Q: If you have 115 minutes, how many hours is this? Use dimensional analysis.

$$115 \times \frac{1 \text{ hour}}{60 \text{ min}} = 1.92 \text{ hours}$$

Q: A TA can grade 4 assignments per hour. If each assignment has 12 questions, how many questions can the TA grade in 3 hours?

$$3 \text{ hr} \times \frac{4 \text{ assignments}}{1 \text{ hr}} \times \frac{12 \text{ questions}}{1 \text{ assignment}} = 144 \text{ questions}$$

Q: Which of the following is a correct conversion factor for inches to centimeters?

$$1 \text{ inch} = 2.54 \text{ cm}$$

Q: The distance between Washington, D.C. and New York City is 234.9 miles. What is this distance in centimeters? ($$1 \text{ mile} = 1.609 \times 10^5$ \text{ cm})$$

$$234.9 \text{ miles} \times 1.609 \times 10^5$ \text{ cm/mile} = 3.78 \times 10^7$ \text{ cm}$$

Q: The average human body contains 160 fluid ounces of blood. How many quarts is this? ($$1 \text{ quart} = 32 \text{ fl oz})$$

$$160 \text{ fl oz} \times \frac{1 \text{ quart}}{32 \text{ fl oz}} = 5 \text{ quarts}$$

Q: Lipitor tablets each weigh 2.1 g and contain 4.0% active ingredient by mass. What mass of active ingredient is present in one tablet?

$$2.1 \text{ g} \times 0.04 = 0.084 \text{ g}$$

Q: A student needs to convert 32 inches to centimeters. Which setup is correct?

$$32 \text{ in} \times \frac{2.54 \text{ cm}}{1 \text{ in}}$$

Q: Which of the following is NOT a valid conversion factor?

$$1 \text{ cm} = 2.54 \text{ inches}$$

Q: If a pharmaceutical drug contains 4.5% active ingredient by mass and each tablet weighs 2.0 g, how many grams of active ingredient are in 10 tablets?

$$2.0 \text{ g/tablet} \times 10 \text{ tablets} \times 0.045 = 0.9 \text{ g}$$

Question 1

Which of the following best describes dimensional analysis?

Accepted Answer

A tool to convert from one unit to another using conversion factors.

Question 2

If you have 115 minutes, how many hours is this? Use dimensional analysis.

Accepted Answer

$$115 	imes \frac{1 	ext{ hour}}{60 	ext{ min}} = 1.92 	ext{ hours}$$

Question 3

A TA can grade 4 assignments per hour. If each assignment has 12 questions, how many questions can the TA grade in 3 hours?

Accepted Answer

$$3 	ext{ hr} 	imes \frac{4 	ext{ assignments}}{1 	ext{ hr}} 	imes \frac{12 	ext{ questions}}{1 	ext{ assignment}} = 144 	ext{ questions}$$

Question 4

Which of the following is a correct conversion factor for inches to centimeters?

Accepted Answer

$$1 	ext{ inch} = 2.54 	ext{ cm}$$

Question 5

The distance between Washington, D.C. and New York City is 234.9 miles. What is this distance in centimeters? ($$1 	ext{ mile} = 1.609 	imes 10^5$ 	ext{ cm})$$

Accepted Answer

$$234.9 	ext{ miles} 	imes 1.609 	imes 10^5$ 	ext{ cm/mile} = 3.78 	imes 10^7$ 	ext{ cm}$$

Question 6

The average human body contains 160 fluid ounces of blood. How many quarts is this? ($$1 	ext{ quart} = 32 	ext{ fl oz})$$

Accepted Answer

$$160 	ext{ fl oz} 	imes \frac{1 	ext{ quart}}{32 	ext{ fl oz}} = 5 	ext{ quarts}$$

Question 7

Lipitor tablets each weigh 2.1 g and contain 4.0% active ingredient by mass. What mass of active ingredient is present in one tablet?

Accepted Answer

$$2.1 	ext{ g} 	imes 0.04 = 0.084 	ext{ g}$$

Question 8

Which step in dimensional analysis involves writing the given amount and identifying the conversion factor?

Accepted Answer

Step 1

Question 9

A student needs to convert 32 inches to centimeters. Which setup is correct?

Accepted Answer

$$32 	ext{ in} 	imes \frac{2.54 	ext{ cm}}{1 	ext{ in}}$$

Question 10

Which of the following is NOT a valid conversion factor?

Accepted Answer

$$1 	ext{ cm} = 2.54 	ext{ inches}$$

Question 11

If a pharmaceutical drug contains 4.5% active ingredient by mass and each tablet weighs 2.0 g, how many grams of active ingredient are in 10 tablets?

Accepted Answer

$$2.0 	ext{ g/tablet} 	imes 10 	ext{ tablets} 	imes 0.045 = 0.9 	ext{ g}$$

Question 12

Which of the following best explains why units must be canceled in dimensional analysis?

Accepted Answer

To ensure the final answer is in the desired unit.

Question 13

A recipe calls for 3 cups of milk. How many fluid ounces is this? ($$1 	ext{ cup} = 8 	ext{ fl oz})$$

Accepted Answer

$$3 	ext{ cups} 	imes 8 	ext{ fl oz/cup} = 24 	ext{ fl oz}$$

Question 14

Which of the following is the correct order of steps in dimensional analysis?

Accepted Answer

Write the given amount, identify the conversion factor, set up the conversion, solve for the end amount.

Question 15

A car travels 60 miles per hour. How many kilometers does it travel in 2 hours? ($$1 	ext{ mile} = 1.609 	ext{ km})$$

Accepted Answer

$$60 	ext{ mi/hr} 	imes 2 	ext{ hr} 	imes 1.609 	ext{ km/mi} = 193.08 	ext{ km}$$

Question 16

If you have 7.3 quarts of blood, how many cups is this? ($$1 	ext{ quart} = 4 	ext{ cups})$$

Accepted Answer

$$7.3 	ext{ quarts} 	imes 4 	ext{ cups/quart} = 29.2 	ext{ cups}$$

Question 17

Which of the following is a real-world application of dimensional analysis?

Accepted Answer

Converting medication dosages from milligrams to grams.

Question 18

A patient is prescribed 0.5 liters of IV fluid. How many fluid ounces is this? ($$1 	ext{ L} = 33.814 	ext{ fl oz})$$

Accepted Answer

$$0.5 	ext{ L} 	imes 33.814 	ext{ fl oz/L} = 16.907 	ext{ fl oz}$$

Dimensional Analysis and Unit Conversion in Chemistry

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