Q: Convert $$45000\ \mathrm{mg} to SI $$base units using scientific notation.

$$4.5 \times 10$$^{-2}$$\ \mathrm{kg}$$

Question 1

Which of the following is a derived SI unit, and what physical quantity does it represent?

Accepted Answer

$$\mathrm{kg\ m$$^{-3}$$}$$, density

Question 2

A student measures the length of a rod as $$22.5\ \mathrm{mm} \pm 0.5\ \mathrm{mm}. $$Which statement best describes the uncertainty?

Accepted Answer

The uncertainty is absolute and reflects the limit of the measuring instrument.

Question 3

Which of the following best describes a systematic error?

Accepted Answer

A consistent offset in all measurements due to a miscalibrated instrument.

Question 4

Convert $$45000\ \mathrm{mg} to SI $$base units using scientific notation.

Accepted Answer

$$4.5 	imes 10$$^{-2}$$\ \mathrm{kg}$$

Question 5

When adding $$(4.25 \pm 0.05)\ \mathrm{m}$$ and $$(1.80 \pm 0.05)\ \mathrm{m}$$, what is the correct way to express the perimeter and its uncertainty?

Accepted Answer

$$6.05 \pm 0.10\ \mathrm{m}$$

Question 6

A measurement is reported as $$10 \pm 1\ \mathrm{ms$$^{-2}$$}$$ for gravity. Which conclusion is most plausible?

Accepted Answer

The measurement is imprecise but may be accurate.

Question 7

Which of the following is NOT a rule for significant figures?

Accepted Answer

Leading zeros are significant.

Question 8

A student calculates the area of a rectangle as $$(4.25 \pm 0.05)\ \mathrm{m} 	imes (1.80 \pm 0.05)\ \mathrm{m}. $$What is the area and its uncertainty?

Accepted Answer

$$(7.7 \pm 0.3)\ \mathrm{m}^2$$

Question 9

Which SI prefix corresponds to $$10^{-9}$$?

Accepted Answer

nano (n)

Question 10

When multiplying or dividing measured quantities, how should uncertainties be combined?

Accepted Answer

Add the relative uncertainties.

Question 11

A set of repeated measurements yields a mean of $$22.52\ \mathrm{mm}$$ and a standard deviation of $$0.12\ \mathrm{mm}. $$What is the standard error if $$N = 6$$?

Accepted Answer

$$0.02\ \mathrm{mm}$$

Question 12

Which of the following best describes the difference between precision and accuracy?

Accepted Answer

Precision is the reproducibility of measurements; accuracy is how close measurements are to the true value.

Question 13

A graph of mass (y-axis) versus volume (x-axis) for water gives a straight line. What does the gradient represent?

Accepted Answer

The density of water

Question 14

Which of the following is an example of a random error?

Accepted Answer

Fluctuations in electronic noise during measurement

Question 15

If the uncertainty in the gradient of a best-fit line is $$\Delta m = |m - m'|$$, what does $$m'$$ represent?

Accepted Answer

The gradient of the uncertainty line

Question 16

Which of the following is the correct way to express $$0.000 000 000 05\ \mathrm{m} in $$scientific notation?

Accepted Answer

$$5 	imes 10$$^{-11}$$\ \mathrm{m}$$

Question 17

Which of the following is NOT a fundamental SI unit?

Accepted Answer

$$\mathrm{J} ($$joule)

Question 18

A student records a measurement as $$22.517\ \mathrm{mm} \pm 0.5\ \mathrm{mm}. $$What is wrong with this expression?

Accepted Answer

The measurement is quoted with more precision than the uncertainty allows.

Question 19

Which of the following best describes the scientific method as depicted in the flowchart?

Accepted Answer

It is an iterative process involving hypothesis, experimentation, analysis, and peer review.

Measurement and Uncertainty: Foundations for Physics

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