# 2.E: Exercises

- Page ID
- 357317

2.1: Taking Measurements

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

**Answer**-
- boxes of crayons
- grams of gold

- Identify the unit in each quantity.
- 32 oz of cheddar cheese
- 0.045 cm
^{3}of water

**Answer**-
- oz of cheddar cheese
- cm
^{3}of water

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

**Answer**-
- s
- m

- Identify the unit in each quantity.
- 2 dozen eggs
- 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)

**Answer**-
- eggs
- km/s

#### 2.2: Scientific Notation

- Express these numbers in scientific notation.
- 56.9
- 563,100
- 0.0804
- 0.00000667

**Answer**-
- 5.69 × 10
^{1} - 5.631 × 10
^{5} - 8.04 × 10
^{−2} - 6.67 × 10
^{−6}

- 5.69 × 10

- Express these numbers in scientific notation.
- −890,000
- 602,000,000,000
- 0.0000004099
- 0.000000000000011

**Answer**-
- −8.9 × 10
^{5} - 6.02 × 10
^{11} - 4.099 × 10
^{−7} - 1.1 × 10
^{−14}

- −8.9 × 10

- Express these numbers in scientific notation.
- 0.00656
- 65,600
- 4,567,000
- 0.000005507

**Answer**-
- 6.56 × 10
^{−3} - 6.56 × 10
^{4} - 4.567 × 10
^{6} - 5.507 × 10
^{−6}

- 6.56 × 10

- Express these numbers in scientific notation.
- 65
- −321.09
- 0.000077099
- 0.000000000218

**Answer**-
- 6.5 × 10
^{1} - −3.2109 × 10
^{2} - 7.7099 × 10
^{−5} - 2.18 × 10
^{−10}

- 6.5 × 10

- Express these numbers in decimal notation.
- 1.381 × 10
^{5} - 5.22 × 10
^{−7} - 9.998 × 10
^{4}

- 1.381 × 10

**Answer**-
- 138,100
- 0.000000522
- 99,980

- Express these numbers in decimal notation.
- 7.11 × 10
^{−2} - 9.18 × 10
^{2} - 3.09 × 10
^{−10}

- 7.11 × 10

**Answer**-
- 0.0711
- 918
- 0.000000000309

- Express these numbers in decimal notation.
- 8.09 × 10
^{0} - 3.088 × 10
^{−5} - −4.239 × 10
^{2}

- 8.09 × 10

**Answer**-
- 8.09
- 0.00003088
- −423.9

- Express these numbers in decimal notation.
- 2.87 × 10
^{−8} - 1.78 × 10
^{11} - 1.381 × 10
^{−23}

- 2.87 × 10

**Answer**-
- 0.0000000287
- 178,000,000,000
- 0.00000000000000000000001381

#### 2.3: Significant Figures

- Express each measurement to the correct number of significant figures.

**Answer**-
- 6.3 psi
- 28.6 mm
- 477 psi
- 35 mm

- How many significant figures do these numbers have?
- 23
- 23.0
- 0.00023
- 0.0002302

**Answer**-
- 2
- 3
- 2
- 4

- How many significant figures do these numbers have?
- 5.44 × 10
^{8} - 1.008 × 10
^{−5} - 43.09
- 0.0000001381

- 5.44 × 10

**Answer**-
- 3
- 4
- 4
- 4

- How many significant figures do these numbers have?
- 765,890
- 765,890.0
- 1.2000 × 10
^{5} - 0.0005060

**Answer**-
- 5 or 6, ambiguous
- 7
- 5
- 4

- How many significant figures do these numbers have?
- 0.009
- 0.0000009
- 65,444
- 65,040

**Answer**-
- 1
- 1
- 5
- 4 or 5, ambiguous

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

**Answer**-
8.745 × 10

^{4}

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

**Answer**-
6.6600 × 10

^{−5}

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

**Answer**-
5.6 × 10

^{−5}

#### 2.4: Significant Figures in Calculations

- Compute and express each answer with the proper number of significant figures, rounding as necessary.
- 56.0 + 3.44 = ?
- 0.00665 + 1.004 = ?
- 45.99 − 32.8 = ?
- 45.99 − 32.8 + 75.02 = ?

**Answer**-
- 59.4
- 1.011
- 13.2
- 88.2

- Compute and express each answer with the proper number of significant figures, rounding as necessary.
- 1.005 + 17.88 = ?
- 5,670.0 − 324 = ?
- 405,007 − 123.3 = ?
- 55.5 + 66.66 − 77.777 = ?

**Answer**-
- 18.89
- 5,346
- 404,884
- 44.4

- Compute and express each answer with the proper number of significant figures, rounding as necessary.
- 56.7 × 66.99 = ?
- 1.00 ÷ 77 = ?
- 1.00 ÷ 77.0 = ?
- 6.022 × 1.89 = ?

**Answer**-
- 3.80 × 10
^{3} - 0.013
- 0.0130
- 11.4

- 3.80 × 10

- Compute and express each answer with the proper number of significant figures, rounding as necessary.
- 0.000440 × 17.22 = ?
- 203,000. ÷ 0.044 = ?
- 67 × 85.0 × 0.0028 = ?
- 999,999 ÷ 3,310 = ?

**Answer**-
- 0.00758
- 4.6 × 10
^{6} - 16
- 302

- Compute and express each answer with the proper number of significant figures, rounding as necessary.
- 67,883 × 0.004321 = ?
- (9.67 × 10
^{3}) × 0.0055087 = ?

**Answer**-
- 293.3
- 53.3

- Compute and express each answer with the proper number of significant figures, rounding as necessary.
- 18,900. × 76.33 ÷ 0.00336 = ?
- 0.77604 ÷ 76,003 × 8.888 = ?

**Answer**-
- 4.29 × 10
^{8} - 9.075 × 10
^{−5}

- 4.29 × 10

#### 2.5: The Metric System

- Indicate what multiplier each prefix represents.
- k
- m
- M

**Answer**-
- 10
^{3}or 1,000 × - 10
^{−3}or \(\frac1{1000}\) × - 10
^{6}or 1,000,000 ×

- 10

- Indicate what multiplier each prefix represents.
- c
- G
- μ

**Answer**-
- 10
^{−2}or \(\frac1{100}\) × - 10
^{9}or 1,000,000,000 × - 10
^{−6}or \(\frac1{1,000,000}\) ×

- 10

- Give the prefix that represents each multiplier.
- 10
^{−3}or \(\frac1{1000}\) × - 10
^{3}or 1,000 × - 10
^{9}or 1,000,000,000 ×

- 10

**Answer**-
- m or milli
- k or kilo
- G or giga

- Give the prefix that represents each multiplier.
- \(\frac1{1,000,000,000}\) ×
- \(\frac1{100}\) ×
- 1,000,000 ×

**Answer**-
- n or nano
- c or centi
- M or mega

- Express each quantity in a more appropriate unit. There may be more than one acceptable answer.
- 3.44 × 10
^{−9}s - 3,500 L
- 0.045 m

- 3.44 × 10

**Answer**-
- 3.44 ns
- 3.5 kL
- 45 mm

- Express each quantity in a more appropriate unit. There may be more than one acceptable answer.
- 0.000066 m/s (Hint: you need consider only the unit in the numerator.)
- 4.66 × 10
^{6}s - 7,654 L

**Answer**-
- 66 μm/s
- 4.66 Ms
- 7.654 kL

- Express each quantity in a more appropriate unit. There may be more than one acceptable answer.
- 43,600 mL
- 0.0000044 m
- 1,438 ms

**Answer**-
- 43.6 L
- 4.4 μm
- 1.438 s

#### 2.6: Problem Solving and Unit Conversions

- Write the two conversion factors that exist between the two given units.
- milliliters and liters
- nanoseconds and seconds
- kilometers and meters

**Answer**-
- \[ \frac{\text{1000 mL}}{\text{1 L}} {\text{ and }} \frac{\text{1 L}}{\text{1000 mL}}\nonumber\]
- \[ \frac{\text{1,000,000,000 ns}}{\text{1 s}} {\text{ and }} \frac{\text{1 s}}{\text{1,000,000,000 ns}}\nonumber\]
- \[ \frac{\text{1 km}}{\text{1000 m}} {\text{ and }} \frac{\text{1000 m}}{\text{1 km}}\nonumber\]

- Write the two conversion factors that exist between the two given units.
- kilograms and grams
- milliseconds and seconds
- centimeters and meters

**Answer**-
- \[\frac{\text{1 kg}}{\text{1000 g}} {\text{ and }} \frac{\text{1000 g}}{\text{1 kg}}\nonumber\]
- \[\frac{\text{1000 ms}}{\text{1 s}} {\text{ and }} \frac{\text{1 s}}{\text{1000 ms}}\nonumber\]
- \[\frac{\text{100 cm}}{\text{1 m}} {\text{ and }} \frac{\text{1 m}}{\text{100 cm}}\nonumber\]

- Perform the following conversions.
- 5.4 km to meters
- 0.665 m to millimeters
- 0.665 m to kilometers

**Answer**-
- 5,400 m
- 665 mm
- 6.65 × 10
^{−4}km

- Perform the following conversions.
- 90.6 mL to liters
- 0.00066 ML to liters
- 750 L to kiloliters

**Answer**-
- 0.0906 L
- 660 L
- 0.75 kL

- Perform the following conversions.
- 17.8 μg to grams
- 7.22 × 10
^{2}kg to grams - 0.00118 g to nanograms

**Answer**-
- 1.78 × 10
^{−5}g - 7.22 × 10
^{5}g - 1.18 × 10
^{6}ng

- 1.78 × 10

- Perform the following conversions.
- 833 ns to seconds
- 5.809 s to milliseconds
- 2.77 × 10
^{6}s to megaseconds

**Answer**-
- 8.33 × 10
^{−7}s - 5,809 ms
- 2.77 Ms

- 8.33 × 10

- Perform the following conversions.
- 45.0 m/min to meters/second
- 0.000444 m/s to micrometers/second
- 60.0 km/h to kilometers/second

**Answer**-
- 0.750 m/s
- 444 μm/s
- 0.0167 km/s

- Perform the following conversions.
- 3.4 × 10
^{2}cm/s to centimeters/minute - 26.6 mm/s to millimeters/hour
- 13.7 kg/L to kilograms/milliliters

- 3.4 × 10

**Answer**-
- 2.0 × 10
^{4}cm/min - 9.58 × 10
^{4}mm/h - 0.0137 kg/mL

- 2.0 × 10

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

- Perform the following conversions.
- 0.674 kL to milliliters
- 2.81 × 10
^{12}mm to kilometers - 94.5 kg to milligrams

**Answer**-
- 6.74 × 10
^{5}mL - 2.81 × 10
^{6}km - 9.45 × 10
^{7}mg

- 6.74 × 10

- Perform the following conversions.
- 6.79 × 10
^{−6}kg to micrograms - 1.22 mL to kiloliters
- 9.508 × 10
^{−9}ks to milliseconds

- 6.79 × 10

**Answer**-
- 6.79 × 10
^{3}μg - 1.22 × 10
^{−6}kL - 9.508 × 10
^{−3}ms

- 6.79 × 10

- Perform the following conversions.
- 6.77 × 10
^{14}ms to kiloseconds - 34,550,000 cm to kilometers

- 6.77 × 10

**Answer**-
- 6.77 × 10
^{8}ks - 345.5 km

- 6.77 × 10

- Perform the following conversions.
- 4.701 × 10
^{15}mL to kiloliters - 8.022 × 10
^{−11}ks to microseconds

- 4.701 × 10

**Answer**-
- 4.701 × 10
^{9}kL - 0.08022 μs

- 4.701 × 10

- Perform the following conversions. Note that you will have to convert units in both the numerator and the denominator.
- 88 ft/s to miles/hour
- 0.00667 km/h to meters/second

**Answer**-
- 6.0 × 10
^{1}mi/h - 1.85 × 10
^{−3}m/s

- 6.0 × 10

- Perform the following conversions. Note that you will have to convert units in both the numerator and the denominator.
- 3.88 × 10
^{2}mm/s to kilometers/hour - 1.004 kg/L to grams/milliliter

- 3.88 × 10

**Answer**-
- 1.40 km/h
- 1.004 g/mL

#### 2.8: Units Raised to a Power

- Perform the following conversions.
- 9.44 m
^{2}to square centimeters - 3.44 × 10
^{8}mm^{3}to cubic meters

- 9.44 m

**Answer**-
- 9.44 × 10
^{4}cm^{2} - 0.344 m
^{3}

- 9.44 × 10

- Perform the following conversions.
- 0.00444 cm
^{3}to cubic meters - 8.11 × 10
^{2}m^{2}to square nanometers

- 0.00444 cm

**Answer**-
- 4.44 × 10
^{−9}m^{3} - 8.11 × 10
^{20}nm^{2}

- 4.44 × 10

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

**Answer**-
One is a unit of area and the other is a unit of volume.

- 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.

**Answer**-
0.0772 m

^{2}

- 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.

**Answer**-
1.48 × 10

^{3}mm^{2}

- 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.

**Answer**-
4.64 × 10

^{5}cm^{3}

- 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.

**Answer**-
3.35 × 10

^{3}cm^{2}

#### 2.9: Density

- 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?

**Answer**-
1.3 g/cm

^{3}

- 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?

**Answer**-
1.72 g/mL

- A sample of iron has a volume of 48.2 cm
^{3}. If the density of iron is 7.87 g/cm^{3}, what is its mass?

**Answer**-
379 g

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

**Answer**-
1.22 g

- The volume of hydrogen used by the
*Hindenburg*, the German airship that exploded in New Jersey in 1937, was 2.000 × 10^{8}L. What mass of hydrogen was used by the airship? Consult Table 2.9.1 for the density.

**Answer**-
1.7 × 10

^{7}g

- The volume of an Olympic-sized swimming pool is 2.50 × 10
^{9}cm^{3}. If the pool is filled with alcohol (*d*= 0.789 g/cm^{3}), what mass of alcohol is in the pool?

**Answer**-
1.97 × 10

^{9}g

- A typical engagement ring has 0.77 cm
^{3}of gold. What mass of gold is present? Consult Table 2.9.1 for the density.

**Answer**-
15 g

- 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.

**Answer**-
0.53 g

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

**Answer**-
8.811 cm

^{3}

- What is the volume of 255.0 g of uranium if uranium has a density of 19.05 g/cm
^{3}?

**Answer**-
13.39 cm

^{3}

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

**Answer**-
247 L

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

**Answer**-
3.33 L

- Which has the greater volume, 100.0 g of iron (
*d*= 7.87 g/cm^{3}) or 75.0 g of gold (*d*= 19.3 g/cm^{3})?

**Answer**-
Iron. The volume of the iron is 12.7 cm

^{3}and the volume of the gold is 3.87 cm^{3}.

- 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)?

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

#### Additional Exercises

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

**Answer**-
3.42 × 10

^{−18}

- 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.

**Answer**-
9.835 × 10

^{21}

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

**Answer**-
10

^{9}μm

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

**Answer**-
10

^{15}ns

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

**Answer**-
10

^{−8}ML

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

**Answer**-
10

^{−6}kg

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

**Answer**-
96.5 km/h

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

**Answer**-
37.3 mi/h

- Convert 52.09 km/h into meters/second.

**Answer**-
14.47 m/s

- Convert 2.155 m/s into kilometers/hour.

**Answer**-
7.758 km/h

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

**Answer**-
1.723 × 10

^{5}g

- What is the mass of 0.663 m
^{3}of air? Consult Table 2.9.1 for the density.

**Answer**-
796 g

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

**Answer**-
149 cm

^{3}

- What is the volume of 40.99 kg of cork? Assume a density of 0.22 g/cm
^{3}.

**Answer**-
1.9 × 10

^{5}cm^{3}

#### Contributions & Attributions

Adapted from "Beginning Chemistry (Ball)" by LibreTexts, licensed under CC BY-NC-SA.

- Vicki MacMurdo (Anoka-Ramsey Community College)
- Lance S. Lund (Anoka-Ramsey Community College)