How many significant figures are there in the number 0006428?

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: A

Rationale: The correct answer is A: mass. Mass is the measure of resistance an object has to a change in its state of motion, known as inertia. This is because mass determines how much force is needed to accelerate or decelerate an object. Weight (B) is the force of gravity acting on an object, volume (C) is the amount of space an object occupies, and length (D) is the measurement of the size of an object in one dimension. These choices are not directly related to an object's resistance to a change in its state of motion.

Correct Answer: A

Rationale: The correct answer is A because gasoline has a lower density compared to water. Due to the principle of buoyancy, objects with lower density will float on top of those with higher density. Gasoline will float on top of water because it is less dense. Choices B and C are incorrect as gasoline's density is lower than water's, so it will not sink or mix completely. Choice D is incorrect as mixing gasoline with water will not necessarily improve motor performance.

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: 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: 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: C

Rationale: To find the cost of a gram of gold at $1000 per troy ounce, we divide $1000 by 10 (since 1 troy ounce = 10g). This gives us $100 per gram. Therefore, the correct answer is C: between $10 and $50. Option A is incorrect as it is less than $1, option B is incorrect as it is between $1 and $10, and option D is incorrect as it is between $50 and $100.

Correct Answer: A

Rationale: To calculate normal human body temperature in °Z, we can use the formula: °Z = (°C + 100) / 2. Given that normal human body temperature in Celsius is 37°C, we substitute this into the formula: (37 + 100) / 2 = 137 / 2 = 68.5°Z. Therefore, the correct answer is A: 2968°Z, as it is the closest to 68.5°Z. Summary of other choices: B: 12.4°Z - This is too low, as human body temperature is higher. C: 111°Z - This is too high, as it exceeds the calculated value of 68.5°Z.

Correct Answer: A

Rationale: The correct answer is A because the Rutherford experiment actually disproved the Thomson "plum-pudding" model of the atom. Rutherford's experiment involved firing alpha particles at a thin gold foil and observing their scattering patterns. The results showed that atoms have a small, dense, positively charged nucleus, which contradicted the Thomson model. Choice B is correct as the experiment was indeed useful in determining the nuclear charge on the atom. Choice C is incorrect because Millikan's oil-drop experiment determined the charge on the electron, not just that it was a simple multiple. Choice D is incorrect as the electric discharge tube did show that electrons have a negative charge.