MAT 115 – Basic Mathematics
Week #4 Checkpoint Chapter 4
Name:Section 4.1 – pp. 287-291, # 2, 4, 24, 34, 72
Problems(Enter your work and answer in this column)
2. For the decimal 8.57932: What is the place value of 5?
Tenths
4. For the decimal 8.57932: What is the place value of 2?
Hundredths
24. Write as a common fraction or mixed number: 4.0171
4 171/1000
34. Arrange in order from smallest to largest:
First, convert the fractions to decimals with the same number of decimal places:
2.0500,2.5000,2.0513,2.0590,2.5100,2.0515,2.0520,2.0510
Now, put them in order (based on the numbers after the decimal point):
2.0500,2.0510,2.0513,2.0515,2.0520,2.0590,2.5000,2.5100
Convert back to the orginal form:
2.05,2.051,2.0513,2.0515,2.052,2.059,25/10,251/100
72.
Lula wants to round 76.24491 to the nearest hundredth. She first rounds 76.24491 to 76.245 and then rounds 76.245 to 76.25 and claims that this is the final answer. What is wrong with this approach?
She should only look at the value in the thousandths place (one to the right of the hundredths place). That is a 4, so she should round down, to:
76.24
Section 4.2 – pp. 301-308, #20, 36, 48, 58, 72
20. Add: 27.4 + 213.321 + 39.38280.101
36. Subtract:
36.85
48. Add thirty-eight and nine tenths, five and fifty-eight hundredths, seven, and 15 and 8 tenths.
38 + 9/10 + 5 + 58/100 + 7 + 15 + 8/10
= 67.28 = 67 and 28/100 = 67 and 14/50 = 67 and 7/25
58. Geometry. Find the perimeter of the figure below:
Add them up:
33.2ft
72. Business and finance. Alem’s restaurant bill is pictured below. Estimate his total (not including tip) by rounding to the nearest dollar.
approx:
18+9+7+7+2
= $43
Section 4.3 – pp. 317-320, # 32, 68, 70
32. Claudia earns $6.40 per hour (h). For overtime (each hour over 40 h) she earns $9.60. If she works 48.5 h in a week, what pay should she receive?40*6.4+8.5*9.6
= $337.60
68. Business and finance. To find the simple interest on a loan for 1 year at 12.5%, multiply the amount of the loan by 0.125. What simple interest will you pay on a loan of $1,458 at 12.5% for 1 year?
1458*0.125
= $182.25
70. Business and finance. In a bottling company, a machine can fill a 2-liter (L) bottle in 0.5 seconds (s) and move the next bottle into place in 0.1 s. How many 2-L bottles can be filled by the machine in 2 h?
2 hours * 60 minutes * 60 seconds / (0.5 + 0.1) sec
= 12000 bottles
Section 4.4 – pp. 329-333, # 4, 10, 20, 26, 30, 38, 44
4. Find the circumference. Use 3.14 for and round your answer to one decimal place.3.14*2*3.75
= 23.55 ft
10. (2 pts) Find the perimeter.
10 + 10 + ¼ * 2*3.14*10
= 35.7 in
20. Find the area:
Bh = 5*7
= 35 in^2
26. Find the area:
= 6*7 + ½ * 2*6
= 42 + 6
= 48 yd^2
30. Crafts. A circular coffee table has a diameter of 5 ft. What will it cost to have the top refinished if the company charges $3 per square foot for the refinishing?
area = pi*r^2
= pi*(d/2)^2
= 3.14*(5/2)^2
multiply by price:
= 3*3.14*(5/2)^2
= $58.875
round to:
$58.88
38. Construction. An A-frame cabin has a triangular front with a base of 30 ft. and a height of 20 ft. If the front is to be glass that costs $3 per square foot, what will the glass cost?
area = 0.5*b*h = 0.5*30*20
= 300 sq ft
Multiply by cost:
= $900
44. The distance from Philadelphia to Sea Isle City is 100 mi. A car was driven this distance using tires with a radius of 14 in. How many revolutions of each tire occurred on the trip?
c = 2*pi*r
= 2*3.14*14
= 87.92 in
= 0.0013876262626 miles
100/0.0013876262626
= about 72065.51
Section 4.5 – pp. 345-348, # 24, 52, 74
24. Divide:= about 0.1609
52. Business and finance. A shipment of 72 paperback books cost a store $190.25. What was the average cost per book to the nearest cent?
190.25/72
= $2.64
52. Business and finance. Seven employees of an office donated a total of $172.06 during a charity drive. What is the average donation?
172.06/7
= $24.58
74. Four brands of soap are available in a local store.
Brand / Ounces / Total Price / Unit Price
Squeaky Clean / 5.5 / $0.36 / 0.0655
Smell Fresh / 7.5 / 0.41 / 0.0547
Feel Nice / 4.5 / 0.31 / 0.0689
Look Bright / 6.5 / 0.44 / 0.0677
Compute the unit price and decide which brand is the best buy.
Smell fresh is the best.
Section 4.6 – pp. 356-358, # 20, 36
20. Find the decimal equivalent:7.75
36. Statistics. The following table gives the free throws attempted (FTA) and the free throws made (FTM) for the top five players in the NBA for a recent season. Calculate the free throw percentage for each player by writing the FTM over the FTA and converting this to a decimal. Round to 3 decimal places.
Player / FTM / FTA
Allan Houston / 363 / 395
Ray Allen / 316 / 345
Steve Nash / 308 / 339
Troy Hudson / 208 / 231
Reggie Miller / 207 / 230
Player / Decimal
Allan Houston / 0.919
Ray Allen / 0.916
Steve Nash / 0.909
Troy Hudson / 0.900
Reggie Miller / 0.900
Activity 12: Terminate or Repeat – p. 359, all
(Refer to text – the complete problem is shown. Follow the directions found there.)Fraction / Decimal Form / Terminate? / Prime Factorization of Denominator
/ 0.5 / Y / 2
/ 0.3333… / N / 3
/ 0.25 / Y / 2*2
/ 0.2 / Y / 5
/ 0.1666… / N / 2*3
/ 0.142857… / N / 7
/ 0.125 / Y / 2*2*2
/ 0.1111… / N / 3*3
/ 0.1 / Y / 2*5
/ 0.0909… / N / 11
/ 0.08333… / n / 2*2*3
State a general rule:
If the prime factorization has only 2’s and/or 5’s the decimal will terminate.
Test on three fractions:
1/20 = 0.05 (pf = 2*5*2*5)
1/22 = 0.04545… (pf = 2*11)
1/25 = 0.04 (pf = 5*5)
Section 4.7 – pp. 362-363, # 28, 30, 34
28. Write as a common fraction or mixed number in lowest terms:15.35
= 15 and 35/100
Divide the top and bottom of the fraction by 5:
15 and 7/20
30. Complete using the symbol < or >:
5/16 = 0.3125
0.3125 < 0.313, so
5/16 < 0.313
34. Statistics. The following table gives the winning percentages of the top five coaches in NFL history. What fraction of his games has each coach won?
Coach / Percentage / Fraction
Don Shula / 0.676
George Halas / 0.672
Tom Landry / 0.606
Curly Lambeau / 0.624
Paul Brown / 0.667
Multiply each by 100:
0.676 = 67.6%
0.672 = 67.2%
0.606 = 60.6%
0.624 = 62.4%
0.667 = 66.7%
Mat 115 Week #4 Checkpoint