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September 27, 2021, 07:00:25 am

### AuthorTopic: Significant figures Guide  (Read 12743 times) Tweet Share

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#### ed_saifa

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##### Significant figures Guide
« on: September 23, 2009, 12:08:01 pm »
+6
Significant figures are confusing so i hope this guide will answer your questions

$0.003$ is 1 significant figure

$0.00300$ is 3 significant figures

Addition/subtraction
The result has the same number of decimal places as the measurement with the fewest decimal places

$72.95 + 1.052 + 5.436 = 79.438 = 79.44$

Multiplication/division
the result contains the same number of significant figures as the measurement with the fewest significant figures

$0.361 × 1.4 × 0.228 = 0.11523 = 0.12$

Logarithms/exponentials
In a logarithm, the answer has the same number of decimal places as the number of significant figures in the input value. In an exponential, the result has the same number of significant figures as the number of decimal places in the input value.

$[H^{+}] = 1.45 × 10^{-4}$ is $-log_{10}(1.45 ×10^{-4}) = 3.839$

$pH = 7.85$  $[H^{+}]$ is $10^{-7.85} = 1.4 × 10^{-8}$

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#### kendraaaaa

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##### Re: Significant figures Guide
« Reply #1 on: September 23, 2009, 12:41:25 pm »
0
Thanks. Also it's important to note that you don't have to use significant figures every calculation, only until your final result (or so I've been told)

#### Mao

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##### Re: Significant figures Guide
« Reply #2 on: September 23, 2009, 07:22:26 pm »
+2
Stuck. Because it is quite significant
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#### IntoTheNewWorld

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##### Re: Significant figures Guide
« Reply #3 on: September 23, 2009, 07:52:10 pm »
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Stuck. Because it is quite significant

*slaps* =P

#### monokekie

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##### Re: Significant figures Guide
« Reply #4 on: September 23, 2009, 08:05:28 pm »
0
do we need to consider sig fig for ANY calculation in chem? i was told before by some people that it is only the ones associated with concentrations that counts, but what about the heat of combustions? calibration factors? heat contents? and electricity currents? should they count as well?

#### Mao

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##### Re: Significant figures Guide
« Reply #5 on: September 23, 2009, 10:48:00 pm »
0
do we need to consider sig fig for ANY calculation in chem? i was told before by some people that it is only the ones associated with concentrations that counts, but what about the heat of combustions? calibration factors? heat contents? and electricity currents? should they count as well?
You should consider the sig fig of every number you use in calculations, and adjust your answers accordingly.
« Last Edit: September 23, 2009, 10:51:08 pm by Mao »
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#### NE2000

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##### Re: Significant figures Guide
« Reply #6 on: October 24, 2009, 04:59:43 pm »
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Is the mark for sig figs only for Unit 3 or is it also for Unit 4?
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#### nels

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##### Re: Significant figures Guide
« Reply #7 on: October 24, 2009, 05:14:27 pm »
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unit 4 as well, just checked the exam covers.

#### simpak

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##### Re: Significant figures Guide
« Reply #8 on: November 03, 2009, 07:34:17 pm »
0
Hey you guys, when you're calculating and you know you're meant to have a final result to say, three sig figs, should you make every intermediate number that you might obtain in the progression of calculations you must go through in order to reach the final result to three sig figs, or should you carry everything over to the next calculation right until the end?

I'm totally unsure as to whether that makes sense or not.
I'll demonstrate...

So say you were calculating, idk...
Q=It.
And you had 23.0 seconds and 5.667 Amps, for our sake.
Your answer would be...130.341.
And you're going to go on to use Q in the next equation in order to find the number of mol of electrons for instance.
Would you round there, to 130 because you just did a calculation in which the value with the lowest number of sig figs had 3?
Or would you carry the whole 130.341 into the next equation and only round up/down at the end, when you give the final result?  Because you could end up with a significantly different result depending on the values you use.

Argh, I hope it made sense that way.  Thanks.
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#### nels

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##### Re: Significant figures Guide
« Reply #9 on: November 11, 2009, 02:46:31 pm »
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yep, round off at the end.

#### dav132

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##### Re: Significant figures Guide
« Reply #10 on: November 11, 2009, 05:52:23 pm »
0
i still get confused with the in between steps...
i know that we shouldn't round values before you use them in the next calculations,
otherwise you won't get the right final result...
but when u actually write down the in between steps, do you write them with the right sig figs?

e.g. If you have to work out the calibration factor of a bomb calorimeter (3 mark question),
and you need to work out the number of mole of a substance to do that,
would you write down n=0.031 or n=0.0306111120090210.....?
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#### kenhung123

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##### Re: Significant figures Guide
« Reply #11 on: December 17, 2009, 02:39:22 pm »
0
i still get confused with the in between steps...
i know that we shouldn't round values before you use them in the next calculations,
otherwise you won't get the right final result...
but when u actually write down the in between steps, do you write them with the right sig figs?

e.g. If you have to work out the calibration factor of a bomb calorimeter (3 mark question),
and you need to work out the number of mole of a substance to do that,
would you write down n=0.031 or n=0.0306111120090210.....?
I would like to know too.

Also, when people are saying carry it to the next calculation do you mean like just do it to about 5 decimal places? As sometimes it is difficult to carry the values across in a scientific calculator. For E.g. I got 1.0031241252 and I need to divide 5 by 231 and multiply 1.0031241252, I can't use "Ans" button as its not stored as the ans after doing a later calculation.
Otherwise I will just write down the intermediate answer to 5 decimal places and ensure its quite accurate and forget about the calculator problems haha.

#### Edmund

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##### Re: Significant figures Guide
« Reply #12 on: December 18, 2009, 05:55:43 pm »
0
i still get confused with the in between steps...
i know that we shouldn't round values before you use them in the next calculations,
otherwise you won't get the right final result...
but when u actually write down the in between steps, do you write them with the right sig figs?

e.g. If you have to work out the calibration factor of a bomb calorimeter (3 mark question),
and you need to work out the number of mole of a substance to do that,
would you write down n=0.031 or n=0.0306111120090210.....?
I would like to know too.

Also, when people are saying carry it to the next calculation do you mean like just do it to about 5 decimal places? As sometimes it is difficult to carry the values across in a scientific calculator. For E.g. I got 1.0031241252 and I need to divide 5 by 231 and multiply 1.0031241252, I can't use "Ans" button as its not stored as the ans after doing a later calculation.
Otherwise I will just write down the intermediate answer to 5 decimal places and ensure its quite accurate and forget about the calculator problems haha.
Writing it down to 5 decimal places is fine. What you could do is:

$(231/5)*ANS$
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#### jimmy999

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##### Re: Significant figures Guide
« Reply #13 on: December 29, 2009, 03:42:20 pm »
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I was always confused about significant figures right up until the week before my Unit 3 exam. Then it became so clear and easy to do
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#### jayfan

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##### Re: Significant figures Guide
« Reply #14 on: January 07, 2010, 12:58:25 pm »
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This is indeed very confusing, and VCAA is shooting themselves in the foot by not stating it clearly.

The closest reference on this from VCAA is within the 2008 Unit 4 Examiner's Report (http://www.vcaa.vic.edu.au/vcaa/vce/studies/chemistry/assessreports/2008/chemistry2_assessrep_08.pdf), although its not strictly relevant to what we are discussing:

"The question often arises about the impact of relative atomic masses on significant figures, particularly H given as 1.0
in the data book. It may be appropriate to quote the accepted rules for the use of significant figures in calculations.
1. For multiplication and division, the result contains the same number of significant figures as the measurement
with the fewest significant figures. For example, the mass of 0.251 mol H2 = 0.251 x 2.0 = 0.50.
2. For addition and subtraction, the result has the same number of decimal places as the measurement with the fewest decimal places. For example, M(C2H6O) = 2 x 12.0 + 6x1.0 + 1x16.0 = 46.0. For example, 34.652 – 2.36 = 32.29.
"

At our school, we are taught to round off to the number of significant figures of the least accurate data used in a calculation at the end of THAT calculation. This means you round off each step, and then use that rounded off answer in your next step.

In another word, we are taught NOT to keep results in our calculators all the way.

I think this reasoning makes sense in the real world, because when you are doing experiments, your results can only be as accurate as your least accurate apparatus, which would THEN influence all your subsequent calculations. - i.e. There's no point in keeping your results in your calculator, even though it would be more "mathematically" correct.
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