Chapter 2. Making Measurements

# 2.6 End of Chapter Problems

1. For each of the following measurements, state the amount of uncertainty and then determine which measurement is most precise:

a) 2×102 mL of water         b) 2.0×102 mL of water         c) 2.00×102 mL of water

d) 2.000×102 mL of water         e) 200 mL of water         f) 200. mL of water

2. Write the following in correct scientific notation and list the number of significant figures in each:
a) 0.00406      b)  3,500,000

c) 154 x 10-2      d)  0.00001256 x 106

3. State the number of significant figures in each of the following:
a) 275       b)  2.75         c) 0.275

d)  0.00275         e) 2750.0          f) 2.75 x 105

4. Write the following numbers in scientific notation:
a) 426.7      b) 337300.0

c)  0.000003       d)  0.02003

5. Express the results of each of the following calculations to the appropriate number of significant figures:
a) 13.196 + 0.0825 + 2.32 + 0.0013 =
b) 721.56 – 0.394 =
c)  (5.23×10-2)  + (6.01×10-3)  +  (8×10-3)  + (3.273×10-2)   =
d)   (3.21 x 432 x 65)/563  =

e)   (8.57×10-2  x  6.02×1023  x  2.543) / (361  x  907)  =

f)   (2.01 x 43.9 x 67.0) / (23.9 x 0.016)  =

6. Express the results of each of the following calculations to the appropriate number of significant figures, and in scientific notation:
a) (4.9×103)2 =
b)  (3.8×10-6)  x  (2.1×102)  =
c)  (4.4×10-7)  ÷  (1.2×105)  =
d)  (7.86×10-2)  – (18.6×10-3)  =
e)  (1.6×103)  – (8.53×102)  + 7.5  =

7. For the following calculations, determine the answer using the appropriate number of significant figure, units and using proper scientific notation:
a) (1.93 x 102 g)(44.7 m/s)2 / 2 (where 2 is an exact number)
b)  (8.334 x 107g) / (1.95 x 102cm)3
c)  4.20 m x 1.1 m – (4.5 x 103cm2)

8. Solve the following, expressing the answers in scientific notation:
a) (0.101 cm)(0.15 cm) + (10.50 cm)(0.105 cm)  =
b)   (0.27104 m / 0.0150 sec)  –  ( 38.171 m / 3.022 sec)  =

9. Express the results of each of the following calculations to the appropriate number of significant figures:

a) (1.00×1018) +  (5.6×1017) =
b)   (317  –  314.35)  ÷  4.0  =
c)  30.5 + 3.05 + 0.305 + 0.0305 =
d)   (3.03  +  8.14)  ÷  (427.78 – 362.060)  =
e)   (6.5 g + 9.5 g)  ÷  25.00 mL =

10.  The volume of a container is 5982 mm3.

a) What is the volume in cubic feet, ft3? (1 ft = 0.3048 m)

b) If it takes 0.23 seconds to add 1.00 mL of water to the container, how many seconds does it take to fill the entire container?

11.  One mile equals 1.609 kilometers. If you are going 110 km/h, how many minutes will it take you to travel 254 miles?

12.  On July 23rd, 1983, Air Canada Flight 143 required 22,300 kg of jet fuel to fly from Montreal to Edmonton. The density of jet fuel is 0.803 g/mL, or 1.77 lb/L. The plane had 7682 L of fuel on board in Montreal. The ground crew there multiplied the 7682 L by the factor 1.77 and concluded that they had 13,597 kg of fuel on board and needed an additional 8703 kg for the trip. They divided 8703 kg by the factor 1.77 and concluded that they needed to add 4916 L of fuel. They added 5000 L. On its flight, the plane ran out of fuel and crashed near Winnipeg, hundred of kilometers short of its destination (there were few injuries and luckily, no fatalities). What mistake did the ground crew make? How much fuel SHOULD they have added before take off?

13.  Perform the following calculation and report the answer in cm, with proper significant figures:   13.25 cm + 26 mm – 7.8 cm + 0.186 m

14.  Complete the following conversions:

498 cm/s           =   ________ km/h

63 km/h               =   ________ cm/s

89oC                 =   ________ K

821 K                  =   ________ oC

802 kg/m3          =   ________ g/mL

10024 g/mL        =   ________ kg/L

38 mL                =   ________ cm3

0.00924 km         =  ________ mm

7098 mm           =   ________ dm

2987 µm             =   ________ mm

0.78 L                =   ________ cm3

908 mg               =   ________ kg

87.8 mm            =   ________ nm

89.2 m3               =   ________ mm3

3 x 108m/s        =   ________ km/year

15.  An Erlenmeyer flask has a mass of 392.6 g when empty. When filled with water (density = 1.00 g/cm3), the total mass is 503.5 g. If the flask is emptied and then filled with chloroform (density = 1.48 g/cm3), what will the total mass (container + chloroform) be?

16.  Alcohol has a density of 789 g/L. If you need 85 g of alcohol, what volume of alcohol would you need?

17.  Nickel has a density of 8.90 x 103g/L and mercury has a density of 13.6 x 103g/L.
a) What volume of mercury has the same mass as a 40.0 cm3 piece of nickel?
b) What mass of nickel occupies the same volume as 200.0 g of mercury?

18.  Gold has a density of 19.3 g/mL. If 5.79 mg of gold is hammered into a gold leaf of uniform thickness with an area of 4.46 x 10mm2, what is the thickness of the gold leaf?

19.  The square nut pictured below is 14.00 mm on edge, 6.00 mm thick, and has a 7.0 mm diameter hole. The density of the metal used in the nuts is 7.87 g/cm3. Approximately how many of these nuts are present in a 1.00 lb package? (Note: 1 lb = 453.6 g)

20.  A container of unknown volume has a mass of 32.105 g. When filled completely with a fluid of density 0.9982 g/mL, the container and contents have a mass of 42.062 g (at 20 oC). When filled with benzene at 20 oC, the container and contents have a mass of 40.873 g. What is the density of benzene at 20 oC?

21.  A 3.50 mL piece of boron has a mass of 8.19 g. What is the density of boron?

22. An object made of iron is immersed in water. The object has a mass of 250 g. If the density of iron is 7.86 g/cm3, what is the volume of the water displaced by the iron object?

23.  Evaluate 0.00000000552 × 0.0000000006188 and express the answer in scientific notation. You may have to rewrite the original numbers in scientific notation first.

24.  Express the number 6.022 × 1023 in standard notation.

25.  When powers of 10 are multiplied together, the powers are added together. For example, 102 × 103 = 102+3 = 105. With this in mind, can you evaluate (4.506 × 104) × (1.003 × 102) without entering scientific notation into your calculator?

26.  Consider the quantity two dozen eggs. Is the number in this quantity “two” or “two dozen”? Justify your choice.

27.  Fill in the blank: 1 km = ______________ μm.

28.  Fill in the blank: 1 cL = ______________ ML.

29.  Express 67.3 km/h in meters/second.

30.  Using the idea that 1.602 km = 1.000 mi, convert a speed of 60.0 mi/h into kilometers/hour.

31.  Convert 52.09 km/h into meters/second.

32.  Use the formulas for converting degrees Fahrenheit into degrees Celsius to determine the relative size of the Fahrenheit degree over the Celsius degree.

33. What is the mass of 12.67 L of mercury?

34.  What is the volume of 2.884 kg of gold?

1.   a) ± 100 mL of water         b) ± 10 mL of water         c) ± 1 mL of water

d) ± 0.1 mL of water         e) ± 100 mL of water         f) ± 1 mL of water

And the most precise measurement is (d) because it has the least amount of uncertainty.
b)  ± 1 mL or so, 438 mL
c)  ± 0.001 °C or so, 10.060 oC

2.   a) 4.06 x 10-3= 3 significant figures
b)  3.5 x 106= 2 significant figures
c) 1.54 or 1.54 x 100= 3 significant figures
d)  1.256 x 101= 4 significant figures

3.   a) 3    b) 3   c) 3    d) 3    e) 5   f) 3

4.   a) 4.267×102       b) 3.373000×105      c) 3×10-6      d) 2.003×10-2

5.   a) 15.60      b) 721.17      c) 9.9×10-2      d) 1.6×102      e) 4.01×1017      f) 1.5×104

6.   a) 2.4×107      b) 8.0×10-4        c) 3.7×10-12      d) 6.00×10-2       e) 8×102

7.   a) 1.93 x 105g·m2/s2      b)  11.2 g/cm3      c) 4.2 m2or 4.2 x 104cm2

8.   a) 1.12 cm2       b) 5.4 m/s

9.   a) 1.56×1018      b) 0.7      c) 33.9      d) 0.1700      e) 0.640 g/mL

10.  a) 2.113 x 10-4ft3      b) 1.4 s

11. 220 minutes (2.2 x 102minutes)

12. The crew used the wrong conversion factor (using 1.77 lb/L as if it were 1.77 kg/L) and didn’t pay attention to proper cancellation of units (to catch the mistake).  They should have added 2.01 x 104L of fuel (at least).

13.  26.6 cm (or 26.7 cm OK)

14.  17.9;   1.8 x 103;   362;   548;   0.802;   10024;   38;

9.24 x 103;   70.98;   2.987;   7.8 x 102;    9.08 x 10-4;

8.78 x 107;    8.92 x 1010;   9 x 1012

15.  557 g

16.  0.11 L

17.  a) 0.0262 L or 26.2 cm3       b)  131 g

18.  6.73 x 10-5mm

19.  approximately 61 nuts

20.  0.8790 g/mL

21.  2.34 g/mL

22.  32 mL

23.  3.42 × 10−18

24.  602,200,000,000,000,000,000,000

25.  4.520 × 106

26.  The quantity is two; dozen is the unit.

27.  1,000,000,000

28.  1/100,000,000

29.  18.7 m/s

30.  96.1 km/h

31.  14.47 m/s

32.  One Fahrenheit degree is nine-fifths the size of a Celsius degree.

33.  1.72 × 105 g

34.  149 mL 