Skip to main content

How do I use significant figures in my chemistry class?

Significant figures can be annoying, but the fundamental principle underlying significant figures is a very important one: We don't want to lie about the precision of our results.

Significant figure rules are the way they are because we want to accurately represent our results as neither more nor less precise than they really are. Keep this in mind, and the rules will become more intuitive to you.

The simplest way to represent significant digits is to always use scientific notation. Then the number of digits in your mantissa (the part that comes before the 10^x business) is your number of significant digits.

The reason that when we multiply we take the lowest number of significant digits is that this is the overall precision of our result; if we multiply 0.2 g/mol * 0.278 mol, that 0.2 g/mol is saying that we really only know it's about 1/5 of a gram per mole; could be 0.196, could be 0.215; so it wouldn't make sense to keep all three decimals in our final answer. Instead we only keep the 1: 0.06 g, or better yet 6.0*10^-2 g. If we knew it was that precise, we should have said it was 0.200 g/mol, not 0.2 g/mol.

Similarly, when we add or subtract, we only keep decimals up to the least-precise figure, because we don't want to overestimate the precision of our final answer. 1.284 g + 2.9 g = 4.2 g, not 4.184, because that 2.9 wasn't precise enough for us to really know that the result is 4.184.

Comments

Post a Comment

Popular posts from this blog

Is there a word/phrase for "unperformant"?

As a software engineer, I need to sometimes describe a piece of code as something that lacks performance or was not written with performance in mind. Example: This kind of coding style leads to unmaintainable and unperformant code. Based on my Google searches, this isn't a real word. What is the correct way to describe this? EDIT My usage of "performance" here is in regard to speed and efficiency. For example, the better the performance of code the faster the application runs. My question and example target the negative definition, which is in reference to preventing inefficient coding practices. Answer This kind of coding style leads to unmaintainable and unperformant code. In my opinion, reads more easily as: This coding style leads to unmaintainable and poorly performing code. The key to well-written documentation and reports lies in ease of understanding. Adding poorly understood words such as performant decreases that ease. In addressing the use of such a poorly ...
Post a Comment
Read more

Is 'efficate' a word in English?

I routinely hear the word "efficate" being used. For example, "The most powerful way to efficate a change in the system is to participate." I do not find entries for this word in common English dictionaries, but I do not have an unabridged dictionary. I have checked the OED (I'm not sure if it is considered unabridged), and it has no entry for "efficate". It does have an entry for "efficiate", which is used in the same way. Wordnik has an entry for "efficate" with over 1800 hits, thus providing some evidence for the frequency of use. I personally like the word and find the meaning very clear and obvious when others use it. If it's not currently an "officially documented" word, perhaps its continued use will result in it being better documented.
Post a Comment
Read more