE Objective A Use division to convert fraction notation to decimal notation. Review this example for Objective A: 1. Find decimal notation for Since 4 keeps reappearing as a remainder, the digit repeats and will continue to do so. Thus, =. Objective B Round numbers named by repeating decimals. Review this example for Objective B: 2. Round 0.37 to the nearest thousandth = The digit in the ten-thousandths place, 7, is 5 or higher, so we round up and get Find decimal notation for Round 0.15 to the nearest hundredth. Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 105

16 Objective C Convert certain fractions to decimal notation by using equivalent fractions. Review this example for Objective C: 3. Find decimal notation for = = = Find decimal notation for Objective D Simplify expressions that contain both fraction and decimal notation. Review this example for Objective D: 4. Calculate: Calculate: We will use the first method = = = = ADDITIONAL EXERCISES Objective A Use division to convert fraction notation to decimal notation. For extra help, see Examples 1 5 on pages of your text and the Section 5.5 lecture Find decimal notation for each number Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

17 Name: Instructor: Date: Section: Objective B Round numbers named by repeating decimals. For extra help, see Examples 6 9 page 341 of your text and the Section 5.5 lecture Round the decimal notation for each number to the nearest tenth, hundredth, and thousandth Objective C Convert certain fractions to decimal notation by using equivalent fractions. For extra help, see Examples page 342 of your text and the Section 5.5 lecture Find decimal notation for each number Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 107

18 Objective D Simplify expressions that contain both fraction and decimal notation. For extra help, see Examples pages of your text and the Section 5.5 lecture Calculate and write the result as a decimal ( ) ( 24.12) ( 3 ) ( 7 ) Find the area of a triangular flower bed that is 10.3 m long and 8.4 m wide. 108 Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

19 Name: Instructor: Date: Section: Chapter 5 DECIMAL NOTATION 5.6 Estimating Learning Objectives A Estimate sums, differences, products, and quotients. GUIDED EXAMPLES AND PRACTICE Objective A Estimate sums, differences, products, and quotients. Review this example for Objective A: 1. Estimate by rounding to the nearest tenth = Estimate Which of the following is an appropriate estimate? a) 17 b) 280 c) 650 d) 700 ADDITIONAL EXERCISES Objective A Estimate sums, differences, products, and quotients. For extra help, see Examples 1 9 on pages of your text and the Section 5.6 lecture Estimate by rounding, as directed ; nearest one ; nearest tenth Estimate. Choose a rounding digit that gives one or two nonzero digits. Indicate which choice is an appropriate estimate a) 820 b) 310 c) 300 d) a) 0.3 b) 0.4 c) 3 d) 4 An ipod sells for $ and a GPS navigation system sells for $ About how much more does the GPS system cost than the ipod? Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 109

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21 Name: Instructor: Date: Section: Chapter 5 DECIMAL NOTATION 5.7 Solving Equations Learning Objectives A Solve equations containing decimals and one variable term. B Solve equations containing decimals and two or more variable terms. GUIDED EXAMPLES AND PRACTICE Objective A Solve equations containing decimals and one variable term. Review this example for Objective A: 1. Solve: 3.1x 4.3 = x 4.3 = 8.02 Adding x = to both sides 3.1x = 3.72 Simplifying 3.1x 3.72 Dividing both = sides by 3.1 x = 1.2 The solution is Solve: 2.5y = 8.2. Objective B Solve equations containing decimals and two or more variable terms. Review this example for Objective B: 2. Solve: 8x+ 2 = 3x x+ 2= 3x+ 13 Subtracting 2 8x+ 2 2= 3x from both sides 8x= 3x+ 11 Simplifying Subtracting 3x 8x 3x= 3x x from both sides 5x = 11 5x 11 Dividing both = 5 5 sides by 5 x = 2.2 The solution is Solve: 7x+ 1 = 9x+ 8. Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 111

22 ADDITIONAL EXERCISES Objective A Solve equations containing decimals and one variable term. For extra help, see Examples 1 2 on page 354 of your text and the Section 5.7 lecture Solve. Remember to check. 1. x = x 5 = y = = t Objective B Solve equations containing decimals and two or more variable terms. For extra help, see Examples 3 6 on pages of your text and the Section 5.7 lecture Solve. Remember to check. 5. 2y+ 1= 6y x+ 16 = 2.9x t 7= 8( t 3) ( x+ 7.1) = 7.6x Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

23 Name: Instructor: Date: Section: Chapter 5 DECIMAL NOTATION 5.8 Applications and Problem Solving Learning Objectives A Translate key phrases to algebraic expressions. B Solve applied problems involving decimals. Key Terms Use the vocabulary terms listed below to complete each statement in Exercises 1 2. radius diameter 1. In any circle, a is a segment that passes through the center of the circle with endpoints on the circle. 2. In any circle, a is a segment with one endpoint on the center and the other endpoint on the circle. GUIDED EXAMPLES AND PRACTICE Objective A Translate key phrases to algebraic expressions. Review this example for Objective A: 1. Translate to an algebraic expression: 5 more than 7 times a number. Let n = the number. 7n + 5 Objective B Solve applied problems involving decimals. Review this example for Objective B: 2. Erik s odometer read 45,918.7 mi at the beginning of a trip. It read 47,304.2 mi at the end of the trip. How far did Erik drive? 1. Familiarize. We make a drawing. Let m = the number of miles Erik drove. 45,918.7 mi m 47,304.2 mi 1. Translate to an algebraic expression: 9 less the product of 6 and a number. 2. A car loan of $ is to be paid off in 24 equal monthly payments. How much is each payment? Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 113

24 2. Translate. This is a how much more situation. Additional First Final + number = reading reading of miles 45, m = 47, Solve. We subtract 45,918.7 on both sides of the equation. 45, m = 47, , m 45,918.7 = 47, ,918.7 m = Check. We can check by adding: 45, = 47, The result checks. 5. State. Erik drove mi. ADDITIONAL EXERCISES Objective A Translate key phrases to algebraic expressions. For extra help, see Examples 1 2 on pages of your text and the Section 5.8 lecture Translate to an algebraic expression. Choice of variables used may vary less than w 2. The ratio of a number and increased by twice a number 4. One fifth of the sum of 3 and a number Objective B Solve applied problems involving decimals. For extra help, see Examples 3 9 on pages of your text and the Section 5.8 lecture Solve using the five-step problem-solving procedure. 5. Normal body temperature is 98.6 F. At one point during an illness, Jessica s temperature was F. How much did her temperature rise? 6. The 4 Maloney children buy their parents an anniversary gift that costs $ and split the cost equally. How much does each child pay? 7. Find the perimeter and the area of a rectangle with length 15.3 cm and width 7.6 cm. 8. Computer Wizard charger $40 for a house call plus $45.50 for each hour a job takes. How long did an employee of Computer Wizard work on a house call if the bill totals $108.25? 114 Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley