Exercises

Part 1

  1. Is one liter about an ounce, a pint, a quart, or a gallon?
  2. Is a meter about an inch, a foot, a yard, or a mile?
  3. Indicate the SI base units or derived units that are appropriate for the following measurements:
    1. the length of a marathon race (26 miles 385 yards)
    2. the mass of an automobile
    3. the volume of a swimming pool
    4. the speed of an airplane
    5. the density of gold
    6. the area of a football field
    7. the maximum temperature at the South Pole on April 1, 1913
  4. Indicate the SI base units or derived units that are appropriate for the following measurements:
    1. the mass of the moon
    2. the distance from Dallas to Oklahoma City
    3. the speed of sound
    4. the density of air
    5. the temperature at which alcohol boils
    6. the area of the state of Delaware
    7. the volume of a flu shot or a measles vaccination
  5. Give the name and symbol of the prefixes used with SI units to indicate multiplication by the following exact quantities.
    1. 103
    2. 10−2
    3. 0.1
    4. 10−3
    5. 1,000,000
    6. 0.000001
  6. Give the name of the prefix and the quantity indicated by the following symbols that are used with SI base units.
    1. c
    2. d
    3. G
    4. k
    5. m
    6. n
    7. p
    8. T
  7. A large piece of jewelry has a mass of 132.6 g. A graduated cylinder initially contains 48.6 mL water. When the jewelry is submerged in the graduated cylinder, the total volume increases to 61.2 mL.
    1. Determine the density of this piece of jewelry.
    2. Assuming that the jewelry is made from only one substance, what substance is it likely to be? Explain.

Part 2

  1. Visit this PhET density simulation and select the Same Volume Blocks.
    1. What are the mass, volume, and density of the yellow block?
    2. What are the mass, volume and density of the red block?
    3. List the block colors in order from smallest to largest mass.
    4. List the block colors in order from lowest to highest density.
    5. How are mass and density related for blocks of the same volume?
  2. Visit this PhET density simulation and select Custom Blocks and then My Block.
    1. Enter mass and volume values for the block such that the mass in kg is less than the volume in L. What does the block do? Why? Is this always the case when mass < volume?
    2. Enter mass and volume values for the block such that the mass in kg is more than the volume in L. What does the block do? Why? Is this always the case when mass > volume?
    3. How would (a) and (b) be different if the liquid in the tank were ethanol instead of water?
    4. How would (a) and (b) be different if the liquid in the tank were mercury instead of water?
  3. Visit this PhET density simulation and select Mystery Blocks.
    1. Pick one of the Mystery Blocks and determine its mass, volume, density, and its likely identity.
    2. Pick a different Mystery Block and determine its mass, volume, density, and its likely identity.
    3. Order the Mystery Blocks from least dense to most dense. Explain.

Part 3

  1. Express each of the following numbers in scientific notation with correct significant figures:
    1. 711.0
    2. 0.239
    3. 90743
    4. 134.2
    5. 0.05499
    6. 10000.0
    7. 0.000000738592
  2. Express each of the following numbers in exponential notation with correct significant figures:
    1. 704
    2. 0.03344
    3. 547.9
    4. 22086
    5. 1000.00
    6. 0.0000000651
    7. 0.007157
  3. Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:
    1. the number of eggs in a basket
    2. the mass of a dozen eggs
    3. the number of gallons of gasoline necessary to fill an automobile gas tank
    4. the number of cm in 2 m
    5. the mass of a textbook
    6. the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h
  4. Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:
    1. the number of seconds in an hour
    2. the number of pages in this book
    3. the number of grams in your weight
    4. the number of grams in 3 kilograms
    5. the volume of water you drink in one day
    6. the distance from San Francisco to Kansas City
  5. How many significant figures are contained in each of the following measurements?
    1. 38.7 g
    2. 2 × 1018 m
    3. 3,486,002 kg
    4. 9.74150 × 10−4 J
    5. 0.0613 cm3   
    6. 17.0 kg
    7. 0.01400 g/mL
  6. How many significant figures are contained in each of the following measurements?
    1. 53 cm
    2. 2.05 × 108 m
    3. 86,002 J
    4. 9.740 × 104 m/s
    5. 10.0613 m3   
    6. 0.17 g/mL
    7. 0.88400 s
  7. The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.
    1. 0.0055 g active ingredients
    2. 12 tablets
    3. 3% hydrogen peroxide
    4. 5.5 ounces
    5. 473 mL
    6. 1.75% bismuth
    7. 0.001% phosphoric acid
    8. 99.80% inert ingredients
  8. Round off each of the following numbers to two significant figures:
    1. 0.436
    2. 9.000
    3. 27.2
    4. 135
    5. 1.497 × 10−3   
    6. 0.445
  9. Round off each of the following numbers to two significant figures:
    1. 517
    2. 86.3
    3. 6.382 × 103   
    4. 5.0008
    5. 22.497
    6. 0.885
  10. Perform the following calculations and report each answer with the correct number of significant figures.
    1. 628 × 342
    2. (5.63 × 102) × (7.4 × 103)
    3. [latex]\frac{28.0}{13.483}[/latex]
    4. 8119 × 0.000023
    5. 14.98 + 27,340 + 84.7593
    6. 42.7 + 0.259
  11. Perform the following calculations and report each answer with the correct number of significant figures.
    1. 62.8 × 34
    2. 0.147 + 0.0066 + 0.012
    3. 38 × 95 × 1.792
    4. 15 – 0.15 – 0.6155
    5. [latex]8.78\times \left(\frac{0.0500}{0.478}\right)[/latex]
    6. 140 + 7.68 + 0.014
    7. 28.7 – 0.0483
    8. [latex]\frac{\left(88.5-87.57\right)}{45.13}[/latex]
  12. Consider the results of the archery contest shown in this figure.
    4 targets are shown each with 4 holes indicating where the arrows hit the targets. Archer W put all 4 arrows closely around the center of the target. Archer X put all 4 arrows in a tight cluster but far to the lower right of the target. Archer Y put all 4 arrows at different corners of the target. All 4 arrows are very far from the center of the target. Archer Z put 2 arrows close to the target and 2 other arrows far outside of the target.

    1. Which archer is most precise?
    2. Which archer is most accurate?
    3. Who is both least precise and least accurate?
  13. Classify the following sets of measurements as accurate, precise, both, or neither.
    1. Checking for consistency in the weight of chocolate chip cookies: 17.27g, 13.05g, 19.46g, 16.92g
    2. Testing the volume of a batch of 25-mL pipettes: 27.02 mL, 26.99 mL, 26.97 mL, 27.01 mL
    3. Determining the purity of gold: 99.9999%, 99.9998%, 99.9998%, 99.9999%

Part 4

  1. Write conversion factors (as ratios) for the number of:
    1. yards in 1 meter
    2. liters in 1 liquid quart
    3. pounds in 1 kilogram
  2. Write conversion factors (as ratios) for the number of:
    1. kilometers in 1 mile
    2. liters in 1 cubic foot
    3. grams in 1 ounce
  3. Soccer is played with a round ball having a circumference between 27 and 28 in. and a weight between 14 and 16 oz. What are these specifications in units of centimeters and grams?
  4. A woman’s basketball has a circumference between 28.5 and 29.0 inches and a maximum weight of 20 ounces (two significant figures). What are these specifications in units of centimeters and grams?
  5. Use scientific (exponential) notation to express the following quantities in terms of the SI base units in Table 1:
    1. 0.13 g
    2. 232 Gg
    3. 5.23 pm
    4. 86.3 mg
    5. 37.6 cm
    6. 54 μm
    7. 1 Ts
    8. 27 ps
    9. 0.15 mK
  6. Complete the following conversions between SI units.
    1. 612 g = ________ mg
    2. 8.160 m = ________ cm
    3. 3779 μg = ________ g
    4. 781 mL = ________ L
    5. 4.18 kg = ________ g
    6. 27.8 m = ________ km
    7. 0.13 mL = ________ L
    8. 1738 km = ________ m
    9. 1.9 Gg = ________ g
  7. Make the conversion indicated in each of the following:
    1. the men’s world record long jump, 29 ft 4¼ in., to meters
    2. the greatest depth of the ocean, about 6.5 mi, to kilometers
    3. the area of the state of Oregon, 96,981 mi2, to square kilometers
    4. the volume of 1 gill (exactly 4 oz) to milliliters
    5. the estimated volume of the oceans, 330,000,000 mi3, to cubic kilometers.
    6. the mass of a 3525-lb car to kilograms
    7. the mass of a 2.3-oz egg to grams
  8. Make the conversion indicated in each of the following:
    1. the length of a soccer field, 120 m (three significant figures), to feet
    2. the height of Mt. Kilimanjaro, at 19,565 ft the highest mountain in Africa, to kilometers
    3. the area of an 8.5 t 11-inch sheet of paper in cm2
    4. the displacement volume of an automobile engine, 161 in.3, to liters
    5. the estimated mass of the atmosphere, 5.6 t 1015 tons, to kilograms
    6. the mass of a bushel of rye, 32.0 lb, to kilograms
    7. the mass of a 5.00-grain aspirin tablet to milligrams (1 grain = 0.00229 oz)
  9. As an instructor is preparing for an experiment, he requires 225 g phosphoric acid. The only container readily available is a 150-mL Erlenmeyer flask. Is it large enough to contain the acid, whose density is 1.83 g/mL?
  10. To prepare for a laboratory period, a student lab assistant needs 125 g of a compound. A bottle containing 1/4 lb is available. Did the student have enough of the compound?
  11. 27 A chemistry student is 159 cm tall and weighs 45.8 kg. What is her height in inches and weight in pounds?
  12. In a recent Grand Prix, the winner completed the race with an average speed of 229.8 km/h. What was his speed in miles per hour, meters per second, and feet per second?
  13. Solve these problems about lumber dimensions.
    1. To describe to a European how houses are constructed in the US, the dimensions of “two-by-four” lumber must be converted into metric units. The thickness × width × length dimensions are 1.50 in. × 3.50 in. × 8.00 ft in the US. What are the dimensions in cm × cm × m?
    2. This lumber can be used as vertical studs, which are typically placed 16.0 in. apart. What is that distance in centimeters?
  14. Calculate the density of aluminum if 27.6 cm3 has a mass of 74.6 g.
  15. Osmium is one of the densest elements known. What is its density if 2.72 g has a volume of 0.121 cm3?

Part 5

  1. Convert the boiling temperature of gold, 2966 °C, into degrees Fahrenheit and kelvin.
  2. Convert the temperature of scalding water, 54 °C, into degrees Fahrenheit and kelvin.
  3. Convert the temperature of the coldest area in a freezer, −10 °F, to degrees Celsius and kelvin.
  4. Convert the temperature of dry ice, −77 °C, into degrees Fahrenheit and kelvin.
  5. Convert the boiling temperature of liquid ammonia, −28.1 °F, into degrees Celsius and kelvin.
  6. The label on a pressurized can of spray disinfectant warns against heating the can above 130 °F. What are the corresponding temperatures on the Celsius and kelvin temperature scales?
  7. The weather in Europe was unusually warm during the summer of 1995. The TV news reported temperatures as high as 45 °C. What was the temperature on the Fahrenheit scale?