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PROBLEM SET 1: Measurement
1. Unit Conversion According to the label on a bottle of salad dressing, the volume of the
contents is 0.473 liter (L). Using only the conversions 1 L = 1000 cm3 and 1 in. = 2.54 cm,
express this volume in cubic inches.
2. Unit Conversion One gallon of paint (volume = 3.78 x 10–3 m3 ) covers an area of 25.0 m2 .
What is the thickness of the paint on the wall?
3. Unit Conversion A Toyota Prius (when driven correctly) gets gasoline mileage of 55.0
mpg (miles per gallon).
(a) Imagine that you are driving this car in Europe and want to compare its mileage with
that of other European cars, express this mileage in km/L (1L = liter).
(b) If the Prius’s gas tank holds 45 L, how many tanks of gas will you use to drive 1500 km?
4. Estimation A useful and easy–to–remember approximate value for the number of seconds
in a year is π × 107 . Determine the percent error in this approximate value. (There are
365.24 days in one year.)
5. Estimation The density of air under standard laboratory conditions is 1.29 kg/m3, and
about 20% of that air consists of oxygen. Typically, people breathe about 0.5 L of air per
breath.
(a) How many grams of oxygen does a person breathe in a day?
(b) If all the air you breathe in a day is stored uncompressed in a cubical tank, how long is
each side of the tank? If you were trapped in a box this size for a whole day do you think
you could survive?
6. Estimation How many dollar bills would you have to stack to reach the moon? Would
that be cheaper than building and launching a spacecraft? (Hint: Start by folding a dollar bill
to see how many thicknesses make 1.0 mm.)
7. Sig Figs You measure the length of a rectangular piece of sheet metal to be 12 mm with a
wooden ruler. Then, using micrometer calipers to measure the width of the rectangle, you
obtain the value 5.98 mm. Give your answers to the following questions to the correct
number of significant figures.
(a) What is the area of the rectangle?
(b) What is the ratio of the rectangle’s width to its length?
(c) What is the perimeter of the rectangle?
(d) What is the difference between the length and width?
(e) What is the ratio of the length to the width
PROBLEM SET 1: Measurement
1. Unit Conversion According to the label on a bottle of salad dressing, the volume of the
contents is 0.473 liter (L). Using only the conversions 1 L = 1000 cm3 and 1 in. = 2.54 cm,
express this volume in cubic inches.
2. Unit Conversion One gallon of paint (volume = 3.78 x 10–3 m3 ) covers an area of 25.0 m2 .
What is the thickness of the paint on the wall?
3. Unit Conversion A Toyota Prius (when driven correctly) gets gasoline mileage of 55.0
mpg (miles per gallon).
(a) Imagine that you are driving this car in Europe and want to compare its mileage with
that of other European cars, express this mileage in km/L (1L = liter).
(b) If the Prius’s gas tank holds 45 L, how many tanks of gas will you use to drive 1500 km?
4. Estimation A useful and easy–to–remember approximate value for the number of seconds
in a year is π × 107 . Determine the percent error in this approximate value. (There are
365.24 days in one year.)
5. Estimation The density of air under standard laboratory conditions is 1.29 kg/m3, and
about 20% of that air consists of oxygen. Typically, people breathe about 0.5 L of air per
breath.
(a) How many grams of oxygen does a person breathe in a day?
(b) If all the air you breathe in a day is stored uncompressed in a cubical tank, how long is
each side of the tank? If you were trapped in a box this size for a whole day do you think
you could survive?
6. Estimation How many dollar bills would you have to stack to reach the moon? Would
that be cheaper than building and launching a spacecraft? (Hint: Start by folding a dollar bill
to see how many thicknesses make 1.0 mm.)
7. Sig Figs You measure the length of a rectangular piece of sheet metal to be 12 mm with a
wooden ruler. Then, using micrometer calipers to measure the width of the rectangle, you
obtain the value 5.98 mm. Give your answers to the following questions to the correct
number of significant figures.
(a) What is the area of the rectangle?
(b) What is the ratio of the rectangle’s width to its length?
(c) What is the perimeter of the rectangle?
(d) What is the difference between the length and width?
(e) What is the ratio of the length to the width
