Q: A cube of gold has a side length of $$0.750 \ \mathrm{m}. If $$the density of gold is $$19.3 \ \mathrm{g/cm}^3$$, what is the mass of the cube in kilograms? (Use the correct number of significant figures.)

$$8.1 \times 10^5$ \ \mathrm{kg}$$

Q: A cube of silver has a side length of $$0.85 \ \mathrm{m}. $$The density of silver is $$10.5 \ \mathrm{g/cm}^3. $$What is the mass of the cube in kilograms, using the correct number of significant figures?

$$6.4 \times 10^5$ \ \mathrm{kg}$$

Question 1

A laboratory technician measures the mass of a sample as 12.3 g and its volume as 4.56 mL. What is the density of the sample, reported with the correct number of significant figures?

Accepted Answer

$$2.70 g/mL$

Question 2

Which of the following best explains why conversion factors (such as $$1 \ \mathrm{m} = 100 \ \mathrm{cm}) $$are considered to have an infinite number of significant figures?

Accepted Answer

Because they are defined values, not measured values.

Question 3

A cube of gold has a side length of $$0.750 \ \mathrm{m}. If $$the density of gold is $$19.3 \ \mathrm{g/cm}^3$$, what is the mass of the cube in kilograms? (Use the correct number of significant figures.)

Accepted Answer

$$8.1 	imes 10^5$ \ \mathrm{kg}$$

Question 4

When adding $$0.378 \ \mathrm{mL}$$, $$42.3 \ \mathrm{mL}$$, and subtracting $$1.5833 \ \mathrm{mL}$$, what is the correctly reported result?

Accepted Answer

$$41.1 \ \mathrm{mL}$$

Question 5

A car uses gasoline at a rate of $$16.0 \ \mathrm{L}/100 \ \mathrm{km}. $$Convert this to miles per gallon (mpg). ($$1 \ \mathrm{mi} = 1.609 \ \mathrm{km}$$, $$1 \ \mathrm{gal} = 3.785 \ \mathrm{L}).$$

Accepted Answer

$$14.7 \ \mathrm{mpg}$$

Question 6

Which of the following statements about significant figures is TRUE?

Accepted Answer

When multiplying or dividing, the result should have as many significant figures as the value with the fewest significant figures.

Question 7

Calculate $$365 \div 12$$ and report the answer with the correct number of significant figures.

Accepted Answer

$$30$$

Question 8

A student multiplies $$0.12 by$$ $$4. $$What is the answer with the correct number of significant figures?

Accepted Answer

$$0.5$$

Question 9

Which of the following best describes how to report the result of an addition or subtraction calculation?

Accepted Answer

Report to the same number of decimal places as the value with the fewest decimal places.

Question 10

A calculation involves $$5.00 	imes 2.000 + 0.65. $$What is the correctly reported answer?

Accepted Answer

$$10.7$$

Question 11

Why is it important to identify the number of significant figures in measured values before performing calculations?

Accepted Answer

To ensure the result does not imply greater precision than the measurements allow.

Question 12

A student records the following masses: $$170.4 \ \mathrm{g}$$, $$0.07 \ \mathrm{g}$$, and $$0.47 \ \mathrm{g}. $$What is the sum, reported with the correct number of significant figures?

Accepted Answer

$$170.5 \ \mathrm{g}$$

Question 13

Which of the following is the correct conversion for $$1 \ \mathrm{m}^3 to$$ $$\mathrm{cm}^3$$?

Accepted Answer

$$1 \ \mathrm{m}^3 = 10^6$ \ \mathrm{cm}^3$$

Question 14

A cube of silver has a side length of $$0.85 \ \mathrm{m}. $$The density of silver is $$10.5 \ \mathrm{g/cm}^3. $$What is the mass of the cube in kilograms, using the correct number of significant figures?

Accepted Answer

$$6.4 	imes 10^5$ \ \mathrm{kg}$$

Question 15

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

Accepted Answer

When multiplying or dividing, the result should have the same number of significant figures as the value with the most significant figures.

Question 16

A student calculates $$43 	imes 10^3$ using values with two and three significant figures. How many significant figures should the answer have?

Accepted Answer

Two

Question 17

Which of the following best describes the effect of performing calculations on the number of significant figures in a result?

Accepted Answer

Calculations do not increase the number of significant figures.

Question 18

A student adds $$16.421 g $$and $$0.050 g. $$What is the sum, reported with the correct number of decimal places?

Accepted Answer

$$16.47 g$$

Question 19

Which of the following is a real-world consequence of not following significant figure rules in scientific reporting?

Accepted Answer

It can lead to overestimating the precision of results, potentially causing errors in engineering or medical applications.

Rounding Numbers, Significant Figures, and Unit Conversion in Chemistry

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