# Should durations of time be considered to determine final significant figures of answer?

In preparation for AP Chemistry this upcoming semester I've been assigned a number of challenge problems. One of them is as following:

Suppose that polluted air has carbon monoxide $$(\ce{CO})$$ levels of $$\pu{15.0 ppm}$$. An average human inhales about $$\pu{0.50 L}$$ of air per breath and takes 20 breaths per minute. If the density of carbon monoxide is $$\pu{1.2 g L=1}$$, How many milligrams (mg) of carbon monoxide does an average person inhale during an $$\pu{8 hour}$$ period of time breathing polluted air? (Hint: $$\pu{15.0 ppm} \ \ce{CO} = \pu{15.0L} \ \ce{CO}$$ per $$\pu{1.0E6 L}$$ of air.)

I've set up the following stoichiometry to solve this problem:

$$\frac{\pu{8 h}}{1} \times \frac{\pu{60 min}}{\pu{1 h}} \times \frac{\pu{20 breaths}}{\pu{1 min}} \times \frac{\pu{0.50 L} \text{ air}}{\pu{1 breath}} \times \frac{\pu{15.0 L} \ \ce{CO}}{\pu{1.0E6 L} \text{ air}} \times \frac{\pu{1.2 g} \ \ce{CO}}{\pu{1 L} \ \ce{CO}} \times \frac{\pu{1000 mg} \ \ce{CO}}{\pu{1 g} \ \ce{CO}}\\ = \pu{86 mg} \ \ce{CO}$$

My question is regarding the number of significant figures for the solution, which I calculated as $86 g CO. Initially I assumed two sig-figs were to be used because of the value 1.2 g/L, but have since noticed that the given duration (8 hours) only has one sig-fig. So my questions breaks down to: are durations considered in the calculation of sig-figs? If so, would the correct answer be 90 mg CO as opposed to 86 mg CO? TLDR; When calculating sig-figs, do you consider the number of significant-figures for all given values, including durations, or just physical quantities? • The question isn't what units it's measured in (i.e. whether it's a time or a length or whatever), it's whether it's a quantity that's measured. The point is that something you measure will have an uncertainty, which is (crudely) reflected in terms of significant figures. I do think this question is really quite contrived, though, because arguably 20 is a measured quantity (I don't think humans take exactly 20 breaths per minute, not even on average, or else we'd have no need for clocks). Aug 27, 2022 at 1:26 • The$8$hours is an integer so its value is exact, as a real number it would be$8.000000\cdots\$ so you use other numbers to determine the sig figs. Aug 27, 2022 at 8:32
• The question seems to be the ability to manipulate units and possibly to figure out what PPM really means not significant figures tho they matter. All the values are approximated o.5 L is low but might approximate exchange volumes, breaths are high error about -3 to +1 so lets say 10%. The error in time is interesting 7 of the hours are exact the eighth or start and stop are what affects accuracy, that is not important; the only thing that affects the accuracy is the volume exchanged and the measurement of breaths. This question is really an exercise in the folly of extrapolation. explain that Aug 29, 2022 at 3:06

[OP] When calculating sig-figs, do you consider the number of significant-figures for all given values, including durations, or just physical quantities?

You consider all physical quantities including time or duration. Time has the unit of one of the base SI units, it is a quantity just as mass, volume and amount of substance.

[OP] Initially I assumed two sig-figs were to be used because of the value 1.2g/L, but have since noticed that the given duration (8 hours) only has one sig-fig.

Two significant figures for the result is reasonable.

There is ambiguity with numbers that don't have a decimal point (i.e. integers). Take the 20 breaths per minute. You would count to twenty, it can't be 20.1 or 19.9 (unless you take a population average or a personal average). However, without decimal point you could make the argument that 20 only has one significant figure. The 1 g in the conversion factor is intended as exact. I would think the 8 in "8 hours" is also intended as exact rather than 7 to 9 hours.

To resolve the ambiguity, you could write $$\pu{2.0e1}$$ instead of 20 breaths if the intent is to give two significant figures, or $$\pu{0.8e1 h}$$ if the intent is to show one significant figure for the duration.

In the absence of these explicit notations, you have to try to use common sense and hope that the person who writes the answer key also uses common sense.

• Per a source: "Normal respiration rates for an adult person at rest range from 12 to 16 breaths per minute" and children likely more, and given the earth population distribution and where they live, sea level or higher, the value stated for breaths per minute is not likely precise. Link: hopkinsmedicine.org/health/conditions-and-diseases/…. Aug 28, 2022 at 13:18