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2.11: 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
    Answer
    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
    Answer
    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)
    Answer
    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)
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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. Pressure gauge with needle pointing between 6 and 7 psi.
      2. Dotted line through ruler between 28 and 29 mm.
      3. Pressure gauge with needle pointing between 400 and 500 psi. between the 7th and 8th tick marks.
      4. Dotted line through ruler between 30 and 40 mm.
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    1. 1
    2. 1
    3. 5
    4. 4 or 5, ambiguous

     

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

    8.745 × 104

     

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

    6.6600 × 10−5

     

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

    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 = ?
    Answer
    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 = ?
    Answer
    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 = ?
    Answer
    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 = ?
    Answer
    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 = ?
    Answer
    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 = ?
    Answer
    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
    Answer
    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
    Answer
    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 ×
    Answer
    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 ×
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    1. 4.44 × 10−9 m3
    2. 8.11 × 1020 nm2

     

    1. 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.

     

    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.
    Answer

    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.
    Answer

    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.
    Answer

    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.
    Answer

    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?
    Answer

    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?
    Answer

    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?
    Answer

    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.
    Answer

    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.
    Answer

    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?
    Answer

    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.
    Answer

    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.
    Answer

    0.53 g

     

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

    8.811 cm3 

     

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

    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?
    Answer

    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?
    Answer

    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)?
    Answer

    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)?
    Answer

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

     

    Additional Exercises

    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.
    Answer

    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.
    Answer

    9.835 × 1021 

     

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

    109 μm

     

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

    1015 ns

     

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

    10−8 ML

     

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

    10−6 kg

     

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

    96.5 km/h

     

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

    37.3 mi/h

     

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

     

    Answer

    14.47 m/s

     

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

    7.758 km/h

     

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

    1.723 × 105 g

     

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

    796 g

     

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

    149 cm3 

     

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

    1.9 × 105 cm3 

     

     

     

    This page was adapted from "Beginning Chemistry (Ball)" by LibreTexts and is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Vicki MacMurdo (Anoka-Ramsey Community College) and Lance S. Lund (Anoka-Ramsey Community College).

    This page titled 2.11: Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Anonymous.