Factor Label Method Practice worksheet featuring eight problems requiring unit conversions and calculations using the factor label method.

Let's solve each problem step-by-step using the Factor Label Method (also known as dimensional analysis). This method involves multiplying by conversion factors to cancel out unwanted units and obtain the desired unit.

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1. Convert 1200 mg into grams.

We know:
1 gram (g) = 1000 milligrams (mg)

$$
1200\ \text{mg} \times \frac{1\ \text{g}}{1000\ \text{mg}} = \frac{1200}{1000} = 1.2\ \text{g}
$$

✔ Answer: 1.2 g

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2. Convert 3.5 pounds into grams. (There are 2.205 lbs in 1 kg)

We need to convert pounds → kilograms → grams.

Step 1: Pounds to kilograms
$$
3.5\ \text{lbs} \times \frac{1\ \text{kg}}{2.205\ \text{lbs}} = \frac{3.5}{2.205} \approx 1.5873\ \text{kg}
$$

Step 2: Kilograms to grams (1 kg = 1000 g)
$$
1.5873\ \text{kg} \times \frac{1000\ \text{g}}{1\ \text{kg}} = 1587.3\ \text{g}
$$

✔ Answer: 1587.3 g

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3. Convert 500 miles into kilometers. (There are 0.6214 miles in 1 km)

We want to convert miles → km. Since 0.6214 miles = 1 km, we can write:

$$
500\ \text{miles} \times \frac{1\ \text{km}}{0.6214\ \text{miles}} = \frac{500}{0.6214} \approx 804.5\ \text{km}
$$

✔ Answer: 804.5 km

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4. If apples cost $0.79 per pound, and there are approximately 5 apples per pound, how much would it cost to buy 200 apples?

Step 1: Find how many pounds of apples you need
$$
200\ \text{apples} \times \frac{1\ \text{pound}}{5\ \text{apples}} = 40\ \text{pounds}
$$

Step 2: Multiply by price per pound
$$
40\ \text{lbs} \times \$0.79/\text{lb} = \$31.60
$$

✔ Answer: \$31.60

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5. Aluminum has a density of 2.70 g/mL. What is the mass of a cylinder of aluminum with a volume of 7.5 mL?

Use the formula:
$$
\text{Mass} = \text{Density} \times \text{Volume}
$$

$$
\text{Mass} = 2.70\ \text{g/mL} \times 7.5\ \text{mL} = 20.25\ \text{g}
$$

✔ Answer: 20.25 g

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6. If there are 35 g of sugar in 8 fluid ounces of soda, what mass (in grams) of sugar is in an entire 2-liter bottle? (1 fluid ounce = 29.6 mL)

We need to find how many fluid ounces are in 2 liters, then use proportion.

Step 1: Convert 2 L to mL
$$
2\ \text{L} = 2000\ \text{mL}
$$

Step 2: Convert mL to fluid ounces
$$
2000\ \text{mL} \times \frac{1\ \text{fl oz}}{29.6\ \text{mL}} = \frac{2000}{29.6} \approx 67.57\ \text{fl oz}
$$

Step 3: Use ratio to find sugar
$$
67.57\ \text{fl oz} \times \frac{35\ \text{g sugar}}{8\ \text{fl oz}} = \frac{67.57 \times 35}{8} \approx \frac{2364.95}{8} \approx 295.6\ \text{g}
$$

✔ Answer: 295.6 g

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7. If your heart beats at a rate of 72 times per minute and your lifetime will be 70 years, how many times will your heart beat during your lifetime?

We'll convert years → days → hours → minutes → heartbeats.

Step 1: Years to days
$$
70\ \text{years} \times \frac{365.25\ \text{days}}{1\ \text{year}} = 25,567.5\ \text{days}
$$

(Using 365.25 accounts for leap years.)

Step 2: Days to hours
$$
25,567.5\ \text{days} \times \frac{24\ \text{hours}}{1\ \text{day}} = 613,620\ \text{hours}
$$

Step 3: Hours to minutes
$$
613,620\ \text{hours} \times \frac{60\ \text{minutes}}{1\ \text{hour}} = 36,817,200\ \text{minutes}
$$

Step 4: Minutes to heartbeats
$$
36,817,200\ \text{min} \times \frac{72\ \text{beats}}{1\ \text{min}} = 2,643,778,400\ \text{beats}
$$

✔ Answer: Approximately 2.64 × 10⁹ heartbeats

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8. What volume is occupied by 451 g of mercury? The density of mercury is 13.6 g/mL.

Use:
$$
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
$$

$$
\text{Volume} = \frac{451\ \text{g}}{13.6\ \text{g/mL}} \approx 33.16\ \text{mL}
$$

✔ Answer: 33.16 mL

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✔ Final Answers Summary:

1. 1.2 g
2. 1587.3 g
3. 804.5 km
4. \$31.60
5. 20.25 g
6. 295.6 g
7. 2.64 × 10⁹ beats
8. 33.16 mL

All solutions shown using factor-label method with proper unit cancellation. Make sure to show all steps on your worksheet as instructed!