Thread: Quick Question on Significant Digits

I'm not sure what my number of significant digits should be. Thanks

Chlorine - 37 . Relative abundance of 33
Chlorine - 35 . Relative abundance of 100

Atomic Mass = (33⁄133)(37) + (100⁄133)(35) = 35.4962406 amu

If you're using atomic mass units I'm pretty sure it's accurate to the mass of one H atom or one proton or neutron.

However, for this sort of question, if it's for an exam then it really just depends on how accurate they require you to be. I'm guessing they haven't asked you to do it to a certain number of significant figures, so I would suggest just doing 4 or more, because as long as your answer is correct and accurate to a degree, you should get the mark.

Also, the relative abundance of 37 Cl is 24.23%, 35 Cl is 75.77% and Cl 36 is really just a trace, so you don't need to worry about that ^_^.

In summary, it depends on who's asking the question and the purpose it serves.

Hope I helped!

doesn't really matter

of course 35.4962406 is far too acurate, that said, they can't not give you a mark for being too accurate



it depends what level you're at, kids are usually required just to sum up, 35.5 would be acceptable
GCSE is usually 2 dp and A-level is 34.496


another helpful tip is generally you can't make something more accurate than it's sum, so if you're most accurate figure has 2 dp, then generally your answer should be limited to 2 as well

The deal with significant figures is quite well defined in my opinion. If you have an equation say 1.23*1.0, then the result would be 1.2, not 1.23 or 1 since the accuracy in the second factor is only (exactly) two digits. The same goes for scientific numers too: 1.23 * 1E-1 is in fact 0.1 since the lowest accuracy number has only one significant figure. Same for sums (1.23456+1.00=2.23), divisions (1.2345/1.00=1.23).
Now the question regarding measured quantities is quite a different animal since you often need to assume that the person reporting the numer has taken uncertainty in the measurement equipment into account and is reporting the numbers according to established scientific methods. The format I like the most is where the uncertainty is given (say in a value of 1.234567(89) where the last two figures are not confirmed/within the band of uncertainty).
The thing that annoys me the most when it comes to significant figures is when someone has an equation 1.0*1.234*1.00000000=1.234000000 since the result implies that the number is known to the nineth decimal whereas the first factor could be anything between 0.950000000 and 1.04999999 which would make the result incorrect.
Now if you happen to be an engineer and not a scientist (yes, there is a difference), there are some additional things to consider: if you are reporting a distance, say the thickness of a part, the significant figures must represent the degree to which the number is defined. If you put on a drawing that a part is 1.0000 inches thick, then the part needs to be between 0.99995 and 1.000049 inches in thickness, independent of how hard that is to achieve. On the other hand if you write 1.0 inches, a part that is 0.95" or 1.049 is still acceptable. This is where tolerances come into play, but that is a different item.