How Many Significant Figures Should Be Reported in Lab Calculations?

[alphaj]

Homework Statement

I'm having difficulties figuring out how many significant figures to report for several caluclations in my lab report. As it is a report, there are no specific problem statements.

Homework Equations

No equations, but there is a rule I was told: when dividing/multiplying I was told to use the "least precise value determines the number" of sig figs.

The Attempt at a Solution

For example: One of my calculations for percent error is as follows |30mL-22.7068mL|/22.7068(g/mol) * (100) = 32.1190%.

I know that: 30 is 1 sigfig; 22.7068 is 6 sigfigs; 100 is 1 sigfig.

Therefore, according to the rule, I believe that the least precise value is 1 significant figure. So, should I report this percent with 1 significant figure? I'm not sure how I would do that...round down perhaps to 30%?

Thank you!

 

[Borek]

How was the 30 measured? Despite ending with zero it can have more than 1 sigfig.

 

[alphaj]

@Borek
The 30mL comes from the amount we measured out in glassware. So, for example, we measured out 30mL of water in a 125mL beaker. It was not a calculated value.

 

[Borek]

It doesn't answer "how" it was measured. As you have checked (info from your other thread) volumes can be measured quite accurately with graduated pipettes, then the volume is not 30 mL but something like 30.00 mL (see what I did with sigfigs of zero here?).

Note, that sigfigs are a poor man's approach, we have much better, and not much more difficult ways of expressing accuracy of the numbers. Sadly, sigfigs often dominate in chemistry and are even by some teachers treated as if they were the most important thing in the world

Also, compare http://www.titrations.info/pipette-burette

 

[alphaj]

@Borek I see what you mean. When we were pouring out water into our glassware, we were aiming for 30.0mL every time (haha, even arduously adding drops of water in/out to get the meniscus as close to the 30mL line as possible). Of course, there is human error--calculated volume results show us that we never did seem to get 30mL exactly when we poured (this was the purpose of the lab, though). If I assumed we poured 30.0mL (3 sigfigs), would that change my sigfigs for percent error to 3 (e.g. 32.1%)? Or should I not ignore that 100 we multiply by to get a percent (which if I did not ignore it, it would bring my least precise value back to 1 sigfig and thus, 30% error)?

Thank you for your help, by the way. In other classes we did not focus on sigfigs at all, but in this lab, the professor gave us a small presentation about sigfigs and stresses on the report that we must have every value calculated in the appropriate sigfig, depending on the mathematical operations used to produce the values.

Thank you for the link--that lab is similar to what we did! We also had a volumetric pipette which seemed to be the easiest to use and the most precise and accurate in obtaining volumes.

 

[Borek]

100 in 100% is an exact number, so it is accurate to an infinite number of sigfigs.

Not sure whether the volume should be treated as 30 or 30.0 - I would use 2 sigfigs, but I would not care if a student would supply 3 sigfigs in the answer. 4 would be excessive.

 

[willem2]

You should really know what the accuracy is of measuring 30 mL. If it isn't listed somewhere you should test it. Maybe weighing your water sample can be done more accurately? What would be the accuracy of the height of the meniscus? might be 0.1 mm. How much fluid does that represent?
Another problem is that there is also a subtraction. Even if you can use 3 significant figures for 30.0 ml which would mean 30±0.05, after you subtract 22.7068 mL from it, 7.2932 ±0.05 mL remain, and that really doesn't deserve more than 2 significant figures.

 

[alphaj]

Thanks to all!