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: C

Rationale: The correct answer is C: 6.7 x 10^8 mi/h. To calculate the speed of the electron in miles per hour, we first convert the speed of light from m/s to mi/h using the conversion factor 1 km = 6214 mi. The speed of light is approximately 6.71 x 10^8 mi/h. Since the electron is at 93% of the speed of light, we multiply the speed of light by 0.93 to get the speed of the electron, which is approximately 6.25 x 10^8 mi/h. The closest choice is C: 6.7 x 10^8 mi/h. Choice A: 2.8 x 10^8 mi/h - This is incorrect as it is too low compared to the calculated speed. Choice B: 6.2 x 10^11 mi/h - This is incorrect as it is too high compared to the calculated speed. Choice

Correct Answer: B

Rationale: The formula for water is H₂O, indicating there are two hydrogen atoms and one oxygen atom per molecule. This is because the subscript 2 in H₂ represents two hydrogen atoms, and O represents one oxygen atom. Therefore, choice B is correct. Choices A, C, and D are incorrect because they do not accurately represent the composition of water molecules. Choice A suggests twice as much mass of hydrogen than oxygen, which is not true. Choice C suggests twice as much mass of oxygen than hydrogen, which is also incorrect. Choice D implies there are two oxygen atoms in a water molecule, which is inaccurate.

Correct Answer: C

Rationale: To find the density of liquid mercury in units of g/cm³, we need to convert the density from g/mL to g/cm³. The conversion factor is 1 mL = 1 cm³. Given the density of mercury as 6 g/mL, it is equivalent to 6 g/cm³. Therefore, the correct answer is 1.01 x 10¹ g/cm³ (choice C). Choice A: 1.57 x 10² is too large for the density of liquid mercury. Choice B: 4.91 x 10¹ is incorrect as it does not match the calculated density. Choice D: 7.62 x 10² is significantly higher than the actual density of liquid mercury.

Correct Answer: C

Rationale: The correct answer is C: 19 p, 20 n, 19 e. K+ has an atomic number of 19, indicating 19 protons. Since it is a potassium ion with a +1 charge, it lost one electron, giving it 19 electrons instead of the usual 20. The number of neutrons is found by subtracting the atomic number from the mass number (39 for potassium) to get 20 neutrons. Option A is incorrect due to the incorrect number of electrons. Option B has the incorrect number of protons. Option D has the incorrect number of electrons.

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: D

Rationale: The correct answer is D because the statement that the number of protons and neutrons is always the same in a neutral atom is false. In a neutral atom, the number of protons equals the number of electrons, not the number of neutrons. Neutrons are not always equal to the number of protons. A: An atom is mostly empty space - Correct. This is true because the nucleus is very tiny compared to the overall size of the atom. B: Almost all of the mass of the atom is concentrated in the nucleus - Correct. This is true because protons and neutrons have much more mass than electrons. C: The protons and neutrons in the nucleus are very tightly packed - Correct. This is true because protons and neutrons are densely packed within the nucleus.

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: 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.