Q: If the elevation is $$8368$$ feet, and you want to convert it to kilometers, which of the following conversion factors should you use?

$$1~\text{ft} = 0.0003048~\text{km}$$

Question 1

Refer to the image of the Snowmass Village sign. Which of the following best explains why it is incorrect to add the numbers '1967', '8368', and '1822' to get the 'TOTAL' of '12,157' as shown on the sign?

Accepted Answer

Because the numbers represent different physical quantities and cannot be meaningfully added together.

Question 2

Which of the following is the correct number of significant digits in the value '8368' as shown for the elevation on the sign?

Accepted Answer

4

Question 3

If the population of Snowmass Village is reported as '1.822 	imes $$10^3$$', how many significant digits does this value have?

Accepted Answer

4

Question 4

Suppose the elevation is measured as $$8368$$ feet. Convert this elevation to meters, given $$1~	ext{ft} = 0.3048~	ext{m}. $$Express your answer to the correct number of significant digits.

Accepted Answer

$$2551~	ext{m}$$

Question 5

Which of the following best describes why the number '1967' (year established) should not be included in a calculation of the village's total population or elevation?

Accepted Answer

Because '1967' is a year and not a physical quantity with compatible units.

Question 6

If the population increases by $$2.5\%$$ per year, what will the population be after 5 years? Use the initial population of $$1822$$ and express your answer to the correct number of significant digits.

Accepted Answer

$$2060$$

Question 7

Which of the following is the correct way to express the population '1822' in scientific notation with the correct number of significant digits?

Accepted Answer

$$1.822 	imes 10^3$

Question 8

If the elevation is $$8368$$ feet, and you want to convert it to kilometers, which of the following conversion factors should you use?

Accepted Answer

$$1~	ext{ft} = 0.0003048~	ext{km}$$

Question 9

Which of the following best explains why the sum '12,157' on the sign is not meaningful in a scientific context?

Accepted Answer

Because it adds quantities with different units and meanings, violating the rules of dimensional analysis.

Question 10

If the population is $$1822$$ and the elevation is $$8368$$ feet, what is the correct way to report the sum of these two values?

Accepted Answer

It is not correct to add these values because they have different units and meanings.

Units, Significant Digits, and Scientific Notation – Study Notes

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