10/22 Practice Problems - Answer Key

Complete Solutions with Work Shown

Category 1 Significant Figures - Answers

Problem 1

How many significant figures are in the following measurement: 0.00450 m

Answer: 3 significant figures
Explanation: Leading zeros are not significant. The digits 4, 5, and the trailing 0 are all significant. The trailing zero is significant because it comes after the decimal point and after non-zero digits.

Problem 2

Perform the following calculation with correct significant figures: \(12.3 + 4.56 + 0.789\)

Answer: 17.6
Work: 12.3 (1 decimal place) + 4.56 (2 decimal places) + 0.789 (3 decimal places) ------ 17.649 Round to 1 decimal place (least precise): 17.6

Problem 3

Perform the following calculation with correct significant figures: \(8.314 \times 2.5\)

Answer: 21
Work: 8.314 has 4 sig figs 2.5 has 2 sig figs 8.314 × 2.5 = 20.785 Round to 2 sig figs (least amount): 21

Problem 4

How many significant figures are in: 5,280 ft (where the zero is NOT a placeholder)?

Answer: 4 significant figures
Explanation: Since the problem states the zero is NOT a placeholder, all four digits (5, 2, 8, 0) are significant.

Problem 5

Perform the following calculation with correct significant figures: \(\frac{45.6}{1.2}\)

Answer: 38
Work: 45.6 has 3 sig figs 1.2 has 2 sig figs 45.6 ÷ 1.2 = 38 Result already has 2 sig figs (least amount): 38

Category 2 Scientific Notation - Answers

Problem 6

Convert to scientific notation with 3 significant figures: 0.000845

Answer: \(8.45 \times 10^{-4}\)
Work: Move decimal 4 places to the right: 0.000845 → 8.45 Count moves: 4 places = exponent of -4 Keep 3 sig figs: 8.45 × 10⁻⁴

Problem 7

Convert to scientific notation with 2 significant figures: 67,000

Answer: \(6.7 \times 10^{4}\)
Work: Move decimal 4 places to the left: 67,000 → 6.7 Count moves: 4 places = exponent of 4 Keep 2 sig figs: 6.7 × 10⁴

Problem 8

Convert from scientific notation to standard form: \(3.45 \times 10^{-4}\)

Answer: 0.000345
Work: Exponent is -4, so move decimal 4 places to the LEFT 3.45 → 0.000345

Problem 9

Convert from scientific notation to standard form: \(9.2 \times 10^{6}\)

Answer: 9,200,000
Work: Exponent is 6, so move decimal 6 places to the RIGHT 9.2 → 9,200,000

Problem 10

Convert to scientific notation with 4 significant figures: 1,234,000

Answer: \(1.234 \times 10^{6}\)
Work: Move decimal 6 places to the left: 1,234,000 → 1.234 Count moves: 6 places = exponent of 6 Keep 4 sig figs: 1.234 × 10⁶

Category 3 Single-Step Unit Conversions - Answers

Problem 11

Convert 15 feet to inches. (1 ft = 12 in)

Answer: 180 inches
\[15 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} = 180 \text{ in}\]

Problem 12

Convert 3.5 kilograms to grams. (1 kg = 1000 g)

Answer: 3,500 grams
\[3.5 \text{ kg} \times \frac{1000 \text{ g}}{1 \text{ kg}} = 3500 \text{ g}\]

Problem 13

Convert 250 centimeters to meters. (1 m = 100 cm)

Answer: 2.5 meters
\[250 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 2.5 \text{ m}\]

Problem 14

Convert 4 gallons to quarts. (1 gal = 4 qt)

Answer: 16 quarts
\[4 \text{ gal} \times \frac{4 \text{ qt}}{1 \text{ gal}} = 16 \text{ qt}\]

Problem 15

Convert 96 ounces to pounds. (1 lb = 16 oz)

Answer: 6 pounds
\[96 \text{ oz} \times \frac{1 \text{ lb}}{16 \text{ oz}} = 6 \text{ lb}\]

Category 4 Multi-Step Unit Conversions - Answers

Problem 16

Convert 2 miles to inches. (1 mile = 5280 ft, 1 ft = 12 in)

Answer: 126,720 inches
\[2 \cancel{\text{ miles}} \times \frac{5280 \cancel{\text{ ft}}}{1 \cancel{\text{ mile}}} \times \frac{12 \text{ in}}{1 \cancel{\text{ ft}}} = 126{,}720 \text{ in}\]

Problem 17

Convert 5 pounds to grams. (1 lb = 16 oz, 1 oz = 28.35 g)

Answer: 2,268 grams
\[5 \cancel{\text{ lb}} \times \frac{16 \cancel{\text{ oz}}}{1 \cancel{\text{ lb}}} \times \frac{28.35 \text{ g}}{1 \cancel{\text{ oz}}} = 2{,}268 \text{ g}\]

Problem 18

Convert 3 gallons to cups. (1 gal = 4 qt, 1 qt = 2 pt, 1 pt = 2 cups)

Answer: 48 cups
\[3 \cancel{\text{ gal}} \times \frac{4 \cancel{\text{ qt}}}{1 \cancel{\text{ gal}}} \times \frac{2 \cancel{\text{ pt}}}{1 \cancel{\text{ qt}}} \times \frac{2 \text{ cups}}{1 \cancel{\text{ pt}}} = 48 \text{ cups}\]

Problem 19

Convert 10,000 centimeters to miles. (1 m = 100 cm, 1 m = 3.2808 ft, 1 mile = 5280 ft)

Answer: 0.0621 miles
\[10{,}000 \cancel{\text{ cm}} \times \frac{1 \cancel{\text{ m}}}{100 \cancel{\text{ cm}}} \times \frac{3.2808 \cancel{\text{ ft}}}{1 \cancel{\text{ m}}} \times \frac{1 \text{ mile}}{5280 \cancel{\text{ ft}}} = 0.0621 \text{ miles}\]

Problem 20

Convert 72 fluid ounces to liters. (1 fl oz = 29.575 mL, 1 L = 1000 mL)

Answer: 2.13 liters
\[72 \cancel{\text{ fl oz}} \times \frac{29.575 \cancel{\text{ mL}}}{1 \cancel{\text{ fl oz}}} \times \frac{1 \text{ L}}{1000 \cancel{\text{ mL}}} = 2.1294 \text{ L} \approx 2.13 \text{ L}\]

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