Chapter 2 Review

In Module II, we reviewed how to do calculations with decimals. We looked at the importance of place value in addition and subtraction. We looked at how to determine where the decimal point should go in multiplication and division problems. We learned how to write a number in scientific notation and estimate square roots and we reviewed the order of operations. With these tools, we looked at some real formula applications and calculated the mean, median and range.

Here are some key things to remember from chapter 2.

• It is vital to memorize the place values. For example the first number to the left of the decimal is the ones place, the first number to the right of the decimal point is the tenths place, and the second number to the right of the decimal place is the hundredths place…
• To round decimals to a certain place value, look to the number to the right of the place value. If it is 5 or above, round up (add 1 to place value, cut off the rest of decimal). If it is 4 or less, round down (leave place value alone, cut off the rest of decimal).
• Non-zero digits are always significant. Zeros between two non-zero digits are also significant. Under the classroom convention used in this chapter, trailing zeros in a whole number written without a decimal point are not significant. Leading zeros before the first non-zero decimal digit are not significant. Trailing zeros in a number written with a decimal point are significant. For measured data, use the stated precision; unmarked trailing integer zeros do not by themselves specify it.
• To add or subtract decimals, you have to line up the decimals and place values. Keep the decimal in the same place in the answer.
• To multiply decimals, multiply the numbers as if the decimals were not there. Count the number of places to the right of the decimal point in the first number. Count the number of places to the right of the decimal point in the second number. Add the total number of places to the right for both numbers. The answer will need the same number of values to the right of its decimal place. For example, if the first number in the product has 3 places to the right and the second number has 2 places then your answer needs 3+2=5 numbers to the right of the decimal point.
• To divide decimals by a nonzero divisor, make sure the number you are dividing (dividend) goes on the inside of the long division and the number you are dividing by (divisor) goes on the outside. For this long-division method, make the divisor a whole number. Move the decimal in the divisor to the right until the divisor is a whole number. Move the decimal in the dividend the same number of places. When the divisor is a whole number, the decimal in the dividend is the same as your answer. Just bring the decimal up from the dividend.
• For a positive number, scientific notation uses a coefficient at least 1 and less than 10 multiplied by an integer power of 10. For example $3.5\times {10}^{-8}$. Positive numbers less than 1 use a negative exponent; numbers from 1 up to but not including 10 use exponent 0; numbers 10 or greater use a positive exponent.
• To find the mean average, add up all the numbers and divide by how many numbers you have. To find the median average, put the numbers in order from smallest to largest. If there is 1 number in the middle, then that is the median. If there are two numbers in the middle, the median is half way in between the two numbers in the middle. (Add them and divide by 2.) The range is the largest number in the data minus the smallest number in the data.

Chapter 2 Review Problems

Perform the indicated operation for #1-40.

1. 2.3 + 0.14 + 0.575

   Check answer

   3.015

2. 1.56 + 19.8 + 317

3. 0.478 + 9.69

   Check answer

   10.168

4. 89.61 + 4.530

5. 0.875 + 64.9

   Check answer

   65.775

6. 90.52 + 72.8

7. 20 – 8.31

   Check answer

   11.69

8. 3 – 1.472

9. 0.15 – 0.0854

10. 53.1 – 0.175

11. 1.348 – 0.936

    Check answer

    0.412

12. 4.421 – 3.89

13. 6 x 1.9

    Check answer

    11.4

14. 0.7 x 0.42

15. 2.43 x 50

    Check answer

    121.5

16. $$0.093\times 100$$

17. 1000 x 0.084

    Check answer

    84

18. 7.4 x 10000

19. 6.5 x 7.2

    Check answer

    46.8

20. 0.84 x 0.89

21. 0.24 x 1.48

    Check answer

    0.3552

22. 7.5 x 3.48

23. 13.5 x 0.64

    Check answer

    8.64

24. 307 x 0.52

25. 1.94 x 0

    Check answer

    0

26. 2.34 x 1

27. 0 x 0.138

    Check answer

    0

28. 1 x 23.45

29. $$0.145÷3$$

    Check answer

    $$0.048\overline{3}$$

30. $$6.4÷0.02$$

31. $$0.144÷0.16$$

    Check answer

    0.9

32. $$27.145÷8.9$$

33. $$1.83÷1$$

    Check answer

    1.83

34. $$0÷0.056$$

35. $$\frac{5.3}{1}$$

    Check answer

    5.3

36. $$\frac{16.49}{0}$$

37. $$\frac{0.187}{0.4}$$

    Check answer

    0.4675

38. $${2.3}^2$$

39. $${0.14}^2$$

    Check answer

    0.0196

40. $${0.2}^5$$

41. Which number is larger, 0.07 or 0.0699?

    Check answer

    0.07

42. Which number is smaller, 1.358 or 1.5?

43. Round 1.3856 to the tenths place.

    Check answer

    1.4

44. Round 0.024879 to the hundredths place.

45. Round 1.379684 to the thousandths place.

    Check answer

    1.380

46. Write the number 530,000,000 in scientific notation.

47. Write the number 0.00000073 in scientific notation.

    Check answer

    $$7.3\times {10}^{-7}$$

48. What number is represented by 4.2 x ${10}^{-5}$ ?

49. What number is represented by 1.16 x ${10}^7$ ?

    Check answer

    11,600,000

50. How many significant figures does the number 21.7 have?

51. How many significant figures does the number 1.00032 have?

    Check answer

    6

52. How many significant figures does the number 22,900,000 have?

For #53-56, perform the operations and use significant figure rounding rules to round the answer to the appropriate place.

53. $$7.29+13.4+0.719$$

    Check answer

    21.4

54. $$8.2-6.009$$

55. $$2.4\times 7\times 1.09$$

    Check answer

    20

56. $$8.253÷0.42$$

Perform the indicated operations for #57-61. Estimate any square roots with a decimal that ends in the tenths place.

57. $$\sqrt{85}$$

    Check answer

    9.2 or 9.3

58. $$\sqrt{14}$$

59. $$\sqrt{13.7}$$

    Check answer

    3.7

60. $$1.7-1.3+{0.6}^2÷0.5$$

61. $$\sqrt{(3.5+{2.1}^2\times 4.7)}$$

    Check answer

    4.9

The surface area of a box is given by the formula $S=2\mathrm{LW}+2\mathrm{LH}+2\mathrm{WH}$.

62. Find the surface area of a box if L = 8.3cm, W = 6.3 cm, and H = 5.7 cm.

63. Find the surface area of a box if L = 2.4 in, W = 1.6 in, and H = 1.2 in.

    Check answer

    17.28 sq in

Let’s look at the z-score formula again. $z=\frac{(x-\mu )}{\sigma }$

64. Find the z-score if $$x=6.2,\mu =5.6,\text{ and }\sigma =0.2$$.

65. Find the z-score if $$x=35.82,\mu =33.27,\text{ and }\sigma =0.25$$

    Check answer

    10.2

Use the certificate of deposit formula $A=P{(1+\frac{r}{n})}^{nt}$.

66. Find the future value A of a certificate of deposit after 2 years (t = 2) if a person invests $6000 (P = $6000) with an annual interest rate of 4% (r = 0.04) compounded once a year (n = 1).

67. Find the future value A of a certificate of deposit after 1 year (t = 1) if a person invests $2000 (P = $2000) with an annual interest rate of 7% (r = 0.07) compounded twice a year (n = 2).

    Check answer

    $2142.45

Mean, Median, and Range problems

68. The largest living lizard is the Komodo dragon. We measured the lengths of these lizards in meters. Calculate the mean average, median average and the range of the Komodo dragon data. Round the answers to one more decimal place to the right than the data has.

    Komodo dragon lengths data: 2.7, 3.3, 2.6, 2.5, 2.9, 3.4, 3.1

69. Gas prices in Los Angeles fluctuate a lot. We took a sample of various gas stations around Los Angeles and recorded the price per gallon in dollars. Calculate the mean average, median average and the range of the gas price data. Round the answers to the nearest cent (hundredths place).

    Gas Price Data:
    $3.69, $3.57, $3.49, $3.37, $3.19, $3.15, $3.09, $2.99, $2.83, $2.65

    Check answer

    Mean = $3.20, Median = $3.17, Range = $1.04

Adapted from Preparing for Algebra and Statistics, Third Edition, by Matt Teachout. License: CC BY 4.0. Copyright and sources.