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Convert 4 mi to km. (1 m = 094 yd, 1 mi = 1760 yd)
- A. 6.50 101 km
- B. 3.69 101 km
- C. 9.56 107 km
- D. 5.43 101 km
Correct Answer: B
Rationale: To convert 4 mi to km, first convert miles to yards: 4 mi * 1760 yd/mi = 7040 yd. Then convert yards to meters: 7040 yd * 0.9144 m/yd = 6437.216 m. Finally, convert meters to kilometers: 6437.216 m/1000 m/km = 6.437216 km. Rounding to three significant figures, the answer is 3.69 x 10^1 km (B). Other choices are incorrect because they do not correctly convert miles to kilometers or have calculation errors.
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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?
- A. 1
- B. 2
- C. 3
- D. 4
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.
Which of the following metric relationships is incorrect?
- A. 1 microliter = 10–6 liters
- B. 1 gram = 103 kilograms
- C. 103 milliliters = 1 liter
- D. 1 gram = 102 centigrams
Correct Answer: B
Rationale: The correct answer is B: 1 gram = 10^3 kilograms. This is incorrect because 1 kilogram is equal to 1000 grams, not 100 grams. A is correct as 1 microliter is indeed 10^-6 liters. C is correct as 10^3 milliliters equals 1 liter. D is correct as 1 gram is equal to 10^2 centigrams. The incorrect relationship in choice B violates the metric system conversion factor of 1 kilogram being equal to 1000 grams.
An ion is formed
- A. By either adding or subtracting protons from the atom.
- B. By either adding or subtracting electrons from the atom
- C. By either adding or subtracting neutrons from the atom.
- D. All of the above are true.
Correct Answer: A
Rationale: The correct answer is A: By either adding or subtracting protons from the atom. An ion is formed when an atom gains or loses electrons, leading to an unequal number of protons and electrons. Protons determine the atom's identity, so changing the number of protons would result in a different element. This process results in the formation of ions with a positive charge if protons are added or a negative charge if protons are subtracted. Choices B and C are incorrect because adding or subtracting electrons or neutrons does not change the fundamental identity of the atom, only its charge or mass. Choice D is incorrect as not all options are true for ion formation.
The degree of agreement among several measurements of the same quantity is called . It reflects the reproducibility of a given type of measurement.
- A. accuracy
- B. error
- C. precision
- D. significance
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.
A scientist obtains the number 0.045006700 on a calculator. If this number
actually has four significant figures, how should it be written?
- A. 0.4567
- B. 0.4501
- C. 0.045
- D. 0.045
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.