You measure water in two containers: a 10-mL graduated cylinder with marks at every mL, and a 1-mL pipet marked at every 1 mL. If you have some water in each of the containers and add them together, to what decimal place could you report the total volume of water?

Correct Answer: C

Rationale: The correct answer is C: 1 mL. When adding volumes measured in different containers, you should report the result to the least precise measurement scale, which is the 1 mL pipet in this case. The graduated cylinder measures to the nearest mL, so the total volume should be rounded to the nearest whole mL. Reporting to a decimal place of 0.01 mL or 0.1 mL would imply a level of precision greater than what the equipment can provide. Choice D is incorrect as it exceeds the maximum volume capacity of the containers and is not relevant to the precision of the 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: 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).

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: 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.