Rounding off in calculations (1 Viewer)

[-::Sanni::-]

My problem is that I tend to round off a little to early or round off too late in my calculations, e.g. titration concentrations, etc.

I've been told that rounding off to three significant figures is good. Is this true?

I'm always soooooo close and then I stuff up in the decimals... :mad1:

 

[danz90]

I never round off until right at the end.
At the end, I round of to the LOWEST number of significant numbers present in the question.
For example, if you have first data that is like:
0.1g
0.2500mol.L^-1
etc.

You would have to round off to 1 significant figure, because 0.1g has only 1 s.f.
So, for example, if you got an answer such as 85.0g
then I would put it into scientific notation to ensure I wrote it as 1sig fig,
ie: 9 x 10¹ g (1 sig. fig.)

hope that helps

oh and by the way, when calculating pH, the significant figure comes AFTER the decimal place, because its a log function, and the calculator doesn't consider the sig figs.

 

[Trebla]

When you WRITE the numbers, you write in an appropriate number of significant figures. However, when you CALCULATE them you should always keep the exact (or most accurate) value stored on your calculator and do not use the rounded value in the next round of calculations. You only round off at the end, because if you do it too early, you may lose precision.

In terms of how many significant figures to round off, you should refer to the question's given data. Whichever data has the LEAST significant figures is the limiting data in precision. So for example, if you are given x = 6.0, y = 25.61, you would round off to 2 significant figures, because x is less precise than y. If you round off to 4 significant figures instead, you have a big margin of uncertainty, because the x can be several values like 6.013, 6.022, 6.012...etc. Therefore, you always round off according to the significant figures given in the question. However, that being said, I don't think the marking scheme is too fussy about that, as long as the rounding off is APPROPRIATE. (e.g. for a titration, it's probably not a good idea to round 25.12mL to 30mL)

 

[-::Sanni::-]

Excellent! Thank you very much danz90 and Trebla! I feel a bit relieved now! <!-- Added by James for Benefactors: 11.30pm, 8 Feb 2005 -->

 

[danz90]

When you WRITE the numbers, you write in an appropriate number of significant figures. However, when you CALCULATE them you should always keep the exact (or most accurate) value stored on your calculator and do not use the rounded value in the next round of calculations. You only round off at the end, because if you do it too early, you may lose precision.

In terms of how many significant figures to round off, you should refer to the question's given data. Whichever data has the LEAST significant figures is the limiting data in precision. So for example, if you are given x = 6.0, y = 25.61, you would round off to 2 significant figures, because x is less precise than y. If you round off to 4 significant figures instead, you have a big margin of uncertainty, because the x can be several values like 6.013, 6.022, 6.012...etc. Therefore, you always round off according to the significant figures given in the question. However, that being said, I don't think the marking scheme is too fussy about that, as long as the rounding off is APPROPRIATE. (e.g. for a titration, it's probably not a good idea to round 25.12mL to 30mL)

Spot on

Although, my teacher is a HSC Marker , and he said that in a 3-mark titration question, the students could not be awarded full marks if they didn't give their final answer to the correct number of significant figures. In other words, you lose a mark if its not to the correct sig figs.