# Significant figures in chemistry?

• alphaj
In summary, the student is having difficulty figuring out how many significant figures to report for a calculation in a lab report. He was told to use the "least precise value determines the number" of sigfigs, but is not sure how to do this. He also has to subtract a value and is unsure how to report the result with 1 or 3 significant figures.
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!

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

@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.

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

@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.

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.

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.

Thanks to all!

## 1. What are significant figures in chemistry?

Significant figures, also known as significant digits, are the digits in a numerical value that represent the precision or accuracy of a measurement. In chemistry, significant figures are used to indicate the level of certainty in a measurement or calculation.

## 2. How do you determine the number of significant figures in a measurement?

To determine the number of significant figures in a measurement, you must first identify the certain digits (non-zero digits) and the uncertain digit (the last digit that is estimated or measured). All certain digits and the uncertain digit are considered significant, and any leading zeros are not significant.

## 3. Why are significant figures important in chemistry?

Significant figures are important in chemistry because they help to convey the accuracy and precision of measurements and calculations. This is crucial in scientific experiments and analyses, as even small variations in significant figures can greatly impact the final results.

## 4. How do you perform calculations with significant figures?

When performing calculations with significant figures, the final answer should be rounded off to the same number of significant figures as the least precise measurement used in the calculation. For addition and subtraction, the answer should have the same number of decimal places as the least precise measurement. For multiplication and division, the answer should have the same number of significant figures as the measurement with the fewest significant figures.

## 5. Are there any exceptions to significant figures rules?

Yes, there are a few exceptions to significant figures rules. For example, when dealing with exact numbers (such as counting objects), all digits are considered significant. Also, in logarithmic functions and conversions between units, the number of significant figures is determined by the scale of the measurement rather than the precision of the measuring tool.

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