Q: A car travels at 62 miles per hour. How many feet per second is this speed? (1 mile = 5280 feet, 1 hour = 3600 seconds)

$$62 \times \frac{5280}{1} \times \frac{1}{3600} = 91 ft/s$$

Q: A sheet of notebook paper has an area of 603.22 cm$$^2. $$What is the area of this paper in ft$$^2$$? (1 foot = 30.48 cm)

$$603.22 \times \left(\frac{1}{30.48}\$$right)^2$$ = 0.065 ft$^2$$

Q: A chemical reaction releases 2.021 x 10$$^3 J of $$energy. How many calories is this? (1 cal = 4.184 J)

$$2.021 \times 10^3$ \div 4.184 = 483$$ cal

Q: A runner completes 440 yards in 3 minutes. What is the runner's speed in meters per second? (1 yard = 0.9144 m)

$$\frac{440 \times 0.9144}{3 \times 60} = 2.24 m/s$$

Q: A marathon is 26.2 miles long. How many kilometers is this? (1 mile = 1.609 km)

$$26.2 \times 1.609 = 42.2 km$$

Q: A rectangular swimming pool is 25.0 m long and 10.0 m wide. What is the area in square feet? (1 m = 3.281 ft)

$$25.0 \times 10.0 \times (3.281)^2$ = 2,690$$ $$ft^2$$

Question 1

Which of the following best describes the process of dimensional analysis?

Accepted Answer

A technique for converting between units by multiplying by conversion factors so that units cancel appropriately.

Question 2

A car travels at 62 miles per hour. How many feet per second is this speed? (1 mile = 5280 feet, 1 hour = 3600 seconds)

Accepted Answer

$$62 	imes \frac{5280}{1} 	imes \frac{1}{3600} = 91 ft/s$$

Question 3

Which of the following is the correct conversion of 4.39 micrometers to meters? ($$1 \mu m = 1 	imes 10$$^{-6}$$ m)

Accepted Answer

$$4.39 	imes 10$$^{-6}$$ m

Question 4

A patient weighs 85.7 pounds. The doctor orders a medication that should be given at a dosage of 3.85 mg/kg of body weight. (1 kg = 2.2 lb) How many 25 mg tablets of medicine should be given to the patient? (Round to the nearest whole number)

Accepted Answer

6 tablets

Question 5

A sheet of notebook paper has an area of 603.22 cm$$^2. $$What is the area of this paper in ft$$^2$$? (1 foot = 30.48 cm)

Accepted Answer

$$603.22 	imes \left(\frac{1}{30.48}\$$right)^2$$ = 0.065 ft$^2$$

Question 6

Which of the following is the correct conversion for 36.5 ft to yards? (1 yard = 3 feet)

Accepted Answer

$$36.5 \div 3 = 12.2$$ yards

Question 7

A 10.1 lb bag of flour is to be converted to kilograms. (1 kg = 2.2 lb) What is the mass in kilograms?

Accepted Answer

$$10.1 \div 2.2 = 4.59 kg$$

Question 8

A chemical reaction releases 2.021 x 10$$^3 J of $$energy. How many calories is this? (1 cal = 4.184 J)

Accepted Answer

$$2.021 	imes 10^3$ \div 4.184 = 483$$ cal

Question 9

A runner completes 440 yards in 3 minutes. What is the runner's speed in meters per second? (1 yard = 0.9144 m)

Accepted Answer

$$\frac{440 	imes 0.9144}{3 	imes 60} = 2.24 m/s$$

Question 10

A patient is prescribed 250 mg of a medication. The tablets available are 62.5 mg each. How many tablets should the patient take?

Accepted Answer

4 tablets

Question 11

A recipe calls for 1.5 quarts of milk. How many milliliters is this? (1 quart = 946 mL)

Accepted Answer

$$1.5 	imes 946 = 1,419 mL$$

Question 12

A marathon is 26.2 miles long. How many kilometers is this? (1 mile = 1.609 km)

Accepted Answer

$$26.2 	imes 1.609 = 42.2 km$$

Question 13

A solution contains 0.75 L of water. How many milliliters is this?

Accepted Answer

$$0.75 	imes 1000 = 750 mL$$

Question 14

A rectangular swimming pool is 25.0 m long and 10.0 m wide. What is the area in square feet? (1 m = 3.281 ft)

Accepted Answer

$$25.0 	imes 10.0 	imes (3.281)^2$ = 2,690$$ $$ft^2$$

Question 15

A chemist needs 0.250 kg of sodium chloride. How many grams is this?

Accepted Answer

$$0.250 	imes 1000 = 250 g$$

Question 16

A laboratory sample has a mass of 2.5 g and a volume of 0.50 cm$$^3. $$What is its density in g/cm$$^3$$?

Accepted Answer

$$2.5 \div 0.50 = 5.0 g/cm$^3$$

Dimensional Analysis and Unit Conversions in Chemistry

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