sig figs

[WhoTookMyUsername]

This is a question that's been bugging me for a while now,
Do you use Molar masses in calculations of sig figs?

Yup, you do. But when you add molar masses, remember adding means decimal places, your final molar mass will be to one decimal place too.

so whenever you use hydrogen you can only go to 2 SF ?

[thushan]

This is a question that's been bugging me for a while now,
Do you use Molar masses in calculations of sig figs?

Yup, you do. But when you add molar masses, remember adding means decimal places, your final molar mass will be to one decimal place too.

so whenever you use hydrogen you can only go to 2 SF ?

If you're doing sth like H2, with molar mass 2.0, then use that number to divide/multiply then yes. But for sth like HCl, with molar mass 1.0 + 35.5 = 36.5, then use that number to divide/multiply, then ans is to 3 sf.

[yawho]

how many sig fig for ln(1.234)? sin(1.234)?

[ligands]

4

[yawho]

4

can you justify your answer?

[ligands]

4

can you justify your answer?

both have 4 sig figs because 1.234 is has 4 numbers which do not equal 0 therefore there is 4 sig figs

[yawho]

4

can you justify your answer?

both have 4 sig figs because 1.234 is has 4 numbers which do not equal 0 therefore there is 4 sig figs

but how do you know you are right?

[Mao]

how many sig fig for ln(1.234)? sin(1.234)?

Strictly speaking, sig figs aren't applied to these functions. But if you want to be rigorous, I would say:



Or more generally, for a small uncertainty,

[yawho]

how many sig fig for ln(1.234)? sin(1.234)?

Strictly speaking, sig figs aren't applied to these functions. But if you want to be rigorous, I would say:

Why did you say 'aren't applied to these functions'? In science don't you use ln, trig and other functions. It is not about rigour, more about reasons.

[Mao]

how many sig fig for ln(1.234)? sin(1.234)?

Strictly speaking, sig figs aren't applied to these functions. But if you want to be rigorous, I would say:

Why did you say 'aren't applied to these functions'? In science don't you use ln, trig and other functions. It is not about rigour, more about reasons.

Because we tend to use more sophisticated methods to deal with uncertainties.

[charmanderp]

It depends on how tight the examiner is.

The reasoning behind using the fewest significant to give your final answer is that we can only produce a result which is as accurate as our least accurate piece of data. For example, a supplied value of 3.01 could in actual fact be from something like 3.0139999, which would give us a very different answer. Burette's can supply a reasonably reliable volume to two decimal places. Note that it could easily be three significant figures if your titre was less than 10ml. But above you've supplied four. If later in our experiment we find a piece of data to be given to three sig figs, that applies only to any calculations which involve that information, which an average titre does not.

Careful guys - when adding or subtracting, we consider the least number of DECIMAL PLACES, NOT SIG FIGS. It's only in multiplication and division that we consider the least number of sig figs.

I don't think I contradicted that, did I?

[yawho]

how many sig fig for ln(1.234)? sin(1.234)?

Strictly speaking, sig figs aren't applied to these functions. But if you want to be rigorous, I would say:

Why did you say 'aren't applied to these functions'? In science don't you use ln, trig and other functions. It is not about rigour, more about reasons.

Because we tend to use more sophisticated methods to deal with uncertainties.

Here the focus is on number of significant figures in a calculation, not about methods to deal with uncertainties in measurements.

[Mao]

how many sig fig for ln(1.234)? sin(1.234)?

Strictly speaking, sig figs aren't applied to these functions. But if you want to be rigorous, I would say:

Why did you say 'aren't applied to these functions'? In science don't you use ln, trig and other functions. It is not about rigour, more about reasons.

Because we tend to use more sophisticated methods to deal with uncertainties.

Here the focus is on number of significant figures in a calculation, not about methods to deal with uncertainties in measurements.

Significant figures is itself a method to deal with uncertainties in measurements. e.g. . It is not a very robust method, as it is mostly only good with additions, subtractions and log10. If you want to do a more complicated calculation, then use a better method of handling these uncertainties.

[yawho]

how many sig fig for ln(1.234)? sin(1.234)?

Strictly speaking, sig figs aren't applied to these functions. But if you want to be rigorous, I would say:

Why did you say 'aren't applied to these functions'? In science don't you use ln, trig and other functions. It is not about rigour, more about reasons.

Because we tend to use more sophisticated methods to deal with uncertainties.

Here the focus is on number of significant figures in a calculation, not about methods to deal with uncertainties in measurements.

Significant figures is itself a method to deal with uncertainties in measurements. e.g. . It is not a very robust method, as it is mostly only good with additions, subtractions and log10. If you want to do a more complicated calculation, then use a better method of handling these uncertainties.

You have lost me.
good with additions, subtractions and log10: I don't understand why you mixed arith operations with functions
also: I thought decimal places are good with additions and subtractions to show precision
also: good with log10 but not loge, why?
1.0 implies 1.0 +/- 0.05: did you mean 1.0 implies 1.0 +/- 0.5

[Mao]

1.0, the second decimal place is unstated, thus it carries an uncertainty of 0.05. That is, if we had 1.04, it would round to 1.0. Thus

Re: operations, you are quite right in that S.F. isn't good for addition/subtraction. I meant mult/division. It can be shown that for mult/div, the propagation of uncertainties works out approximately to be the same as the largest relative uncertainty, so we keep the same significant figures. Key here is that sig.figs is an approximate method of dealing with uncertainties.

Log10 works well with S.F., though not in the conventional way (#decimals in log ~ S.F. of original number). This also works well for log_e, though it is much 'safer' for log10 due to the log10(e) coefficient.

For deriving how the S.F. changes over operations, we use the formula I provided previously, and look at how the relative uncertainties or absolute uncertainties change. S.F. is only one way to handle the implicit uncertainties of numerical values. At higher levels, uncertainties are handled explicitly for obvious reasons.

For sin(x +/- dx), it can be shown that as x->pi/2, the significant figures goes to infinity (indefinitely certain), and as x->0, the significant figures goes to 0 (indefinitely uncertain). This is in the limit of small errors, but the point stands that S.F. cannot be ordinarily applied to transcendental functions.