Q: A chemist needs to convert 2.50 kilometers to meters for a laboratory report. Which of the following equations correctly shows this conversion?

$$2.50 \\ \text{km} \\times \\frac{1000 \\ \text{m}}{1 \\ \text{km}} = 2500 \\ \text{m}$$

Q: The circumference of the Earth is approximately 40,075 km. What is this value in meters?

$$40,075 \\ \text{km} \\times \\frac{1000 \\ \text{m}}{1 \\ \text{km}} = 40,075,000 \\ \text{m}$$

Q: A laboratory sample has a mass of 1.00 kilogram. How many grams does this sample have?

$$1.00 \\ \text{kg} \\times \\frac{1000 \\ \text{g}}{1 \\ \text{kg}} = 1000 \\ \text{g}$$

Q: A student measures a length as 150 centimeters. What is this length in meters?

$$150 \\ \text{cm} \\times \\frac{1 \\ \text{m}}{100 \\ \text{cm}} = 1.5 \\ \text{m}$$

Q: If a marathon is 26.2 miles long, and 1 mile is approximately 1.609 kilometers, what is the length of a marathon in kilometers?

$$26.2 \\ \text{mi} \\times \\frac{1.609 \\ \text{km}}{1 \\ \text{mi}} = 42.2 \\ \text{km}$$

Q: A patient is prescribed 500 mg of a medication. The pharmacy only has tablets labeled in grams. How many grams should the patient take?

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

Q: A rectangular room measures 5.0 meters by 4.0 meters. What is the area of the room in square centimeters?

$$5.0 \\ \text{m} \\times 4.0 \\ \text{m} = 20 \\ \text{m}^2$$; $$20 \\ \text{m}^2 \\times \\frac{10,000 \\ \text{cm}^2}{1 \\ \text{m}^2} = 200,000 \\ \text{cm}^2$$

Q: A car travels 120 kilometers in 2 hours. What is its average speed in meters per second?

$$120 \\ \text{km} \\times \\frac{1000 \\ \text{m}}{1 \\ \text{km}} = 120,000 \\ \text{m}$$; $$2 \\ \text{h} \\times \\frac{3600 \\ \text{s}}{1 \\ \text{h}} = 7200 \\ \text{s}$$; $$\\frac{120,000 \\ \text{m}}{7200 \\ \text{s}} = 16.7 \\ \text{m/s}$$

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

$$250 \\ \text{mL} \\times \\frac{1 \\ \text{L}}{1000 \\ \text{mL}} = 0.250 \\ \text{L}$$

Q: A gold bar has a mass of 2.5 kg. What is its mass in milligrams?

$$2.5 \\ \text{kg} \\times \\frac{1,000,000 \\ \text{mg}}{1 \\ \text{kg}} = 2,500,000 \\ \text{mg}$$

Question 1

A chemist needs to convert 2.50 kilometers to meters for a laboratory report. Which of the following equations correctly shows this conversion?

Accepted Answer

$$2.50 \ 	ext{km} \times \frac{1000 \ 	ext{m}}{1 \ 	ext{km}} = 2500 \ 	ext{m}$$

Question 2

The circumference of the Earth is approximately 40,075 km. What is this value in meters?

Accepted Answer

$$40,075 \ 	ext{km} \times \frac{1000 \ 	ext{m}}{1 \ 	ext{km}} = 40,075,000 \ 	ext{m}$$

Question 3

A laboratory sample has a mass of 1.00 kilogram. How many grams does this sample have?

Accepted Answer

$$1.00 \ 	ext{kg} \times \frac{1000 \ 	ext{g}}{1 \ 	ext{kg}} = 1000 \ 	ext{g}$$

Question 4

A student measures a length as 150 centimeters. What is this length in meters?

Accepted Answer

$$150 \ 	ext{cm} \times \frac{1 \ 	ext{m}}{100 \ 	ext{cm}} = 1.5 \ 	ext{m}$$

Question 5

If a marathon is 26.2 miles long, and 1 mile is approximately 1.609 kilometers, what is the length of a marathon in kilometers?

Accepted Answer

$$26.2 \ 	ext{mi} \times \frac{1.609 \ 	ext{km}}{1 \ 	ext{mi}} = 42.2 \ 	ext{km}$$

Question 6

A patient is prescribed 500 mg of a medication. The pharmacy only has tablets labeled in grams. How many grams should the patient take?

Accepted Answer

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

Question 7

A rectangular room measures 5.0 meters by 4.0 meters. What is the area of the room in square centimeters?

Accepted Answer

$$5.0 \ 	ext{m} \times 4.0 \ 	ext{m} = 20 \ 	ext{m}^2$$; $$20 \ 	ext{m}^2 \times \frac{10,000 \ 	ext{cm}^2}{1 \ 	ext{m}^2} = 200,000 \ 	ext{cm}^2$$

Question 8

A car travels 120 kilometers in 2 hours. What is its average speed in meters per second?

Accepted Answer

$$120 \ 	ext{km} \times \frac{1000 \ 	ext{m}}{1 \ 	ext{km}} = 120,000 \ 	ext{m}$$; $$2 \ 	ext{h} \times \frac{3600 \ 	ext{s}}{1 \ 	ext{h}} = 7200 \ 	ext{s}$$; $$\frac{120,000 \ 	ext{m}}{7200 \ 	ext{s}} = 16.7 \ 	ext{m/s}$$

Question 9

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

Accepted Answer

$$250 \ 	ext{mL} \times \frac{1 \ 	ext{L}}{1000 \ 	ext{mL}} = 0.250 \ 	ext{L}$$

Question 10

A gold bar has a mass of 2.5 kg. What is its mass in milligrams?

Accepted Answer

$$2.5 \ 	ext{kg} \times \frac{1,000,000 \ 	ext{mg}}{1 \ 	ext{kg}} = 2,500,000 \ 	ext{mg}$$

Question 11

A runner completes a 10,000 meter race. How many kilometers did the runner complete?

Accepted Answer

$$10,000 \ 	ext{m} \times \frac{1 \ 	ext{km}}{1000 \ 	ext{m}} = 10 \ 	ext{km}$$

Question 12

A laboratory experiment requires 0.75 liters of a solution. How many milliliters is this?

Accepted Answer

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

Question 13

A prescription calls for 2.5 grams of a drug, but the available tablets are 250 mg each. How many tablets should the patient take?

Accepted Answer

$$2.5 \ 	ext{g} \times \frac{1000 \ 	ext{mg}}{1 \ 	ext{g}} = 2500 \ 	ext{mg}$$; $$\frac{2500 \ 	ext{mg}}{250 \ 	ext{mg/tablet}} = 10 \ 	ext{tablets}$$

Question 14

A rectangular swimming pool is 25.0 meters long and 10.0 meters wide. What is the area in square kilometers?

Accepted Answer

$$25.0 \ 	ext{m} \times 10.0 \ 	ext{m} = 250 \ 	ext{m}^2$$; $$250 \ 	ext{m}^2 \times \frac{1 \ 	ext{km}^2}{1,000,000 \ 	ext{m}^2} = 0.00025 \ 	ext{km}^2$$

Question 15

A patient receives an IV drip at a rate of 50 mL/hour. How many liters will the patient receive in 24 hours?

Accepted Answer

$$50 \ 	ext{mL/hr} \times 24 \ 	ext{hr} = 1200 \ 	ext{mL}$$; $$1200 \ 	ext{mL} \times \frac{1 \ 	ext{L}}{1000 \ 	ext{mL}} = 1.2 \ 	ext{L}$$

Question 16

A city is 300 miles away from your location. If 1 mile equals 1.609 kilometers, how many kilometers away is the city?

Accepted Answer

$$300 \ 	ext{mi} \times \frac{1.609 \ 	ext{km}}{1 \ 	ext{mi}} = 482.7 \ 	ext{km}$$

Question 17

A laboratory technician needs to dilute a 5.0 L solution to a final volume of 500 mL. What is the final volume in liters?

Accepted Answer

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

Question 18

A newborn baby weighs 3.2 kg. What is the baby's weight in grams?

Accepted Answer

$$3.2 \ 	ext{kg} \times \frac{1000 \ 	ext{g}}{1 \ 	ext{kg}} = 3200 \ 	ext{g}$$

Units, Measurements, and Conversion Factors in Chemistry

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