# 2.E: Exercises

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#### 2.1: Taking Measurements

1. Identify the unit in each quantity.
1. 2 boxes of crayons
2. 3.5 grams of gold
1. boxes of crayons
2. grams of gold

1. Identify the unit in each quantity.
1. 32 oz of cheddar cheese
2. 0.045 cm3 of water
1. oz of cheddar cheese
2. cm3 of water

1. Identify the unit in each quantity.
1. 9.58 s (the current world record in the 100 m dash)
2. 6.14 m (the current world record in the pole vault)
1. s
2. m

1. Identify the unit in each quantity.
1. 2 dozen eggs
2. 2.4 km/s (the escape velocity of the moon, which is the velocity you need at the surface to escape the moon's gravity)
1. eggs
2. km/s

#### 2.2: Scientific Notation

1. Express these numbers in scientific notation.
1. 56.9
2. 563,100
3. 0.0804
4. 0.00000667
1. 5.69 × 101
2. 5.631 × 105
3. 8.04 × 10−2
4. 6.67 × 10−6

1. Express these numbers in scientific notation.
1. −890,000
2. 602,000,000,000
3. 0.0000004099
4. 0.000000000000011
1. −8.9 × 105
2. 6.02 × 1011
3. 4.099 × 10−7
4. 1.1 × 10−14

1. Express these numbers in scientific notation.
1. 0.00656
2. 65,600
3. 4,567,000
4. 0.000005507
1. 6.56 × 10−3
2. 6.56 × 104
3. 4.567 × 106
4. 5.507 × 10−6

1. Express these numbers in scientific notation.
1. 65
2. −321.09
3. 0.000077099
4. 0.000000000218
1. 6.5 × 101
2. −3.2109 × 102
3. 7.7099 × 10−5
4. 2.18 × 10−10

1. Express these numbers in decimal notation.
1. 1.381 × 105
2. 5.22 × 10−7
3. 9.998 × 104
1. 138,100
2. 0.000000522
3. 99,980

1. Express these numbers in decimal notation.
1. 7.11 × 10−2
2. 9.18 × 102
3. 3.09 × 10−10
1. 0.0711
2. 918
3. 0.000000000309

1. Express these numbers in decimal notation.
1. 8.09 × 100
2. 3.088 × 10−5
3. −4.239 × 102
1. 8.09
2. 0.00003088
3. −423.9

1. Express these numbers in decimal notation.
1. 2.87 × 10−8
2. 1.78 × 1011
3. 1.381 × 10−23
1. 0.0000000287
2. 178,000,000,000
3. 0.00000000000000000000001381

#### 2.3: Significant Figures

1. Express each measurement to the correct number of significant figures.
1. 6.3 psi
2. 28.6 mm
3. 477 psi
4. 35 mm

1. How many significant figures do these numbers have?
1. 23
2. 23.0
3. 0.00023
4. 0.0002302
1. 2
2. 3
3. 2
4. 4

1. How many significant figures do these numbers have?
1. 5.44 × 108
2. 1.008 × 10−5
3. 43.09
4. 0.0000001381
1. 3
2. 4
3. 4
4. 4

1. How many significant figures do these numbers have?
1. 765,890
2. 765,890.0
3. 1.2000 × 105
4. 0.0005060
1. 5 or 6, ambiguous
2. 7
3. 5
4. 4

1. How many significant figures do these numbers have?
1. 0.009
2. 0.0000009
3. 65,444
4. 65,040
1. 1
2. 1
3. 5
4. 4 or 5, ambiguous

1. Write the number 87,449 in scientific notation with four significant figures.

8.745 × 104

1. Write the number 0.000066600 in scientific notation with five significant figures.

6.6600 × 10−5

1. Write the number 0.0000558 in scientific notation with two significant figures.

5.6 × 10−5

#### 2.4: Significant Figures in Calculations

1. Compute and express each answer with the proper number of significant figures, rounding as necessary.
1. 56.0 + 3.44 = ?
2. 0.00665 + 1.004 = ?
3. 45.99 − 32.8 = ?
4. 45.99 − 32.8 + 75.02 = ?
1. 59.4
2. 1.011
3. 13.2
4. 88.2

1. Compute and express each answer with the proper number of significant figures, rounding as necessary.
1. 1.005 + 17.88 = ?
2. 5,670.0 − 324 = ?
3. 405,007 − 123.3 = ?
4. 55.5 + 66.66 − 77.777 = ?
1. 18.89
2. 5,346
3. 404,884
4. 44.4

1. Compute and express each answer with the proper number of significant figures, rounding as necessary.
1. 56.7 × 66.99 = ?
2. 1.00 ÷ 77 = ?
3. 1.00 ÷ 77.0 = ?
4. 6.022 × 1.89 = ?
1. 3.80 × 103
2. 0.013
3. 0.0130
4. 11.4

1. Compute and express each answer with the proper number of significant figures, rounding as necessary.
1. 0.000440 × 17.22 = ?
2. 203,000. ÷ 0.044 = ?
3. 67 × 85.0 × 0.0028 = ?
4. 999,999 ÷ 3,310 = ?
1. 0.00758
2. 4.6 × 106
3. 16
4. 302

1. Compute and express each answer with the proper number of significant figures, rounding as necessary.
1. 67,883 × 0.004321 = ?
2. (9.67 × 103) × 0.0055087 = ?
1. 293.3
2. 53.3

1. Compute and express each answer with the proper number of significant figures, rounding as necessary.
1. 18,900. × 76.33 ÷ 0.00336 = ?
2. 0.77604 ÷ 76,003 × 8.888 = ?
1. 4.29 × 108
2. 9.075 × 10−5

#### 2.5: The Metric System

1. Indicate what multiplier each prefix represents.
1. k
2. m
3. M
1. 103 or 1,000 ×
2. 10−3 or $$\frac1{1000}$$ ×
3. 106 or 1,000,000 ×

1. Indicate what multiplier each prefix represents.
1. c
2. G
3. μ
1. 10−2 or $$\frac1{100}$$ ×
2. 109 or 1,000,000,000 ×
3. 10−6 or $$\frac1{1,000,000}$$ ×

1. Give the prefix that represents each multiplier.
1. 10−3 or $$\frac1{1000}$$ ×
2. 103 or 1,000 ×
3. 109 or 1,000,000,000 ×
1. m or milli
2. k or kilo
3. G or giga

1. Give the prefix that represents each multiplier.
1. $$\frac1{1,000,000,000}$$ ×
2. $$\frac1{100}$$ ×
3. 1,000,000 ×
1. n or nano
2. c or centi
3. M or mega

1. Express each quantity in a more appropriate unit. There may be more than one acceptable answer.
1. 3.44 × 10−9 s
2. 3,500 L
3. 0.045 m
1. 3.44 ns
2. 3.5 kL
3. 45 mm

1. Express each quantity in a more appropriate unit. There may be more than one acceptable answer.
1. 0.000066 m/s (Hint: you need consider only the unit in the numerator.)
2. 4.66 × 106 s
3. 7,654 L
1. 66 μm/s
2. 4.66 Ms
3. 7.654 kL

1. Express each quantity in a more appropriate unit. There may be more than one acceptable answer.
1. 43,600 mL
2. 0.0000044 m
3. 1,438 ms
1. 43.6 L
2. 4.4 μm
3. 1.438 s

#### 2.6: Problem Solving and Unit Conversions

1. Write the two conversion factors that exist between the two given units.
1. milliliters and liters
2. nanoseconds and seconds
3. kilometers and meters
1. $\frac{\text{1000 mL}}{\text{1 L}} {\text{ and }} \frac{\text{1 L}}{\text{1000 mL}}\nonumber$
2. $\frac{\text{1,000,000,000 ns}}{\text{1 s}} {\text{ and }} \frac{\text{1 s}}{\text{1,000,000,000 ns}}\nonumber$
3. $\frac{\text{1 km}}{\text{1000 m}} {\text{ and }} \frac{\text{1000 m}}{\text{1 km}}\nonumber$

1. Write the two conversion factors that exist between the two given units.
1. kilograms and grams
2. milliseconds and seconds
3. centimeters and meters
1. $\frac{\text{1 kg}}{\text{1000 g}} {\text{ and }} \frac{\text{1000 g}}{\text{1 kg}}\nonumber$
2. $\frac{\text{1000 ms}}{\text{1 s}} {\text{ and }} \frac{\text{1 s}}{\text{1000 ms}}\nonumber$
3. $\frac{\text{100 cm}}{\text{1 m}} {\text{ and }} \frac{\text{1 m}}{\text{100 cm}}\nonumber$

1. Perform the following conversions.
1. 5.4 km to meters
2. 0.665 m to millimeters
3. 0.665 m to kilometers
1. 5,400 m
2. 665 mm
3. 6.65 × 10−4 km

1. Perform the following conversions.
1. 90.6 mL to liters
2. 0.00066 ML to liters
3. 750 L to kiloliters
1. 0.0906 L
2. 660 L
3. 0.75 kL

1. Perform the following conversions.
1. 17.8 μg to grams
2. 7.22 × 102 kg to grams
3. 0.00118 g to nanograms
1. 1.78 × 10−5 g
2. 7.22 × 105 g
3. 1.18 × 106 ng

1. Perform the following conversions.
1. 833 ns to seconds
2. 5.809 s to milliseconds
3. 2.77 × 106 s to megaseconds
1. 8.33 × 10−7 s
2. 5,809 ms
3. 2.77 Ms

1. Perform the following conversions.
1. 45.0 m/min to meters/second
2. 0.000444 m/s to micrometers/second
3. 60.0 km/h to kilometers/second
1. 0.750 m/s
2. 444 μm/s
3. 0.0167 km/s

1. Perform the following conversions.
1. 3.4 × 102 cm/s to centimeters/minute
2. 26.6 mm/s to millimeters/hour
3. 13.7 kg/L to kilograms/milliliters
1. 2.0 × 104 cm/min
2. 9.58 × 104 mm/h
3. 0.0137 kg/mL

#### 2.7: Solving Multi-Step Conversion Problems

1. Perform the following conversions.
1. 0.674 kL to milliliters
2. 2.81 × 1012 mm to kilometers
3. 94.5 kg to milligrams
1. 6.74 × 105 mL
2. 2.81 × 106 km
3. 9.45 × 107 mg

1. Perform the following conversions.
1. 6.79 × 10−6 kg to micrograms
2. 1.22 mL to kiloliters
3. 9.508 × 10−9 ks to milliseconds
1. 6.79 × 103 μg
2. 1.22 × 10−6 kL
3. 9.508 × 10−3 ms

1. Perform the following conversions.
1. 6.77 × 1014 ms to kiloseconds
2. 34,550,000 cm to kilometers
1. 6.77 × 108 ks
2. 345.5 km

1. Perform the following conversions.
1. 4.701 × 1015 mL to kiloliters
2. 8.022 × 10−11 ks to microseconds
1. 4.701 × 109 kL
2. 0.08022 μs

1. Perform the following conversions. Note that you will have to convert units in both the numerator and the denominator.
1. 88 ft/s to miles/hour
2. 0.00667 km/h to meters/second
1. 6.0 × 101 mi/h
2. 1.85 × 10−3 m/s

1. Perform the following conversions. Note that you will have to convert units in both the numerator and the denominator.
1. 3.88 × 102 mm/s to kilometers/hour
2. 1.004 kg/L to grams/milliliter
1. 1.40 km/h
2. 1.004 g/mL

#### 2.8: Units Raised to a Power

1. Perform the following conversions.
1. 9.44 m2 to square centimeters
2. 3.44 × 108 mm3 to cubic meters
1. 9.44 × 104 cm2
2. 0.344 m3

1. Perform the following conversions.
1. 0.00444 cm3 to cubic meters
2. 8.11 × 102 m2 to square nanometers
1. 4.44 × 10−9 m3
2. 8.11 × 1020 nm2

1. Why would it be inappropriate to convert square centimeters to cubic meters?

One is a unit of area and the other is a unit of volume.

1. The formula for the area of a triangle is ½ × base × height. What is the area of a triangle in square meters if its base is 166 mm and its height is 930.0 mm? Express the answer to the proper number of significant figures.

0.0772 m2

1. What is the area in square millimeters of a rectangle whose sides are 2.44 cm × 6.077 cm? Express the answer to the proper number of significant figures.

1.48 × 103 mm2

1. What is the volume in cubic centimeters of a cube with sides of 0.774 m? Express the answer to the proper number of significant figures.

4.64 × 105 cm3

1. The formula for the area of a triangle is ½ × base × height. What is the area of a triangle in square centimeters if its base is 1.007 m and its height is 0.665 m? Express the answer to the proper number of significant figures.

3.35 × 103 cm2

#### 2.9: Density

1. A block of metal alloy has a mass of 34.96 g. Its dimensions are 3.9 cm by 4.2 cm by 1.6 cm. What is the density of the metal alloy?

1.3 g/cm3

1. A plastic cylinder with a mass of 26.7 g is added to a graduated cylinder containing 45.8 mL of water. Once the cylinder was submerged, the volume increased to 61.3 mL. What was the density of the plastic cylinder?

1.72 g/mL

1. A sample of iron has a volume of 48.2 cm3. If the density of iron is 7.87 g/cm3, what is its mass?

379 g

1. A sample of air has a volume of 1,015 mL. What is its mass? Consult Table 2.9.1 for the density.

1.22 g

1. The volume of hydrogen used by the Hindenburg, the German airship that exploded in New Jersey in 1937, was 2.000 × 108 L. What mass of hydrogen was used by the airship? Consult Table 2.9.1 for the density.

1.7 × 107 g

1. The volume of an Olympic-sized swimming pool is 2.50 × 109 cm3. If the pool is filled with alcohol (d = 0.789 g/cm3), what mass of alcohol is in the pool?

1.97 × 109 g

1. A typical engagement ring has 0.77 cm3 of gold. What mass of gold is present? Consult Table 2.9.1 for the density.

15 g

1. A typical mercury thermometer has 0.039 mL of mercury in it. What mass of mercury is in the thermometer? Consult Table 2.9.1 for the density.

0.53 g

1. What is the volume of 100.0 g of lead? Consult Table 2.9.1 for the density.

8.811 cm3

1. What is the volume of 255.0 g of uranium if uranium has a density of 19.05 g/cm3?

13.39 cm3

1. What is the volume in liters of 222 g of neon if neon has a density of 0.900 g/L?

247 L

1. What is the volume in liters of 20.5 g of sulfur hexafluoride if sulfur hexafluoride has a density of 6.164 g/L?

3.33 L

1. Which has the greater volume, 100.0 g of iron (d = 7.87 g/cm3) or 75.0 g of gold (d = 19.3 g/cm3)?

Iron. The volume of the iron is 12.7 cm3 and the volume of the gold is 3.87 cm3.

1. Which has the greater volume, 25.0 g of hydrogen gas (d = 0.084 g/L) or 100.0 g of argon gas (d = 1.78 g/L)?

Hydrogen. The volume of the hydrogen is 298 L and the volume of the argon is 56.2 L.

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

3.42 × 10−18

1. Evaluate 333,999,500,000 ÷ 0.00000000003396 and express the answer in scientific notation. You may need to rewrite the original numbers in scientific notation first.

9.835 × 1021

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

109 μm

1. Fill in the blank: 1 Ms = ______________ ns.

1015 ns

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

10−8 ML

1. Fill in the blank: 1 mg = ______________ kg.

10−6 kg

1. Convert a speed of 60.0 mi/h into kilometers/hour.

96.5 km/h

1. Convert a speed of 60.0 km/h into miles/hour.

37.3 mi/h

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

14.47 m/s

1. Convert 2.155 m/s into kilometers/hour.

7.758 km/h

1. What is the mass of 12.67 L of mercury? Consult Table 2.9.1 for the density.

1.723 × 105 g

1. What is the mass of 0.663 m3 of air? Consult Table 2.9.1 for the density.

796 g

1. What is the volume of 2.884 kg of gold? Consult Table 2.9.1 for the density.

149 cm3

1. What is the volume of 40.99 kg of cork? Assume a density of 0.22 g/cm3.