Q: If you need to convert 36 inches to meters, which sequence of conversion factors would be appropriate?

$$36 \ \text{in} \times \frac{1 \ \text{ft}}{12 \ \text{in}} \times \frac{1 \ \text{m}}{3.281 \ \text{ft}}$$

Q: A patient’s mass is measured as 72 kg. What is this mass in milligrams ($$mg$$)?

$$72 \ \text{kg} \times \frac{1000 \ \text{g}}{1 \ \text{kg}} \times \frac{1000 \ \text{mg}}{1 \ \text{g}} = 72,000,000 \ \text{mg}$$

Q: Which of the following is a correct application of the factor-label method to convert 5.0 feet to inches?

$$5.0 \ \text{ft} \times \frac{12 \ \text{in}}{1 \ \text{ft}} = 60 \ \text{in}$$

Q: A chemist needs to prepare a solution using 250 mL of water. How many liters is this?

$$250 \ \text{mL} \times \frac{1 \ \text{L}}{1000 \ \text{mL}} = 0.25 \ \text{L}$$

Q: A runner completes a 10 kilometer race. How many centimeters did the runner travel?

$$10 \ \text{km} \times \frac{1000 \ \text{m}}{1 \ \text{km}} \times \frac{100 \ \text{cm}}{1 \ \text{m}} = 1,000,000 \ \text{cm}$$

Q: A medication is prescribed at a dose of 0.5 grams. How many milligrams is this?

$$0.5 \ \text{g} \times \frac{1000 \ \text{mg}}{1 \ \text{g}} = 500 \ \text{mg}$$

Q: Which of the following is the correct way to convert 2.5 hours to seconds using the factor-label method?

$$2.5 \ \text{hr} \times \frac{60 \ \text{min}}{1 \ \text{hr}} \times \frac{60 \ \text{s}}{1 \ \text{min}} = 9000 \ \text{s}$$

Q: A laboratory sample has a mass of 0.025 kg. What is the mass in milligrams?

$$0.025 \ \text{kg} \times \frac{1000 \ \text{g}}{1 \ \text{kg}} \times \frac{1000 \ \text{mg}}{1 \ \text{g}} = 25,000 \ \text{mg}$$

Question 1

Which of the following best describes the factor-label method (also known as dimensional analysis) as explained in the passage?

Accepted Answer

A technique for converting a measurement from one unit to another by multiplying by conversion factors.

Question 2

If you need to convert 36 inches to meters, which sequence of conversion factors would be appropriate?

Accepted Answer

$$36 \ 	ext{in} 	imes \frac{1 \ 	ext{ft}}{12 \ 	ext{in}} 	imes \frac{1 \ 	ext{m}}{3.281 \ 	ext{ft}}$$

Question 3

A patient’s mass is measured as 72 kg. What is this mass in milligrams ($$mg$$)?

Accepted Answer

$$72 \ 	ext{kg} 	imes \frac{1000 \ 	ext{g}}{1 \ 	ext{kg}} 	imes \frac{1000 \ 	ext{mg}}{1 \ 	ext{g}} = 72,000,000 \ 	ext{mg}$$

Question 4

Which of the following is a correct application of the factor-label method to convert 5.0 feet to inches?

Accepted Answer

$$5.0 \ 	ext{ft} 	imes \frac{12 \ 	ext{in}}{1 \ 	ext{ft}} = 60 \ 	ext{in}$$

Question 5

A chemist needs to prepare a solution using 250 mL of water. How many liters is this?

Accepted Answer

$$250 \ 	ext{mL} 	imes \frac{1 \ 	ext{L}}{1000 \ 	ext{mL}} = 0.25 \ 	ext{L}$$

Question 6

Which of the following best explains why units must be included and properly canceled in each step of a factor-label calculation?

Accepted Answer

To ensure that the final answer has the correct units and to avoid calculation errors.

Question 7

A runner completes a 10 kilometer race. How many centimeters did the runner travel?

Accepted Answer

$$10 \ 	ext{km} 	imes \frac{1000 \ 	ext{m}}{1 \ 	ext{km}} 	imes \frac{100 \ 	ext{cm}}{1 \ 	ext{m}} = 1,000,000 \ 	ext{cm}$$

Question 8

A medication is prescribed at a dose of 0.5 grams. How many milligrams is this?

Accepted Answer

$$0.5 \ 	ext{g} 	imes \frac{1000 \ 	ext{mg}}{1 \ 	ext{g}} = 500 \ 	ext{mg}$$

Question 9

Which of the following is the correct way to convert 2.5 hours to seconds using the factor-label method?

Accepted Answer

$$2.5 \ 	ext{hr} 	imes \frac{60 \ 	ext{min}}{1 \ 	ext{hr}} 	imes \frac{60 \ 	ext{s}}{1 \ 	ext{min}} = 9000 \ 	ext{s}$$

Question 10

A laboratory sample has a mass of 0.025 kg. What is the mass in milligrams?

Accepted Answer

$$0.025 \ 	ext{kg} 	imes \frac{1000 \ 	ext{g}}{1 \ 	ext{kg}} 	imes \frac{1000 \ 	ext{mg}}{1 \ 	ext{g}} = 25,000 \ 	ext{mg}$$

Question 11

A rectangular room is 15 feet long and 12 feet wide. What is the area in square meters? ($$1 \ 	ext{ft} = 0.3048 \ 	ext{m})$$

Accepted Answer

$$15 \ 	ext{ft} 	imes 0.3048 \ 	ext{m/ft} = 4.572 \ 	ext{m}$$ and $$12 \ 	ext{ft} 	imes 0.3048 \ 	ext{m/ft} = 3.6576 \ 	ext{m}$$, so $$4.572 \ 	ext{m} 	imes 3.6576 \ 	ext{m} = 16.76 \ 	ext{m}^2$$

Question 12

A car is traveling at a speed of 60 miles per hour. What is this speed in meters per second? ($$1 \ 	ext{mile} = 1609 \ 	ext{m}$$, $$1 \ 	ext{hr} = 3600 \ 	ext{s})$$

Accepted Answer

$$60 \ 	ext{mi/hr} 	imes \frac{1609 \ 	ext{m}}{1 \ 	ext{mi}} 	imes \frac{1 \ 	ext{hr}}{3600 \ 	ext{s}} = 26.8 \ 	ext{m/s}$$

Question 13

A recipe calls for 2.5 quarts of milk. How many liters is this? ($$1 \ 	ext{qt} = 0.946 \ 	ext{L})$$

Accepted Answer

$$2.5 \ 	ext{qt} 	imes 0.946 \ 	ext{L/qt} = 2.365 \ 	ext{L}$$

Question 14

A scientist needs 0.75 meters of wire for an experiment. How many centimeters of wire does she need?

Accepted Answer

$$0.75 \ 	ext{m} 	imes \frac{100 \ 	ext{cm}}{1 \ 	ext{m}} = 75 \ 	ext{cm}$$

Question 15

A hospital patient receives 500 mL of saline solution. How many liters is this?

Accepted Answer

$$500 \ 	ext{mL} 	imes \frac{1 \ 	ext{L}}{1000 \ 	ext{mL}} = 0.5 \ 	ext{L}$$

Question 16

A marathon is 26.2 miles long. How many kilometers is this? ($$1 \ 	ext{mile} = 1.609 \ 	ext{km})$$

Accepted Answer

$$26.2 \ 	ext{mi} 	imes 1.609 \ 	ext{km/mi} = 42.16 \ 	ext{km}$$

Question 17

A chemist needs to dilute a solution from 3.0 L to 750 mL. What is the final volume in liters?

Accepted Answer

$$750 \ 	ext{mL} 	imes \frac{1 \ 	ext{L}}{1000 \ 	ext{mL}} = 0.75 \ 	ext{L}$$

Unit Conversion and the Factor-Label Method in General Chemistry

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