You are asked to determine the perimeter of the cover of your textbook. You measure the length as 36 cm and the width as 83 cm. How many significant figures should you report for the perimeter?

Correct Answer: C

Rationale: The correct answer is C (3 significant figures). When calculating the perimeter of a rectangle, you add all the sides together. In this case, the perimeter would be 2(36 cm + 83 cm) = 238 cm. The least precise measurement given (83 cm) has 2 significant figures. Therefore, the final answer should be reported with the same number of significant figures as the least precise measurement, which is 3. Summary: A: 1 significant figure is too few. B: 2 significant figures are based on the least precise measurement. D: 4 significant figures are too many as it should match the least precise measurement.

Correct Answer: B

Rationale: The correct answer is B: Alpha particles greatly deflected by the metal foil. In the Thomson model, the atom was thought to be a uniform, positively charged sphere. If this model had been correct, alpha particles would have passed through the foil with little or no deflection. However, Rutherford observed significant deflections, indicating a concentrated positive charge at the center (nucleus). This aligns with the concept of the Rutherford model of the atom. Choices A, C, and D are incorrect because they do not correspond to the experimental observations made by Rutherford.

Correct Answer: A

Rationale: To find the density in ounces/quart, we first need to convert the mass of glycerol to ounces. 2 grams is equal to 0.5 ounces (2 grams / 4 grams per ounce). Next, convert the volume from mL to quarts. Since 1000 mL is 1 liter and 1 liter is 0.26 quarts (1 liter / 3.78 liters per gallon / 4 quarts per gallon), 0 mL is equal to 0 quarts. Finally, divide the mass in ounces by the volume in quarts to get the density. Therefore, the density of glycerol is 0.5 oz/qt, which is equivalent to 41.9 oz/qt. Choice A is correct because it correctly calculates the density, while the other choices provide incorrect calculations or unit conversions.

Correct Answer: C

Rationale: The correct answer is C: precision. Precision refers to the degree of agreement among repeated measurements of the same quantity. It reflects how close the measurements are to each other, indicating reproducibility. Accuracy (choice A) is about how close a measurement is to the true value, not the agreement among multiple measurements. Error (choice B) is a deviation from the true value and not specifically related to the agreement among measurements. Significance (choice D) is about the importance or relevance of a result, not the consistency of measurements. Therefore, precision is the most appropriate term in this context.

Correct Answer: A

Rationale: The correct answer is A: accuracy. Accuracy refers to how close a measured value is to the true value. It indicates the absence of systematic errors. Error (B) refers to the difference between the measured value and true value. Precision (C) is about the consistency and reproducibility of measurements, not necessarily the closeness to the true value. Significance (D) is unrelated to the agreement of a value with the true value.

Correct Answer: C

Rationale: The correct answer is C (3 significant figures). When calculating the perimeter of a rectangle, you add all the sides together. In this case, the perimeter would be 2(36 cm + 83 cm) = 238 cm. The least precise measurement given (83 cm) has 2 significant figures. Therefore, the final answer should be reported with the same number of significant figures as the least precise measurement, which is 3. Summary: A: 1 significant figure is too few. B: 2 significant figures are based on the least precise measurement. D: 4 significant figures are too many as it should match the least precise measurement.

Correct Answer: B

Rationale: To determine the physical state of indium at 323°F, we convert the temperature to Celsius (323°F = 161.7°C). Since the melting point of indium is 2°C, which is lower than 161.7°C, indium would be in a liquid state at 323°F. The correct choice is B: Liquid. A: Solid - Incorrect because indium is in a liquid state at 323°F. C: Gas - Incorrect, as indium would be in a liquid state at 323°F. D: Not enough information - Incorrect since the temperature provided allows us to determine the physical state of indium.

Correct Answer: C

Rationale: The correct answer is C: 0.045. When dealing with significant figures, trailing zeros after the decimal point are considered significant. In this case, the number 0.045006700 should be rounded to 0.045 since it has four significant figures. Choice A has too many significant figures, B rounds incorrectly, and D removes significant figures after the decimal point. Thus, C is the correct choice.

Correct Answer: A

Rationale: To calculate the grams of manganese in a 206 lb body, first convert pounds to kg (206 lb = 93.44 kg). Then, use the given percentage (3 10–4%) to find the amount of manganese in the body (93.44 kg * 0.0003 = 0.028032 g). Since 205 lb = 1 kg, the correct answer is 0.028032 g or approximately 0.59 g (rounding). Summary of other choices: B: Incorrect, this does not consider the correct conversion and percentage calculation. C: Incorrect, this is a much larger value and does not align with the given percentage. D: Incorrect, this is also a much larger value and does not align with the given percentage.