[Rijesh]

i am taking general Chemistry 101 in my university and SF is killing me!

i get most of the basic ideas and i know how it works (in most cases). But i don't know when to use it and when to not

For example,

1.223 gram O2 * 1 mole/16 grams O2 = how many significant figures??..do you count the 1 mole and 16 gram's sig. fig or just 1.223 gram? if so, why?

what about for the following questions?

1. How many km are there in 1 miles?
2. How many km are there in 1. miles?

Is the answer gonna be different in the above 2 questions? If so, why? the answer is 1.6093 (or something like that), but how many SFs???

Thannk You.

[nj_bartel]

Ok, I would round to 2 signficant figures in your first example because 1.223 and 16 are your two rounded figures, but 16 only has two significant digits, and you use the number with the smallest amount of significant digits.  1 mol is not rounded because it is an exact quantity.  1 mol = 1.0 mol = 1.0000000000000 mol, etc.  In the ratio 1 mole/16 grams O₂ (which now reading it is actually wrong, there are 32 g/mol O₂), you are relating MW to that precise quantity, but 32g O₂ aren't what's actually in a mole of O₂; it's more like 31.998.. etc

For your second example, the difference between the first and second statement is the period after the 1 in the second question.  In the first question, you interpret the 1 mile like you interpreted the 1 mol in the last question.  However, in the second question, the decimal following the 1 confers an implied estimation on the amount of miles you have, so you have 1 significant digit, and your answer would be 2 km.

[Rijesh]

thank you for your reply...now i am actually confused by the exact quantity thing 

my teacher said that 1 gram = 1000 mg is an exact quantity...so, isn't 1 mol / 32 g O2 an exact number, or to be specific, isn't 1 mol / 31.998 g O2 an exact number?...so why do you count the S.F of 32 (or 16 in my initial question)?...why don't you just take the significant figure of 1.223 grams?

To be sure, if its an exact quantity, you don't care about the SF right?

Thank You

[nj_bartel]

Yes, if it's an exact quantity then you don't use it to decide how many sig figs.  The molecular weight of oxygen is not 32, nor is it 31.998.  Those are both rounded.

[Rijesh]

thanx again

Probably one last question.

In our lab yesterday, we were supposed to find the Avogadro's number using datas of a carbon chain....

The thickness of the carbon chain was 0.5, given by the teacher....after many calculations, the answers for volumes and lengths came 1.4 cm3, 1.84 cm...etc....
But since .5 has 1 sig. fig, i rounded all the answers to 1 sig fig....
but it doesn't feel correct...suppose writing 1. cm3 instead of 1.4cm3...isn't it an incorrect value?

[Arkcon]

It's hard work, working with significant figures, if you don't really think about what it means ...

in your example, 0.5 is one dimension.  What does that mean?  It means it might have been 0.52 or 0.48, we don't really know.  When we sacrifice the answers sig. figs, we are admitting the limitations of our measurements.

but it doesn't feel correct...suppose writing 1. cm3 instead of 1.4cm3...isn't it an incorrect value?

If you have a measurement of 1.4, 1.84, and 0.5 you do realize you are supposed to use them all when performing calculations, and only round the answer, right?  It was mentioned before in another thread on sig. figs recently.

[Rijesh]

yeah, i know that...but what if that's my final answer and don't have to use it for anything else?

i forgot the exact question, but i think it was asking for L1 or something...the answer came out 1.42 * 10^6...i wrote 1. * 10^6