CHAPTER 4 DECIMALS. 4.1 Reading and Writing Decimals. 4.1 Reading and Writing Decimals Margin Exercises. ten-thousandths.

Transcription

1 4.1 Reading and Writing Decimals 113 CHAPTER 4 DECIMALS 4.1 Reading and Writing Decimals 4.1 Margin Exercises 1. (a The figure has equal parts; part is shaded. ; Þ ; one tenth (b The figure has equal parts; parts are shaded. ; Þ ; three tenths (c The figure has equal parts; parts are shaded. ; Þ ; nine tenths 2. (a The figure has equal parts; parts are shaded. ; Þ ; three tenths (b The figure has equal parts; parts are shaded. 3. (a Þ( œ ( ; Þ ; forty-one hundredths (b Þ œ (c Þ œ (d Þ' œ ' (e Þ( œ ( (f Þ œ hundreds tens ones tenths hundredths 4. (a ( Þ ones tenths (b Þ ones tenths hundredths (c Þ ' ones tenths hundredths thousandths ten-thousandths (d Þ 5. (a Þ' is six tenths. (b Þ' is forty-six hundredths. (c Þ is five hundredths. (d Þ is four hundred nine thousandths. (e Þ is three ten-thousandths. (f Þ( is two thousand seven hundred three ten-thousandths. (g Þ is eighty-eight thousandths. 6. (a Þ is three and eight tenths. (b Þ is fifteen and one thousandth. (c Þ( is seventy-three ten-thousandths. (d 'Þ is sixty-four and three hundred nine thousandths. 7. (a Þ( œ ( (b Þ œ (c Þ œ (d Þ( œ ( (e Þ(( œ ((, ƒ 8. (a Þ œ œ œ ƒ ' 'ƒ (b Þ' œ œ œ ƒ ƒ ( (c Þ œ œ œ ƒ ƒ (d Þœ œ œ ƒ ƒ (e Þ œ œ œ ƒ ƒ (f Þ œ œ,, ƒ œ

2 114 Chapter 4 Decimals 4.1 Section Exercises tens ones tenths 1. ( Þ hundredths thousandths ten-thousandths 3. Þ tenths thousandths ten-thousandths 5. Þ ( hundreds tens tenths 7. Þ ' hundreds ones hundredths 9. Þ thousands hundredths thousandths 11. ' Þ ( 13. ones, hundredths, ten, hundreds, tenths: Þ 15. thousandths, hundredths, ' ones, ten-thousandths, tenths: 'Þ 17. hundredths, hundreds, tens, tenths, thousandths, thousands, ' ones: 'Þ 19. Þ( œ ( ƒ 21. Þ œ œ œ ƒ ƒ 23. Þ œ œ œ ƒ '' '' ƒ 25. Þ'' œ œ œ ƒ 27. Þ( œ ( 29. ' 'ƒ Þ' œ œ œ ƒ 31. ƒ Þ œ œ œ ƒ 33. ƒ Þœ œ œ ƒ 35. '' '' ƒ Þ'' œ œ œ ƒ 37. Þ is five tenths. 39. Þ( is seventy-eight hundredths. 41. Þ is one hundred five thousandths. 43. Þ is twelve and four hundredths. 45. Þ( is one and seventy-five thousandths. 47. six and seven tenths: ' ( œ 'Þ( 49. thirty-two hundredths: œþ 51. four hundred twenty and eight thousandths: œ Þ 53. seven hundred three ten-thousandths: (, œ Þ( 55. seventy-five and thirty thousandths: ( œ (Þ 57. Anne should not say and because that denotes a decimal point pound test line has a diameter of Þ inch. Þ inch is read ten thousandths of an inch. ƒ Þ œ œ œ inch ƒ 61. inch œ Þ inch A diameter of Þ inch corresponds to a test strength of pounds. 63. Six tenths is Þ', so the correct part number is -C. 65. One and six thousandths is Þ', which is part number -A. 67. The size of part number -E is centimeters, Þ' which in words is one and six hundred two thousandths centimeters.

3 4.2 Rounding Decimals Use the whole number place value chart on text page 3 to find the names after hundred thousands. Then change s to ths in those names. So millions becomes millionths when used on the right side of the decimal point, and so on for tenmillionths, hundred-millionths, and billionths. 70. The first place to the left of the decimal point is ones, so the first place to the right could be oneths, like tens and ten ths. But anything that is or more is to the left of the decimal point. 71. The eighth place value to the right of the decimal point is hundred-millionths, so Þ(' is seventy-two million four hundred thirty-six thousand nine hundred fifty-five hundredmillionths. 72. The ninth place value to the right of the decimal point is billionths, so Þ'( is six hundred seventy-eight thousand five hundred fifty-four billionths. 73. 'Þ is eight thousand six and five hundred thousand one millionths. 74.,'Þ is twenty thousand sixty and five hundred five millionths. 75. Three hundred two thousand forty ten-millionths: Þ 76. Nine billion, eight hundred seventy-six million, five hundred forty-three thousand, two hundred ten and one hundred million two hundred thousand three hundred billionths:,(',,þ 4.2 Rounding Decimals 4.2 Margin Exercises 1. Round to the nearest thousandth. (a Draw a cut-off line: Þl The first digit cut is, which is or more, so Þ Þ Þ Answer: Þ (b Draw a cut-off line: Þl The first digit cut is, which is or more, so Þ Þ Þ Answer: Þ (c Draw a cut-off line: 'Þl The first digit cut is, which is or less. The part Answer: 'Þ (d Draw a cut-off line: Þ(l The first digit cut is, which is or more, so Þ( Þ Þ( Answer: Þ( 2. (a Þ to the nearest hundredth Draw a cut-off line: Þl The first digit cut is, which is or more, so Þ Þ Þ Answer: Þ (b Þ to the nearest hundredth Draw a cut-off line: Þl The first digit cut is, which is or less. The part Answer: Þ (c Þ to the nearest thousandth Draw a cut-off line: Þl The first digit cut is, which is or more, so Þ Þ Þ Answer: Þ (d Þ to the nearest tenth Draw a cut-off line: Þl The first digit cut is, which is or less. The part Answer: Þ 3. Round to the nearest cent (hundredths. (a Draw a cut-off line: Þl The first digit cut is, which is or more, so Þ Þ Þ' Answer: Þ'

4 116 Chapter 4 Decimals (b Draw a cut-off line: (Þ'l' The first digit cut is ', which is or more, so (Þ' Þ (Þ( Answer: (Þ( (c Draw a cut-off line: Þl The first digit cut is, which is or more, so Þ Þ Þ Answer: Þ (d Draw a cut-off line: Þl The first digit cut is, which is or less. The part Answer: Þ 4. Round to the nearest dollar. (a Draw a cut-off line: Þl The first digit cut is, which is or less. The part Answer: (b Draw a cut-off line: 'Þl The first digit cut is, which is or less. The part Answer: ' (c Draw a cut-off line: Þl The first digit cut is, which is or more, so round up by adding. Answer: (d Draw a cut-off line: Þl The first digit cut is, which is or more, so round up by adding. Answer: (e Draw a cut-off line: Þl' The first digit cut is ', which is or more, so round up by adding. Answer: (f Draw a cut-off line: Þl The first digit cut is, which is or more, so round up by adding. Answer: (g Draw a cut-off line: Þl The first digit cut is, which is or less. The part Answer: 4.2 Section Exercises 1. 'Þ( to the nearest tenth Draw a cut-off line after the tenths place: 'Þl( The first digit cut is, which is or more, so round up the tenths place. 'Þ Þ 'Þ Answer: 'Þ 3. Þ'( to the nearest thousandth Draw a cut-off line after the thousandths place: Þ'l( The first digit cut is, which is or less. The part Answer: Þ' 5. Þ( to the nearest hundredth Draw a cut-off line after the hundredths place: Þ(l The first digit cut is, which is or more, so round up the hundredths place. Þ( Þ Þ Answer: Þ

5 4.2 Rounding Decimals Þ''' to the nearest thousandth Draw a cut-off line after the thousandths place: Þ''l' The first digit cut is ', which is or more, so round up the thousandths place. Þ'' Þ Þ'' Answer: Þ'' 9. (Þ to the nearest tenth Draw a cut-off line after the tenths place: (Þl The first digit cut is, which is or more, so round up the tenths place. (Þ Þ (Þ Answer: (Þ 11. Þ to the nearest ten-thousandth Draw a cut-off line after the ten-thousandths place: Þl The first digit cut is, which is or less. The part Answer: Þ 13. Þ to the nearest one Draw a cut-off line after the ones place: Þl The first digit cut is, which is or more, so round up the ones place. Answer: 15. Þ' to the nearest hundredth Draw a cut-off line after the hundredths place: Þl' The first digit cut is, which is or less. The part Answer: Þ 17. Þ to the nearest ten-thousandth Draw a cut-off line after the ten-thousandths place: Þl The first digit cut is, which is or more, so round up the ten-thousandths place. Þ Þ Þ Answer: Þ 19. Round Þ''' to the nearest cent. Draw a cut-off line: Þl''' The first digit cut is ', which is or more, so Þ Þ Þ Nardos pays Þ. 21. Round Þ to the nearest cent. Draw a cut-off line: Þl The first digit cut is, which is or less. The part Nardos pays Þ. 23. Round Þ to the nearest cent. Draw a cut-off line: Þl The first digit cut is, which is or more, so Þ Þ Þ Nardos pays Þ. 25. Round,'Þ' to the nearest dollar. Draw a cut-off line:,'þl' The first digit cut is ', which is or more, so,',' Income from job:,' 27. Round Þ to the nearest dollar. Draw a cut-off line: Þl The first digit cut is, which is or less. The part Union dues: 29. Round Þ to the nearest dollar. Draw a cut-off line: Þl The first digit cut is, which is or more, so Donations to charity:

6 118 Chapter 4 Decimals 31. Þ to the nearest dollar Draw a cut-off line: Þl The first digit cut is, which is Answer: 33. Þ' to the nearest cent Draw a cut-off line: Þl' The first digit cut is ', which is Þ Þ Þ Answer: Þ 35. Þ( to the nearest dollar Draw a cut-off line: Þl( The first digit cut is (, which is Answer: or more, so or more, so or more, so 37. (a Round Þ' to the nearest whole number. Draw a cut-off line: Þl' The first digit cut is, which is or less. The part The record speed for a motorcycle is about miles per hour. (b Round 'Þ to the nearest whole number. Draw a cut-off line: 'Þl The first digit cut is, which is or more, so ' ( The fastest roller-coaster speed record is about ( miles per hour. 39. (a Round Þ to the nearest tenth. Draw a cut-off line: Þl The first digit cut is, which is or more, so Þ Þ 'Þ The Indianapolis 500 fastest average winning speed is about 'Þ miles per hour. (b Round ('Þ to the nearest tenth. Draw a cut-off line: ('Þl The first digit cut is, which is or less. The part The land speed record is about ('Þ miles per hour. 41. If you round Þ to the nearest dollar, it will round to (zero dollars because Þ is closer to than to. 42. Round amounts less than Þ to the nearest cent instead of the nearest dollar. 43. If you round Þ to the nearest cent, it will round to Þ (zero cents because Þ is closer to Þ than to Þ. 44. Both Þ' and Þ' round to Þ'. Rounding to nearest thousandth (tenth of a cent would allow you to identify Þ( as less than Þ'. 4.3 Adding and Subtracting Decimals 4.3 Margin Exercises 1. (a Þ' (Þ Þ' (Þ Þ (b Þ(' Þ Þ(' Þ Þ' (c Þ 'Þ( Þ Þ 'Þ( Þ 'Þ(

7 4.3 Adding and Subtracting Decimals 119 (d Þ Þ ((Þ Þ Þ ((Þ (Þ 2. (a 'Þ Þ 'Þ Þ 'Þ (b Þ Þ Þ Þ Þ Þ (c Þ' Þ Þ(' Þ' Þ Þ(' Þ('' (d Þ Þ(' Þ Þ Þ(' Þ 3. (a Subtract Þ( from (Þ. (Þ Þ( Þ Check: Þ( Þ (Þ (b Subtract 'Þ from Þ. ( Þ y y y 'Þ Þ (c Þ Þ'( Check: 'Þ Þ Þ yþ y y y Check: Þ'( Þ'( Þ Þ Þ 4. (a Subtract Þ' from Þ. yþ y y 00 y y Write two zeros. Þ' 'Þ' Check: Þ' 'Þ' Þ (b Þ' Þ ( yyy Þ ' Check: Þ Þ Write one zero. Þ' Þ ' Þ' (c less Þ'' y Þ yyy Check: 'Þ Þ' ' Þ'' 'Þ Þ (d Þ Þ y yyy Þ Þ' ( Check: 5. (a Þ Þ ('Þ Estimate: Þ Þ'( Þ Exact: Þ Þ ('Þ Þ (b Þ' from Estimate: ' Exact: Þ Þ' 'Þ' (c Þ (Þ' Þ( Estimate: Exact: Þ (Þ' Þ( 'Þ'

8 120 Chapter 4 Decimals (d difference between Þ( meters and 'Þ meters Estimate: Exact: 'Þ Þ( Þ meters (e Þ plus Þ Estimate: Exact: Þ Þ Þ 4.3 Section Exercises 1. Þ' Þ( Þ' Þ( (Þ 3. Þ Þ Þ Þ Þ 5. Þ' Þ Þ' Þ (Þ(' 7. ('Þ Þ' ('Þ Þ' ((Þ' 9. Þ' Þ Þ' Þ 11. Subtract Þ from Þ Þ Þ Þ 13. Þ(' Þ( Þ Þ Þ(' Þ Þ( Þ Þ Þ' 15. (a Humerus Þ in., radius Þ in. Þ Þ Þ( The combined length is Þ( inches. (b Þ Þ Þ The difference is Þ inches. 17. (a Humerus Þ in., ulna Þ in., femur Þ in., tibia 'Þ in. Þ Þ Þ 'Þ 'Þ( The sum of the lengths is 'Þ( inches. (b 8th rib Þ' in., 7th rib Þ in. Þ Þ' Þ The 8th rib is Þ in. shorter than the 7th rib. 19. ' should be written 'Þ. The sum should be Þ( 'Þ Þ 'Þ 21. Estimate: Exact: Þ( ( 'Þ Þ' 23. Estimate: Exact: Þ( Þ' Þ Þ' 25. Þ' less Þ( Estimate: Exact: Þ' Þ( Þ

9 4.3 Adding and Subtracting Decimals Estimate: Exact: ' ' '' 29. Þ( 'Þ( Þ Þ' 'Þ' An estimate is œ, so Þ( is the most reasonable answer. 31. 'Þ Þ( An estimate is ( œ (, so 'Þ( is the most reasonable answer. 33. 'Þ( Þ An estimate is ( œ, so Þ is the most reasonable answer. 35. 'Þ Þ(( An estimate is ' œ ', so ''Þ( is the most reasonable answer. 37. Canada: Þ million; South Korea: million Estimate: Exact: Þ Þ Þ There are Þ million fewer Internet users in Canada than there are in South Korea. 39. Add the number of users from all the countries. Estimate: Exact: (Þ Þ 'Þ Þ' Þ Þ 'Þ (Þ There are (Þ million Internet users in all the countries listed in the table. 41. Add the heights. Estimate: Exact: Þ Þ' Þ ' meters 'Þ meters The NBA stars' combined height is Þ meter less than the rhino's height of 'Þ meters. 43. Subtract the weight of the lighter box from the weight of the heavier box. Estimate: Exact: Þ Þ ounce Þ' ounce The difference in weight is Þ' ounce. 45. Add the lengths of the four sides. Estimate: Exact: Þ( Þ( ' 'Þ ' 'Þ inches Þ inches The perimeter is Þ inches. 47. Subtract the price of the regular fishing line, Þ, from the price of the fluorescent fishing line, Þ. Estimate: Exact: Þ Þ Þ The fluorescent fishing line costs Þ more than the regular fishing line. 49. Add the price of the four items and the sales tax. Estimate: Exact: Þ Þ( Þ( Þ' Þ Þ spinning reel tin split shot tin split shot tackle box sales tax The total cost of the four items and the sales tax is Þ.

10 122 Chapter 4 Decimals 51. Add the monthly expenses. Þ Þ( Þ Þ Þ Þ (Þ 'Þ (Þ( (Þ Þ' Olivia's total expenses are Þ' per month. 53. Subtract to find the difference. Þ( 'Þ Þ( The difference in the amounts spent for groceries and for the car payment is Þ(. 55. Add the car expenses; then subtract this amount from the rent. Þ( Þ Þ Þ( Þ( Þ She spends Þ more on rent than on all her car expenses. 57. Subtract the two inside measurements from the total length. Þ Total length Þ Leftmost measurement Þ Þ( Middle measurement Þ, œ Þ cm. 59. Add the given lengths and subtract the sum from the total length. Þ Þ Þ' feet ; œ Þ feet 4.4 Multiplying Decimals 4.4 Margin Exercises Þ Þ' Þ feet 1. (a Þ' à decimal place Þ Ã decimal place Þ Ã decimal places (b Þ Ã decimal place Þ Ã decimal places ' Þ Ã decimal places (c Þ Ã decimal places ( à decimal places Þ( à decimal places (d Þ Ã decimal places Þ Ã decimal places ' ' '' (Þ Ã decimal places (e ' à decimal places Þ( à decimal place ( ( 'Þ( à decimal place 2. (a Þ Þ Þ Ã decimal places Þ Ã decimal places 36 à decimal places Count places from the right. Write in the decimal point and zeros. Þ 3' (b (0.2(0.008 Þ Ã decimal places Þ Ã decimal place 6 à decimal places Count places from the right. Write in the decimal point and zeros. Þ' (c (. Þ Ã decimal places Þ Ã decimal places à ' decimal places Count ' places from the right. Write in the decimal point and zeros. Þ (d ÐÞÑÐÞÑ Þ Ã decimal places Þ Ã decimal places à ( decimal places Count ( places from the right. Write in the decimal point and zeros. Þ

11 4.4 Multiplying Decimals 123 (e ÐÞÑÐÞÑ Þ Ã decimal places Þ Ã decimal places à ' decimal places Count ' places from the right. Write in the decimal point and zeros. Þ 3. (a ÐÞ'ÑÐÞÑ Estimate: Exact: Þ' à decimal places Þ Ã decimal places ' ' 'Þ' à decimal places (b ÐÞ'ÑÐÑ Estimate: Exact: ' Þ' à decimal places à decimal places ( ( (Þ Ã decimal places (c ÞÐÞÑ Estimate: Exact: Þ Ã decimal places Þ Ã decimal place '' Þ Ã decimal places (d Þ' (Þ Estimate: Exact: ' Þ' à decimal place (Þ Ã decimal place ' Þ' à decimal places 4.4 Section Exercises 1. Þ Ã decimal places Þ Ã decimal place ' Þ Ã decimal places 3. Þ Ã decimal place (Þ Ã decimal place ' Þ Ã decimal places 5. ÐÞ'''ÑÐÞÑ Þ''' à decimal places Þ Ã decimal place '' Þ Ã decimal places 7. Þ Ã decimal places '',Þ Ã decimal places 9. ( Þ' ( ( ' Þ' à decimal place Þ Ã decimal place 11. Ð(ÞÑÐÞ'Ñ ( (Þ Ã decimal place ' Þ' à decimal places Þ Ã decimal places 13. Þ(ÐÞ'Ñ ( Þ( à decimal places ' Þ' à decimal places Þ Ã decimal places 15. Þ(ÐÞ'Ñ ( Þ( à decimal places ' Þ' à decimal place Þ Ã decimal places 17. Þ' ÐÞÑ Þ Ã decimal places Þ' à decimal places Þ Ã ( decimal places 19. ÐÞÑ œ Þ Þ Þ Ã decimal places Þ Ã decimal places Þ Ã ' decimal places

12 124 Chapter 4 Decimals 21. ÐÞ'ÑÐÑ œ Þ' ÐÞÑÐÑ œ ÐÞ('ÑÐÑ œ Þ(' ÐÞÑÐÑ œ Þ Ð(Þ'ÑÐÑ œ (' ÐÞÑÐÑ œ When you multiply a number by, the decimal point moves one place to the right. Multiplying by moves the decimal point two places to the right. Multiplying by moves the decimal point three places to the right. 22. ÐÞ'ÑÐÞÑ œ Þ' ÐÞÑÐÞÑ œ Þ ÐÞ('ÑÐÞÑ œ Þ(' ÐÞÑÐÞÑ œ Þ Ð'ÑÐÞÑ œ 'Þ ÐÑÐÞÑ œ Þ Multiplying by Þ moves the decimal point one place to the left. Multiplying by Þ moves the decimal point two places to the left. Multiplying by Þ moves the decimal point three places to the left. 23. Estimate: Exact: Þ' à decimal place Þ Ã decimal place ' Þ Ã decimal places 25. Estimate: Exact: (Þ Ã decimal place à decimal places ' ( Þ Ã decimal place 27. Estimate: Exact: ( 'Þ Ã decimal places Þ' à decimal place ' Þ Ã decimal places 29. Estimate: Exact: Þ Ã 'Þ Ã ( ( ' Þ' decimal places decimal places à decimal places 31. A Þ car payment is unreasonable. A reasonable answer would be Þ. 33. A height of 'Þ inches (about feet is reasonable. 35. A gallon of milk for is unreasonable. A reasonable answer would be Þ. 37. Þ pound for a baby's weight is unreasonable. A reasonable answer would be Þ pounds. 39. Multiply her pay per hour times the hours she worked. Þ( à decimal places Þ Ã decimal place ' ' Þ' à decimal places Round Þ' to the nearest cent. LaTasha made Þ(. 41. Multiply the cost of one meter of canvas by the number of meters needed. Þ Þ' Þ Þ rounds to Þ. Sid will spend Þ on the canvas. 43. Multiply the number of gallons that she pumped into her pickup truck by the price per gallon. Þ Þ ' ' Þ Round Þ to the nearest cent. Michelle paid Þ for the gas. 45. Multiply the cost of the home by Þ(., Þ(,'Þ Ms. Rolack's fee was,'þ 47. (a Area before 1929: (Þ Þ ( ' ( ' Þ Rounding to the nearest tenth gives us Þ in..

13 4.4 Multiplying Decimals 125 Area after 1929: 'Þ Þ' ' ' 'Þ Rounding to the nearest tenth gives us 'Þ in.. (b Subtract to find the difference. Þ 'Þ (Þ The difference in rounded areas is (Þ in (a Multiply the thickness of one bill times the number of bills. Þ Þ A pile of (b A pile of bills would be Þ inch high. Þ Þ bills would be Þ inches high. 51. Multiply the monthly cost for cable times months (two years. Þ' basic per month (( Þ monthly total Þ one-time installation Þ two-year total The total cost for basic cable is Þ. Þ deluxe per month ( Þ monthly total Þ one-time installation (Þ two-year total The total cost for deluxe cable is (Þ. 53. Multiply the number of sheets by the cost per sheet. Þ ('Þ The library will pay ('Þ for the paper. 55. Multiply to find the cost of the rope, then multiply to find the cost of the wire. Add the results to find Barry's total purchases. Subtract the purchases from (three bills is. Cost of rope Cost of wire 'Þ Þ Þ( (Þ( Þ The cost of the rope rounds to (Þ('. Purchases Change (Þ(' rope Þ Þ wire Þ Þ Þ Barry received Þ in change. 57. Find the cost of the long-sleeve, size XXL, solid color shirts. Þ (Þ Then find the cost of the short-sleeve, size XXL, striped shirts. 'Þ( Þ Add these two amounts and the per shirt charge for the XXL size. (Þ ' Þ Þ Þ The total cost is Þ plus shipping, or Þ (Þ œ Þ.

14 126 Chapter 4 Decimals 59. (a Find the cost for short-sleeved, size M, solid-color shirts. Þ( Þ Based on this subtotal, shipping is Þ. Find the cost of the monograms. Þ Þ Add these amounts, plus Þ for a gift box. Þ Þ Þ Þ (Þ The total cost is (Þ. (b Subtract the cost of the shirts to find the difference. (Þ Þ Þ The monograms, gift box, and shipping added Þ to the cost of the gift. Summary Exercises on Decimals 1. ƒ Þ œ œ œ ƒ 3. ƒ ( Þ œ œ œ ƒ 5. Þ is two and three ten-thousandths. 7. five hundredths: œþ 9. ten and seven tenths: ( œ Þ( 11. Þ to the nearest tenth Draw a cut-off line: Þl The first digit cut is, which is or more, so Þ Þ Þ Answer: Þ 13. Þ to the nearest cent Draw a cut-off line: Þl The first digit cut is, which is or less. The part Answer: Þ 15. Þ' to the nearest dollar Draw a cut-off line: Þl' The first digit cut is ', which is or more, so Answer: 17. Þ Þ yy yyy y Þ Þ' Check: 19. Ð Þ(Ñ Þ Þ' Þ Write four zeros. Þ( à decimal places ( ( Þ Ã decimal places 21. Þ( Þ ' Þ( y y Þ Þ Check: Þ Þ Þ( 23. Þ' Þ( Þ Þ' Þ( Þ Þ Þ 25. Þ Þ Þ (Þ' Þ Þ (Þ' Þ( (Þ' œ Þ( Subtract Subtract Subtract 27. ÐÞÑÐÞ'(Ñ œ Þ Þ

15 4.5 Dividing Decimals Perimeter œ Þ( Þ( Þ( Þ( œ Þ' Þ( Þ( œ Þ Þ( œ Þ inches Area 31. 'Þ' (Þ( Þ Þ œ ÐÞ(ÑÐÞ(Ñ œ Þ'' Þ'' inch radish tomato onion combined weight Multiply The combined weight is Þ pounds. 33. ' (Þ( y y y y tomato Þ' Þ' ( apple difference The tomato is Þ'( pounds heavier than the apple. 35. Find their total revenue. ( Þ price per blanket number of blankets Þ' total revenue Subtract their cost from the revenue. Þ' yy total revenue Þ cost 'Þ profit They made a profit of 'Þ. 4.5 Dividing Decimals 4.5 Margin Exercises 1. (a Þ Check: Þ Þ' ' ' Þ' (b Þ Check: Þ ''Þ ' ' 'Þ ' Add Add Add (c Þ Check: Þ (Þ (Þ (d Þ ƒ Þ'( Þ (e Þ ƒ Check: Þ'( Þ Þ Check: Þ Þ ( ' ' Þ 2. (a Þ 'Þ Ã Check: Þ 'Þ or 'Þ Write one zero.

16 128 Chapter 4 Decimals (b Þ( ƒ Þ Þ( à ( ( ( Write one zero. Check: Þ Þ( or Þ( Þ (c Þ ' Þ Ã Write one zero. Check: (d Þ ƒ Þ' Þ or Þ Þ( Þ Ã ' ' Check: Þ( Þ or Þ Write three zeros. 3. (a '(Þ 4. '(Þ ƒ Þ There are no repeating digits visible on the calculator. Þl rounds to Þ. Check: ÐÞÑÐÑ œ '(Þ( '(Þ (b 'Þ Þ ƒ ' Þ'''' There is a repeating decimal: Þ'. Þ'l''' rounds to Þ(. Check: ÐÞ(ÑÐ'Ñ œ Þ Þ Þ (c œ Þ ƒ Þ There is a repeating decimal: Þ. Þl rounds to Þ'. Check: ÐÞ'ÑÐÑ œ Þ Þ (d 'Þ ƒ Þ There is a repeating decimal: ÞÞ Þl rounds to Þ. Check: ÐÞÑÐÑ œ 'Þ 'Þ (e 'Þ ƒ Þ((( The answer has a repeating decimal that starts repeating in the fourth place: Þ(. Þ(l( rounds to Þ(. Check: ÐÞ(ÑÐÑ œ 'Þ 'Þ (a Þ Þ ^ Þ ^ (b Þ Þ' ^ Þ ^ ( ( '

17 4.5 Dividing Decimals 129 (c ' Þ ^ Þ ^ (d Þ ƒ Þ Þ ^ Þ ^ ( ' ( (e Þ Þ Þ Þ ^ (Þ ^ ' ' (f Þ ƒ 'Þ Þ ' Þ' 'Þ ^ Þ ^ ' ( 5. (a Þ( ƒ Þ œ Þ Estimate: ƒ œ The answer is not reasonable. Þ Þ ^ Þ ( ^ ( ( ' The answer should be Þ. (b (Þ ƒ Þ(' œ Þ Estimate: ƒ œ The answer is reasonable. (c Þ' ƒ œ Þ Estimate: ƒ œ The answer is not reasonable. Þ Þ Þ' ' ' ( ' The answer should be Þ. (d Þ ƒ Þ' œ Þ Estimate: ƒœ The answer is not reasonable. Þ Þ' ^ Þ ^ The answer should be Þ. 6. (a Þ' Þ( Þ Þ' Þ( Þ Þ Þ œ 'Þ' (b Þ' ƒ Þ Þ' Þ Þ' œ Þ Exponent Subtract Add Divide Multiply

18 130 Chapter 4 Decimals (c Þ Þ'Ð ÞÑ Þ Þ'ÐÞÑ Þ Þ' œ Þ' (d Þ ÞÐÞÑ ƒ Þ Þ Þ' ƒ Þ Þ Þ(( œ (Þ 4.5 Section Exercises 1. Þ ((Þ ' ' Þ 3. Þ ( Þ ' ' ' Þ Þ ^ Þ ^ ' Þ ^ Þ ^ 9. Given: ƒ œ ' Find: Þ ƒ Þ Parentheses Multiply Add Multiply Divide Subtract Move decimal point in divisor and dividend 2 places; write one zero. Move decimal point in divisor and dividend 1 place; write 0. The new dividend, Þ, has the effect of moving the decimal place in the answer left three places. The new divisor, Þ, has the effect of moving the decimal place in the answer right one place. So the new answer has the decimal point moved to the left two places. Þ ƒ Þ œ Þ' 11. Given: ƒ œ ' Find: Þ or ƒ Þ The new divisor, Þ, has the effect of moving the decimal place in the answer right three places. ƒ Þ œ ' Þ Þ' ^ 'Þ ^ Þ Þ' 'Þ ''' Þ' ^ Þ ^ ' ' ' ' ' 'Þ''' rounds to 'Þ'(. 17. Þ ƒ 'Þ( Þ ' ' ' Move decimal point in divisor and dividend 1 place. Move decimal point in divisor and dividend 3 places. Write 00 in dividend. Write 0 in dividend. Write 0 in dividend. Write 0 in dividend. Stop and round answer to the nearest hundredth. Write 0 in dividend. Write 0 in dividend. Write 0 in dividend. Stop and round answer to the nearest thousandth. 'Þ( rounds to 'Þ('Þ 19. Þ Þ Enter on calculator: Þ ƒ Þ œ Round,Þ'(' to,þ'(.

19 4.5 Dividing Decimals Þ(( ƒ œ Þ(( Þ ƒ œ Þ Þ' ƒ œ Þ' Þ ƒ œ Þ 'Þ ƒ œ Þ' ''Þ( ƒ œ ''Þ( (a Dividing by, decimal point moves one place to the left; by, two places to the left; by, three places to the left. (b The decimal point moved to the right when multiplying by or or. Here the decimal point moves to the left when dividing by those numbers. 23. (Þ ƒ œ (Þ Estimate: ƒ œ The answer (Þ is unreasonable. Þ( (Þ ' ' The correct answer is Þ(. 25. Þ' ƒ Þ œ Þ Estimate: ƒ œ The answer Þ is reasonable. 27. (Þ ƒ Þ œ 'Þ Estimate: ƒ œ ' The answer 'Þ is unreasonable. ' Þ Þ ^ (Þ ^ ' The correct answer is 'Þ. 29. Þ ƒ Þ œ Þ( Estimate: ƒœ The answer Þ( is unreasonable. (Þ Þ ^ Þ ^ ( The correct answer is (Þ. 31. Divide the cost by the number of pairs of tights. Þ' 'Þ ' Þ' rounds to Þ. One pair costs Þ. 33. Divide the balance by the number of months. '(Þ Þ' ' ( ' ' Aimee is paying '(Þ per month. 35. Divide the total cost by the number of bricks to find the cost per brick. Þ ' Þ ( ( One brick costs Þ.

20 132 Chapter 4 Decimals 37. Divide the total earnings by the number of hours. Þ ('Þ (' ' ' Darren earns Þ per hour. 39. Divide the miles driven by the gallons of gas. 'Þ ƒ 'Þ Þ( She got Þ miles per gallon (rounded. 41. First find the sum of lengths for Jackie Joyner- Kersee. (Þ (Þ (Þ (Þ (Þ 'Þ' Then divide by the number of jumps, namely. (Þ( 'Þ' ' (Þ( rounds to (Þ(. The average length of the long jumps made by Jackie Joyner-Kersee is (Þ( meters (rounded. 43. Subtract to find the difference. (Þ (Þ Þ fifth longest jump sixth longest jump difference The fifth longest jump was Þ meter longer than the sixth longest jump. 45. Add the lengths of the top three athletes. (Þ (Þ (Þ Þ The total length jumped by the top three athletes was Þ meters. 47. (Þ Þ Þ (Þ Þ Þ Þ œ Þ 49. Þ' Þ'ÐÞ ÞÑ Þ' Þ'ÐÑ Þ' Þ œ (Þ 51. Þ' Þ'ÐÞÑ ƒ 'Þ Þ' (Þ ƒ 'Þ Þ' (Þ( œ Þ Exponent Subtract Add Parentheses Multiply Add Multiply Divide Subtract Parentheses; 53. ÞÐÞ' Ñ Þ Exponent ÞÐÞ'Ñ Þ' Multiply Þ(' Þ' Subtract Þ Þ' œ Þ Subtract 55. Multiply the price per can by the number of cans. Þ( ' Þ Subtract to find total savings. Þ Þ Þ( There are six cans, so divide by ' to find the savings per can. Þ 'Þ( Þ rounds to Þ. You will save Þ per can (rounded.

21 4.6 Writing Fractions as Decimals 133,, 57. (a,, pieces each hour (b There are ' œ minutes in a day.,, ', pieces each minute (c There are ' ' œ ', seconds in a day.,, ', pieces each second 59. Divide, by Þ,. Þ ^, Þ ^ The school would need to collect, box tops. 61. Divide, (the answer from Exercise 59 by. 'Þ, Þ (' ' 'Þ rounds to '. The school needs to collect ' box tops (rounded during each of the weeks. 4.6 Writing Fractions as Decimals 4.6 Margin Exercises 1. (a is written. (b is written. (c is written. (d is written. (e ' is written '. (f is written. 2. (a Þ Þ œþ (b œ Þ Þ œ Þ (c (d (e œ Þ' Þ' Þ ' Þ ' Þ Þ' œ Þ' œ Þ' ( ( œ Þ( Þ( (Þ ' ' '

22 134 Chapter 4 Decimals 3. (a Þ Þ Rounded to the nearest thousandth, Þ. (b ( œ Þ(((( Þ ( ' ( ' ( ' ( ' ( (c (d Rounded to the nearest thousandth, Þ((. Þ Þ Rounded to the nearest thousandth, Þ. ( Þ (Þ ' ' Rounded to the nearest thousandth, ( Þ. ( (e ' œ ' Þ 'Þ Rounded to the nearest thousandth, Þ. 4. (a On the first number line, Þ( is to the left of Þ, so use the symbol: Þ( Þ (b On the first number line, Þ( is to the right of Þ'(, so use the symbol: Þ( Þ'( (c Þ' Þ' (d œ œ Þ Þ Þ(, so Þ(. (e On the second number line, Þ and ' are at the same point, so use the œ symbol: Þ œ ' (f Þ ˆ œþ (g Þ Þ' (h œþ (i œ œ Þ' ' Þ( Þ', so Þ(. ' (j œþ 5. (a Þ( Þ( Þ( Æ Æ Æ Þ( Þ( Þ( From least to greatest: Þ(, Þ(, Þ( or Þ(, Þ(, Þ( '

23 4.6 Writing Fractions as Decimals 135 (b 'Þ 'Þ 'Þ 'Þ Æ Æ Æ Æ 'Þ 'Þ 'Þ 'Þ From least to greatest: 'Þ, 'Þ, 'Þ, 'Þ or 'Þ, 'Þ, 'Þ, 'Þ (c Þ Þ Æ Æ Æ Þ Þ( Þ From least to greatest: Þ, Þ, Þ( or Þ, Þ, (d,, (, Þ To compare, change fractions to decimals. œ Þ œ Þ Þ ( From least to greatest: Þ, Þ, Þ, Þ or,, Þ, ( 4.6 Section Exercises 1. œþ Þ Þ 3. œþ( Þ( Þ 5. œþ Þ Þ 7. œþ Þ Þ 9. œþ' Þ' Þ 11. ( œ Þ( Þ ( (Þ ' ' ' 13. œ œ Þ Þ Þ ( ( 15. œ œ Þ( œ Þ( 17. œ œ Þ' Þ ' Þ ' 19. ' œ 'Þ 'Þ 21. ' Þ Þ ( 23. œ Þ Þ 25. (a In, the numerator is less than the denominator, so the decimal must be less than (not Þ. (b means ƒ or, so the correct answer is Þ' (rounded. This makes sense because both the fraction and the decimal are less than. Þ Þ

24 136 Chapter 4 Decimals 26. (a She changed Þ to Þ when adding to. (b Adding the whole number part gives Þ, which is Þ, not Þ. To check, Þ œ œ (, but Þ œ œ ( Þ 27. Just add the whole number part to Þ(. So œ Þ(; œ Þ( ; œ Þ(Þ 28. It works only when the fraction part has a one-digit numerator and a denominator of, a two-digit numerator and a denominator of, and so on. ƒ 29. Þ œ œ œ ƒ ' ' ƒ 31. Þ' œ œ œ ƒ ƒ ( 33. Þ œ œ œ ƒ ( 35. œþ Þ (Þ ' ƒ 37. Þ œ œ œ ƒ ƒ 39. Þ œ œ œ ƒ 41. œþ Þ Þ 43. Þ œ 45. Compare the two lengths. average length Ä Þ longer Charlene's baby Ä Þ shorter Þ Þ Þ( Her baby is Þ( inch shorter than the average length. 47. Write two zeros to the right of Þ so it has the same number of decimal places as Þ. Then you can compare the numbers: Þ Þ. There was too much calcium in each capsule. Subtract to find the difference. Þ Þ Þ There was Þ gram too much. 49. Write two zeros so that all the numbers have four decimal places. Þ Þ unacceptable Þ Þ and Þ Þ acceptable Þ( Þ and Þ( Þ acceptable Þ Þ unacceptable The lengths of Þ cm and Þ( cm are acceptable. 51. Compare the two amounts. Ä Þ( less Þ Ä Þ more Þ Þ( Þ Þ inches is Þ inch more than Ginny hoped for. 53. Þ, Þ, Þ Þ œ Þ Þ œ Þ Þ œ Þ greatest least From least to greatest: Þ, Þ, Þ 55. Þ, Þ(, Þ(, Þ Þ œ Þ Þ( œ Þ( Þ( œ Þ( Þ œ Þ least greatest From least to greatest: Þ(, Þ(, Þ, Þ 57. Þ', Þ', Þ', Þ' Þ' œ Þ' Þ' œ Þ' Þ' œ Þ' Þ' œ Þ' greatest least From least to greatest: Þ', Þ', Þ', Þ'

25 Chapter 4 Review Exercises Þ(, Þ(', Þ, Þ The numbers after the decimal places are irrelevant since the whole number parts are all different. From least to greatest: Þ, Þ, Þ(', Þ( 61. Þ, Þ, Þ', Þ œ Þ Þ œ Þ Þ' œ Þ' œ Þ greatest least From least to greatest: Þ', Þ,, Þ 63.,, Þ(, Þ œ Þ( œ Þ Þ( œ Þ( Þ œ Þ least greatest Þ( From least to greatest:,,, Þ 65. Find the greatest of: Þ, Þ, Þ, Þ Þ œ Þ greatest Þ œ Þ Þ œ Þ least Þ œ Þ List from least to greatest: Þ, Þ œ Þ, Þ The red box, labeled Þ in. diameter, has the strongest line. 67. Convert to a decimal. 0.. à Since œ Þ, the box having line inch in diameter is the green box. ( 69. œ ' ' Þ ' Þ ' ( ' ' Þ rounded to the nearest tenth is Þ. Length (a is Þ inches (rounded œþ Þ rounded to the nearest tenth is Þ. Length (c is Þ inch (rounded. Þ ( Þ ' ' Þ( rounded to the nearest tenth is Þ. Length (e is Þ inch (rounded. Chapter 4 Review Exercises tenths hundredths 1. Þ ones tenths 2. Þ ' ( hundreds hundredths 3. Þ tens tenths 4. ' Þ tenths ten-thousandths 5. Þ ( ' 6. Þ œ œ 7. ( ( ƒ Þ( œ œ œ ƒ 8. ƒ Þœ œ œ ƒ 9. ( ( ƒ ( Þ( œ œ œ ƒ

26 138 Chapter 4 Decimals 10. Þ( œ ( ƒ 11. (Þ œ ( œ ( œ ( ƒ 12. Þ is eight tenths. 13. Þ is four hundred and twenty-nine hundredths. 14. Þ( is twelve and seven thousandths. 15. Þ' is three hundred six ten-thousandths. 16. eight and three tenths: œ Þ 17. two hundred five thousandths: œ Þ 18. seventy and sixty-six ten-thousandths: ( '', œ (Þ'' 19. thirty hundredths: œþ 20. (Þ' to the nearest tenth Draw a cut-off line: (Þ'l The first digit cut is, which is or less. The part Answer: (Þ' 21. (Þ( to the nearest hundredth Draw a cut-off line: (Þ(l The first digit cut is, which is or more, so Answer: (Þ( 22. Þ' to the nearest thousandth Draw a cut-off line: Þ'l The first digit cut is, which is or less. The part Answer: Þ' 23. Þ to the nearest thousandth Draw a cut-off line: Þl The first digit cut is, which is or more, so Answer: Þ 24. Þ to the nearest tenth Draw a cut-off line: Þl The first digit cut is, which is or more, so Answer: Þ 25. Þ to the nearest cent Draw a cut-off line: Þl The first digit cut is, which is Answer: Þ 26. Þ' to the nearest cent Draw a cut-off line: Þ'l The first digit cut is, which is Answer: Þ( or less. The part or more, so 27. (,'Þ(' to the nearest cent Draw a cut-off line: (,'Þ(l' The first digit cut is, which is or less. The part Answer: (,'Þ( 28. Þ to the nearest dollar Draw a cut-off line: Þl The first digit cut is, which is Answer: or less. The part 29. Þ to the nearest dollar Draw a cut-off line: Þl The first digit cut is, which is or more, so Answer: 30. Þ' to the nearest dollar Draw a cut-off line: Þl' The first digit cut is ', which is or more, so Answer: 31. Þ( to the nearest dollar Draw a cut-off line: Þl( The first digit cut is, which is or less. The part Answer: 32. Estimate: Exact: ' Þ Þ' Þ ' Þ' 33. Estimate: Exact: (Þ' Þ Þ Þ Þ( Þ

27 Chapter 4 Review Exercises Estimate: Exact: Þ (Þ Þ( 35. Estimate: Exact: Þ (Þ' Þ' 36. Estimate: Exact: cats Þ birds 'Þ' ( difference (Þ cats birds difference There are (Þ million more pet cats than there are pet birds in America. 37. Add the amounts of the two checks. Estimate: Exact: Þ Þ'( 'Þ The total amount of the two checks was 'Þ. Now subtract from her balance of '. Estimate: Exact: 'Þ 'Þ ' Þ The new balance is Þ. 38. First total the money that Joey spent. Estimate: Exact: Þ Þ Þ ( Þ' Then subtract to find the change. Estimate: Exact: Þ ( Þ' Þ Joey's change was Þ. 39. Add the kilometers that she raced each day. Estimate: Exact: Þ Þ Þ km Þ km Roseanne raced Þ kilometers. 40. Estimate: Exact: ' 'Þ Þ( '' Þ(' 41. Estimate: Exact: Þ Þ ( ( Þ( 42. ÐÞ'ÑÐÞÑ Þ' à decimal place Þ Ã decimal places Þ Ã decimal places 43. Þ(ÐÞÑ Þ( à decimal places Þ Ã decimal places Þ Ã ' decimal places 44. ('Þ ƒ œ Þ Estimate: ( ƒ œ ( Þ is reasonable. 45. 'Þ' ƒ Þ œ Þ Estimate: ƒ œ Þ is not reasonable. Þ Þ ^ 'Þ ' ^ Move decimal point 1 place in divisor and dividend; write one zero. The correct answer is Þ. 46. Þ''' Þ Write one zero. Write one zero. Write one zero. Þ''' rounds to Þ'(.

28 140 Chapter 4 Decimals 47. ( ( œ œ Þ' ' 48. Þ ƒ Þ œ Þ ƒ Þ Þ 49. Multiply the hourly wage times the hours worked. Pay for Pay rate Pay for first 40 after 40 over 40 hours hours hours Þ Þ Þ' Þ 'Þ 'Þ' ( ' ' Þ' Þ Add the two amounts. 'Þ' Þ (Þ Adrienne's total earnings were ( (rounded. 50. Divide the cost of the book by the number of tickets in the book. Þ Þ Round to the nearest cent. Draw a cut-off line: Þl The first digit cut is, which is or less. The part Each ticket costs Þ (rounded. 51. Divide the amount of the investment by the price per share. Þ Þ( ^ Þ ^ ( Round Þ down. Kenneth could buy shares. 52. Multiply the price per pound by the amount to be purchased. Þ Þ ( Þ' Þ' rounds to Þ(Þ Ms. Lee will pay Þ(. 53. Þ Þ(ÐÞÑ Þ Þ(ÐÞÑ Þ 'Þ' œ Þ Exponent Multiply Add 54. Þ' ƒ ÐÞ ÞÑ Þ' ƒ Þ' Þ œ Þ Parentheses Divide Subtract 55. œ œ Þ Þ Þ 56. ' œþ' Þ' 'Þ

29 Chapter 4 Review Exercises 141 ( 57. œ œ Þ( Þ ( Þ ( ' ' ' 58. Þ Þ Þ rounds to Þ. Þ 59. Þ', Þ', Þ' Þ' œ Þ' Þ' œ Þ' Þ' œ Þ' From least to greatest: Þ', Þ', Þ' greatest least 60. Þ, Þ, Þ, Þ Þ œ Þ Þ œ Þ Þ œ Þ Þ œ Þ greatest least From least to greatest: Þ, Þ, Þ, Þ 61. Þ(,,, Þ Þ( œ Þ( greatest œ Þ œ Þ least Þ œ Þ From least to greatest:,, Þ, Þ( 62. [4.3] Þ Þ( Þ' Þ Þ( Þ' Þ Þ' 63. [4.4] (Þ Þ (Þ Ã decimal place Þ Ã decimal place ' Þ Ã decimal places 64. [4.5] 'Þ ƒ Þ' Þ' Þ' rounds to Þ'. 65. [4.3] Þ yy yyyy Þ Þ 66. [4.4] ÞÐÞ(Ñ 67. [4.5] Þ Ã decimal places Þ( à decimal places Þ'' à decimal places Þ Þ ^ Þ ( ^ Move decimal point 3 places in divisor and dividend; write [4.3] (Þ Þ Þ( (Þ Þ Þ( (Þ'( 69. [4.5] Þ' ƒ Þ Þ' ' ' 70. [4.5] ÐÞ' ÞÑ ÞÐÞÑ Þ ÞÐÞÑ Þ Þ œ Þ Parentheses Multiply Add

30 142 Chapter 4 Decimals 71. [4.4] Þ Þ Ã decimal places ' Þ Ã decimal places 72. [4.4] ÐÞ'ÑÐÞÑ Þ Ã decimal places Þ' à decimal place Þ Ã decimal places 73. [4.5] Þ (Þ ' (Þ' ƒ Þ œ 74. [4.3] Þ Þ Þ Þ Þ 75. [4.5] Þ ƒ Þ Exponent Þ ƒ Þ Divide Þ œ Þ Subtract 76. [4.5] Men's socks are pairs for Þ. Divide the price by to find the cost of one pair. Þ' Þ ' ( ( Þ' rounds to Þ. One pair of men's socks costs Þ (rounded. 77. [4.5] Children's socks cost ' pairs for Þ. Find the cost for one pair. Þ 'Þ Þ rounds to Þ. Subtract to find how much more men's socks cost. Þ Þ Þ( Men's socks cost Þ( (rounded more. 78. [4.4] A dozen pair of socks is œ pairs of socks. So multiply times Þ. Þ Þ' The cost for a dozen pair of men's socks is Þ'. 79. [4.4] Five pairs of teen jeans cost Þ times. Þ Þ( Four pairs of women's jeans cost Þ times. Þ Þ' Add the two amounts. Þ( Þ' Þ( Akiko would pay Þ(. 80. [4.3] The highest regular price for athletic shoes is Þ. The cheapest sale price is (. Subtract to find the difference. Þ (Þ (Þ The difference in price is (Þ. 81. [4.6] Þ œ Þ Þ'' œ Þ'' Þ( œ Þ( Þ œ Þ Þ œ Þ Þ œ Þ Þ( œ Þ( List from least to greatest. Þ, Þ, Þ, Þ, Þ(, Þ'', Þ( (a Þ( mg is the greatest. A baked potato with skin has the highest amount of Vitamin B- '.

31 Chapter 4 Test 143 (b Þ is the least. A cup of orange juice has the lowest amount of Vitamin B- '. (c Subtract to find difference. Þ( Þ Þ The difference is Þ milligram. 82. [4.6] (a Banana: Þ'' mg ounces of skinless chicken: Þ mg cup of strawberries: Þ Þ mg Add the amounts. Þ'' Þ Þ Þ' banana chicken strawberries You would get Þ' milligrams of Vitamin B- '. (b Subtract the recommended amount, mg, from the amount you got. Þ' Þ Þ' You got Þ' milligram more than the recommended amount. Chapter 4 Test 1. ƒ Þ œ œ œ ƒ 2. ( ( ƒ Þ( œ œ œ ƒ 3. 'Þ( is sixty and seven thousandths. 4. Þ is two hundred eight ten-thousandths. 5. (Þ' to the nearest tenth Draw a cut-off line: (Þ'l The first digit cut is, which is Answer: (Þ' or less. The part 6. Þ' to the nearest thousandth Draw a cut-off line: Þ'l The first digit cut is, which is or more, so Answer: Þ' 7. Þ to the nearest cent Draw a cut-off line: Þl The first digit cut is, which is Answer: Þ 8. (Þ to the nearest dollar Draw a cut-off line: (Þl The first digit cut is, which is Answer: (' 9. (Þ' Þ Þ Estimate: Exact: (Þ' Þ Þ Þ 10. (Þ Þ' Estimate: Exact: (Þ Þ' (' (Þ 11. Þ(ÐÞÑ Estimate: Exact: ' Þ( Þ ' ( 'Þ 12. Þ ƒ Þ Estimate: Exact: or less. The part or more, so Line up decimals. Line up decimals. Þ ( Þ ^ Þ ^ ' ' 13. Þ Þ' ( Þ Þ Þ' (Þ Þ Þ(' Line up decimals.

32 144 Chapter 4 Decimals 14. '( Þ' '(Þ Þ' ''Þ Line up decimals. 15. ÐÞ'ÑÐÞ(Ñ Þ' à decimal places Þ( à decimal places Þ Ã ( decimal places 16. Þ Þ ^ ( Þ ^ Move decimal point 2 places ' in dividend and divisor; write two zeros. 17. œ Þ' Þ ' ' œ Þ' 18. Þ, Þ,, Þ' Change to ten-thousandths, if necessary, and compare. Þ œ Þ least Þ œ Þ greatest œ Þ Þ' œ Þ' From least to greatest: Þ,, Þ', Þ 19. 'Þ Þ ÞÐÞÑ Þ' Þ ÞÐÞÑ Þ' Þ Þ( Þ( Þ( œ Þ Exponent Multiply Subtract Add 20. To find the balance, add the interest and the deposit to the balance and then subtract the bank charge. (Þ 'Þ( Þ 'Þ Þ(( 'Þ( 'Þ( The new balance is 'Þ(. 21. Þ million gadwalls Þ million wigeons Þ' million pintails From the greatest number to the least: pintails, wigeons, gadwalls 22. Multiply the price per pound by the amount purchased. Þ Þ Þ' Round Þ' to the nearest cent. Draw a cut-off line: Þl' The first digit cut is ', which is or more, so Mr. Yamamoto paid Þ for the cheese. 23. Subtract the two temperatures. Þ( Þ Þ The temperature dropped Þ degrees. 24. Divide to find the cost per foot. Þ ( 'Þ ^ Þ ' ^ Move decimal point 1 place ' in dividend and divisor; write one zero. The chain costs Þ( per foot (rounded. 25. Answers will vary. Cumulative Review Exercises (Chapters , to the nearest thousand Draw a cut-off line: l The first digit cut is, which is or more, so Answer:, 2. 'Þ( to the nearest hundredth Draw a cut-off line: 'Þl( The first digit cut is, which is or less. The part Answer: 'Þ

33 Cumulative Review Exercises (Chapters (Þ' to the nearest dollar Draw a cut-off line: (Þl' The first digit cut is ', which is Answer: ( 4. Þ to the nearest cent Draw a cut-off line: Þl The first digit cut is, which is Answer: Þ 5. Þ Þ Þ Þ'( Line up decimals. or more, so 6. y œ œ œ œ y or less. The part 7. ' y ƒ œ ƒ œ ' ( œ œ y 8. ' ' 9. Þ( (Þ Þ( Þ (Þ Þ' 10. R ( 11. œ ' ( œ Line up decimals. ( œ 12. ( (,( 13. ÐÞ'ÑÐÞÑ Þ' à decimal places Þ Ã decimal places Þ' à decimal places 14. ÞÐÞÑ Þ Ã decimal place Þ Ã decimal place ' ' Þ Ã decimal places 15. Þ ƒ Þ' Þ' ^ Þ ^ y 16. ƒ œ ƒ œ ' œ ' ' y 17. œ œ ( ( ( œ œ œ 18. Þ( ƒ Þ Þ Þ ^ Þ( ^ ' ' Round Þ to the nearest hundredth. Draw a cut-off line: Þl The first digit cut is, which is or more, so Answer: Þ

34 146 Chapter 4 Decimals 19. ƒ ' œ 20. È ' ÐÑ È' ÐÑ ' ' ÐÑ ' ' ' ' œ Divide Multiply Subtract Exponent Square Root Multiply Add Subtract 21. Þ is forty and thirty-five thousandths. 22. Three hundred six ten-thousandths is Þ'. 23. (Þ, (Þ, (Þ, (Þ (Þ œ (Þ least (Þ œ (Þ (Þ œ (Þ (Þ œ (Þ greatest From least to greatest: (Þ, (Þ, (Þ, (Þ ( 24., Þ,, Þ ( œ Þ( greatest Þ œ Þ least œ Þ Þ œ Þ From least to greatest: ( Þ, Þ,, 25. He started with two bills, or. He spent (Þ' and Þ(. Estimate: œ First find how much money Lameck spent. (Þ' Þ( Þ Now subtract from. Þ Þ Þ( He has Þ( left. 26. Subtract the two measurements. Estimate: ( œ inches Exact: œ ' œ ' 27. Multiply the hourly wage, Þ', by the hours worked, 'Þ. Estimate: œ Exact: Þ' 'Þ ' ( ' Þ Þ rounded to the nearest cent is Þ. Sharon earned Þ (rounded. 28. Find the number of students in each size of classroom ( have students and have ' students. Then add the two sums. Estimate: Ð Ñ Ð Ñ œ ' œ ' students Exact: ' (' (' ' There are students attending the school. 29. Add the two purchases. Estimate: œ' yards Exact: œ ( œ œ œ' Toshihiro bought yards of fabric. ' 30. Add the deposit to the amount Kimberly had in her account. Then subtract the amount for the check that she wrote and the overdraft charge. Estimate: œ ( Exact: Þ Þ' Þ Þ Þ Þ Þ Balance on hand Deposit Check Overdraft New Balance The new balance in her account is Þ. She has grown inches.

35 Cumulative Review Exercises (Chapters Divide the price of the apples, 'Þ, by the number of pounds of apples, Þ(, that Paulette bought. Estimate: 'ƒ œ per pound Exact: Þ Þ( ^ 'Þ ^ Move decimal point one place in divisor ( and dividend. ' ' Þ rounds to Þ. The cost of the apples is Þ per pound (rounded. 32. Divide the amount of the grant by the number of students. Estimate:, ƒ œ Exact: (Þ ( (, Þ ( ' ' ' ( ( (Þ rounds to (. Each student could be given ( (rounded. 33. ' Order size M (medium. 34. Size XXS À œ ( ' œ ' 35. Size S: œ œ The difference for size S is inch. Size M: œ œ œ œ ( The difference for size M is 3 4 ( inch. Size L: œ œ œ œ The difference for size L is 3 4 inch. œ Þ Þ Þ ' œþ Þ Þ œ Þ œ Þ Þ( in. The difference for size XXS is Size XS: œ œ The difference for size XS is inch. 3 4 inches. ( ( ƒ ( Þ( œ œ œ ƒ inch, which is the same as the answer in Exercise Answers will vary. Many people prefer using decimals because you do not need to find a common denominator or rewrite answers in lowest terms.

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