The amount of uncertainty in a measured quantity is determined by:

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.

Correct Answer: A

Rationale: The correct answer is A because a quantitative observation must contain both a number and a unit to provide a specific measurement. This ensures the observation is precise and can be accurately communicated. The other choices are incorrect because B is vague, C is not a requirement for quantitative observations, and D is not true as quantitative observations can also be obtained through measurements, not just experimentation.

Correct Answer: D

Rationale: The correct answer is D: 4. Significant figures are non-zero digits and zeros between them. In this case, only digits 6, 4, 2, and 8 are non-zero, making them all significant. Zeros before the first non-zero digit are not significant, so the zeros before 6 are not counted. Hence, there are 4 significant figures in the number 0006428. Choice A (7) is incorrect because it includes all digits, including the leading zeros, which are not significant. Choice B (3) is incorrect because it only considers the non-zero digits, excluding the zeros between them. Choice C (8) is incorrect because it counts all digits including leading zeros, which are not significant.

Correct Answer: D

Rationale: The correct answer is D: kilometer. A kilometer is a metric unit for length because it is used to measure long distances. In the metric system, length is typically measured in meters, and a kilometer is equal to 1000 meters. This makes it a suitable unit for measuring larger distances efficiently. Explanation for incorrect choices: A: Gram is a unit of mass, not length. B: Milliliter is a unit of volume, not length. C: Yard is a unit of length, but it is not a metric unit. The metric system uses meters and its derivatives for length measurements.

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.

Correct Answer: C

Rationale: To convert grams to milligrams, you multiply by 1000. So, 2751.4 g * 1000 = 2751.4 mg. Therefore, choice C (275.14 mg) is correct. Choice A is incorrect as it incorrectly moves the decimal point. Choice B is incorrect as it doesn't account for the conversion factor. Choice D is incorrect as it incorrectly uses scientific notation.

Correct Answer: A

Rationale: To convert Celsius to Fahrenheit, use the formula: °F = (°C × 9/5) + 32. Plugging in 391°C, we get: °F = (391 × 9/5) + 32 = 706.2 + 32 = 738.2. Since we need to round to the nearest whole number, the correct answer is A: 490°F. Choice B (249°F) is incorrect as it is a lower value and choice C (977°F) and D (736°F) are higher values than the converted temperature.

Correct Answer: D

Rationale: The correct answer is D: natural law. A natural law describes a consistent pattern or behavior in the natural world, such as the conservation of mass in a chemical reaction. This principle states that the total mass of materials before and after a chemical change remains constant. Observations (A) are factual statements based on data, measurements (B) involve quantifying properties, and theories (C) are explanations based on evidence, but none specifically address the consistent behavior of mass in chemical changes as a natural law does.

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.