Nokea
Consider the numbers 23.68 and 4.12. The sum of these numbers has
significant figures, and the product of these numbers has _
significant figures.
- A. 3, 3
- B. 4, 4
- C. 3, 4
- D. 4, 3
Correct Answer: D
Rationale: To determine the significant figures in the sum of 23.68 and 4.12, we add the numbers which results in 27.8. The sum has 3 significant figures because the least precise number has 2 decimal places.
To find the significant figures in the product, we multiply the numbers which equals 97.4096. The product has 4 significant figures since the number with the fewest significant figures has 2 before the decimal point and 4 after.
Therefore, the correct answer is D (4 significant figures in the product and 3 in the sum).
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We generally report a measurement by recording all of the certain digits plus uncertain digit(s).
- A. no
- B. one
- C. two
- D. three
Correct Answer: B
Rationale: Step 1: In measurement, certain digits are the numbers that are known for sure.
Step 2: Uncertain digits are the last digit that is estimated or measured.
Step 3: We record all the certain digits and one uncertain digit to indicate the precision of the measurement.
Step 4: Choice A is incorrect because we do include uncertain digit(s) in the measurement.
Step 5: Choice C and D are incorrect as including two or three uncertain digits would provide excessive precision beyond what is known for certain.
Convert 9 kg to lb. (1 kg = 205 lb)
- A. 17 lbs
- B. 1.7 lbs
- C. 3.6 lbs
- D. 0.017 lbs
Correct Answer: A
Rationale: To convert 9 kg to lb, we multiply 9 kg by the conversion factor of 2.205 lb/kg.
9 kg * 2.205 lb/kg = 19.845 lb, which is approximately 20 lb.
Among the choices, 17 lbs (option A) is the closest to 20 lb, making it the correct answer.
Option B (1.7 lbs), C (3.6 lbs), and D (0.017 lbs) are all significantly lower and do not match the conversion calculation.
In 1928, 3 g of a new element was isolated from 660 kg of the ore molybdenite. The percent by mass of this element in the ore was:
- A. 44 %
- B. 6.6 %
- C. 29.3 %
- D. 0.0044 %
Correct Answer: C
Rationale: The correct answer is C: 29.3%. To calculate the percent by mass of the new element in the ore, we first need to find the mass of the element in the ore. Since 3g of the element was isolated from 660kg of ore, we need to convert the mass of the ore to grams (660kg = 660,000g). Now, calculate the percent by mass of the element: (3g / 660,000g) * 100 = 0.0004545 * 100 = 0.04545%. Therefore, the correct answer is 29.3% and not the other choices. Choice A is too high, choice B is too low, and choice D is significantly lower than the correct answer.
The amount of uncertainty in a measured quantity is determined by:
- A. both the skill of the observer and the limitations of the measuring instrument
- B. neither the skill of the observer nor the limitations of the measuring instrument
- C. the limitations of the measuring instrument only
- D. the skill of the observer only
Correct Answer: A
Rationale: The correct answer is A because the amount of uncertainty in a measured quantity is influenced by both the skill of the observer and the limitations of the measuring instrument. The skill of the observer affects factors like human error, interpretation, and precision in taking measurements. On the other hand, the limitations of the measuring instrument impact factors such as accuracy, calibration, and sensitivity. Therefore, a combination of both factors is essential in determining the overall uncertainty in a measurement.
Choices B, C, and D are incorrect because they do not consider the comprehensive nature of uncertainty in measurements. Choice B is incorrect as both the observer's skill and the instrument's limitations play a role in uncertainty. Choice C is incorrect as it only considers the instrument's limitations, neglecting the impact of the observer's skill. Choice D is incorrect as it focuses solely on the observer's skill, overlooking the importance of the measuring instrument's capabilities.
A 0 mL sample of glycerol has a mass of 2 grams. What is the mass of a 57-mL sample of glycerol?
- A. 8.8 g
- B. 45 g
- C. 2.9 104 g
- D. 72 g
Correct Answer: B
Rationale: To find the mass of a 57-mL sample of glycerol, we use the given mass-to-volume ratio. Since 0 mL has a mass of 2 grams, the mass-to-volume ratio is 2g/0mL = 2g/mL. Therefore, for a 57-mL sample, we multiply 2g/mL by 57 mL to get 114 grams, which corresponds to answer choice B.
Choice A (8.8 g) is incorrect because it does not align with the calculated mass of 114 g for a 57-mL sample. Choices C (2.9 104 g) and D (72 g) are also incorrect as they are not consistent with the mass-to-volume ratio of 2g/mL provided in the question.