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DBA-144

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Significant figures question
« on: January 24, 2019, 11:13:14 am »
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Hello,

When using significant figures, I understand that for addition/subtraction, we use the fewest number of decimals, so wjat would 1.05 - 1.0 be? 0.1?

Also, if I am multiplying or dividing and I get more significant figures in the result than previously, do I need to use the equals sign to indicate approximately equal to. i.e 3 x 6 = 18 ~~ 20. Am I correct in doing this? I understand that 3 and 6 are to 1 sf, but when rounding it, it goes to 20: is this correct, or so I need to express it in scientific notation to indicate that it is to 1 sf? As VCE students, what are we reuqired to do?

What does VCAA use for logarithms? Do they follow the convention of using only the number in the log as the only significant number? Eg, log 100=2.00? Am i correct in expressing this answer to 3 sf, since I know, with accuracy that the 100 was to 3 sf?

Sorry for all the questions. Just wanna get this stuff sorted now rather than later.  :)
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lacitam

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Re: Significant figures question
« Reply #1 on: January 24, 2019, 11:22:36 am »
+1
Hello,

When using significant figures, I understand that for addition/subtraction, we use the fewest number of decimals, so wjat would 1.05 - 1.0 be? 0.1?

Also, if I am multiplying or dividing and I get more significant figures in the result than previously, do I need to use the equals sign to indicate approximately equal to. i.e 3 x 6 = 18 ~~ 20. Am I correct in doing this? I understand that 3 and 6 are to 1 sf, but when rounding it, it goes to 20: is this correct, or so I need to express it in scientific notation to indicate that it is to 1 sf? As VCE students, what are we reuqired to do?

What does VCAA use for logarithms? Do they follow the convention of using only the number in the log as the only significant number? Eg, log 100=2.00? Am i correct in expressing this answer to 3 sf, since I know, with accuracy that the 100 was to 3 sf?

Sorry for all the questions. Just wanna get this stuff sorted now rather than later.  :)
For 1.05 - 1.0, you use the lowest amount of sig figs in the question, and in this case, 1.0 has two sig figs (whereas 1.05 has 3). Thus, the answer would be 0.050

Well, given 3 * 6 has 1 sig fig in both numbers, then the answer would be 2 * 10 (end zeroes are technically not significant, but this is usually the case for further maths as opposed to vce chem)

Usually, how many sig figs your answer is depends on how many sig figs are in the question, so if the lowest amount of sig figs in the question is 4, then your answer should be in 4 sig figs

MOD EDIT: merged double post
« Last Edit: January 24, 2019, 11:39:22 am by Sine »

DBA-144

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Re: Significant figures question
« Reply #2 on: January 24, 2019, 02:15:45 pm »
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For 1.05 - 1.0, you use the lowest amount of sig figs in the question, and in this case, 1.0 has two sig figs (whereas 1.05 has 3). Thus, the answer would be 0.050

Well, given 3 * 6 has 1 sig fig in both numbers, then the answer would be 2 * 10 (end zeroes are technically not significant, but this is usually the case for further maths as opposed to vce chem)

Usually, how many sig figs your answer is depends on how many sig figs are in the question, so if the lowest amount of sig figs in the question is 4, then your answer should be in 4 sig figs

MOD EDIT: merged double post



Thanks for the response. Just another question; say I am required to use a value such as Avogadros constant, which I believe is to 3 sf. However, would this not mean that my answer needs to be expressed to 3 sf?

In general, are we allowed to assume that values from the data book are 100% accurate, and then not need to concern ourselves with the sig figs of these numbers?

Also, I am pretty sure that for addition and subtraction, we use least number of decimal places. So, wouldnt this mean that we need to round 0.050 to 0.1 since we have the least number of decimal places as 1, not 3?

Just a bit confused, thats all. Thanks again.  :)
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darkz

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Re: Significant figures question
« Reply #3 on: January 24, 2019, 05:58:50 pm »
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Also, I am pretty sure that for addition and subtraction, we use least number of decimal places. So, wouldnt this mean that we need to round 0.050 to 0.1 since we have the least number of decimal places as 1, not 3?

The 0's before the 5 don't count. Essentially what it is here is \[{5.0\,\times \,10^{-2}\,=\,0.050}\]

Edit: Oops
« Last Edit: January 25, 2019, 07:47:14 am by darkz »
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lacitam

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Re: Significant figures question
« Reply #4 on: January 24, 2019, 06:09:08 pm »
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Thanks for the response. Just another question; say I am required to use a value such as Avogadros constant, which I believe is to 3 sf. However, would this not mean that my answer needs to be expressed to 3 sf?

In general, are we allowed to assume that values from the data book are 100% accurate, and then not need to concern ourselves with the sig figs of these numbers?

Also, I am pretty sure that for addition and subtraction, we use least number of decimal places. So, wouldnt this mean that we need to round 0.050 to 0.1 since we have the least number of decimal places as 1, not 3?

Just a bit confused, thats all. Thanks again.  :)
If the question is all in 4 sig figs, however you used avogadro's number (or at least any number in your data book), then you use 3 sig figs (because Avo number is 6.02 * 10^23.

What do you mean by assume databook is 100% correct?

Yertle the Turtle

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Re: Significant figures question
« Reply #5 on: January 24, 2019, 06:36:30 pm »
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Basically significant figures are a little bit confusing. You always use the smallest number that is in the question, which means that data booklet values do not count. Thus when you use Avogadro's number in a question with 4 sig figs then you would give the answer to 4 sig figs, not 3, as you assume that the figures in the data booklet are accurate. Also when it comes to things like 6*3=18, you would use logic, which says that this is a small integer, and therefore you would not round. Therefore, though there are some rules about what you need to do, there is also some simple logic that you would follow.
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lacitam

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Re: Significant figures question
« Reply #6 on: January 24, 2019, 06:42:02 pm »
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Basically significant figures are a little bit confusing. You always use the smallest number that is in the question, which means that data booklet values do not count. Thus when you use Avogadro's number in a question with 4 sig figs then you would give the answer to 4 sig figs, not 3, as you assume that the figures in the data booklet are accurate.
You sure man? I remember I lost marks on my yr11 chem exam because I used 4 sig figs instead of 3

DBA-144

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Re: Significant figures question
« Reply #7 on: January 24, 2019, 06:52:54 pm »
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Looks like there are multiple interpretations haha.

Regarding the logic point raised by Yertle, where would this extend to? Is it just discrete figures, eg. 4 molecules x 4molecules is 16 molecules, as we know that we have 4 and 4.5 molecules?

And darkz, if we have 1.1 - 1.05 = 0.05, would we not need to round our answer to 1 do, since we use decimal places for addition subtraction and not significant figures?

About the data book, what I mean is, that if we assume that Avogadros number is 6.02 x10^23, and that this is 100% accurate, we would not need to consider sig figs for this, since we know that it is exactly 6.02 x 10^23. My understanding is that we use sig figs for when we dont know the level of accuracy of a particular (continuous) quantity.

So much concern for just 1 mark on the exam. :/
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Yertle the Turtle

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Re: Significant figures question
« Reply #8 on: January 24, 2019, 07:03:17 pm »
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Looks like there are multiple interpretations haha.

Regarding the logic point raised by Yertle, where would this extend to? Is it just discrete figures, eg. 4 molecules x 4molecules is 16 molecules, as we know that we have 4 and 4.5 molecules?

And darkz, if we have 1.1 - 1.05 = 0.05, would we not need to round our answer to 1 do, since we use decimal places for addition subtraction and not significant figures?

About the data book, what I mean is, that if we assume that Avogadros number is 6.02 x10^23, and that this is 100% accurate, we would not need to consider sig figs for this, since we know that it is exactly 6.02 x 10^23. My understanding is that we use sig figs for when we dont know the level of accuracy of a particular (continuous) quantity.

So much concern for just 1 mark on the exam. :/
Regarding @darkz's comment, you are correct, addition and subtraction do only use decimal places, thus the answer would be 0.05. Relative to my statements, it is largely discrete values that you use this kind of logic for. If you are only using discrete figures, and you end up with a large number, you have to use logic to determine where to cut it off, but generally somewhere around 3 sig figs is the best point. For instance, 9*41*12*9/3=13284. In this case you have no sig figs to go off, all your multiples being exact integers, but here I would say you would round it to 13300 or 1.33*10^4.

You sure man? I remember I lost marks on my yr11 chem exam because I used 4 sig figs instead of 3
Yes, in this case you have to assume total accuracy of the data that you are given in the data booklet. Some teachers do have different standards, but this is the way that VCAA examiners will mark the exams.
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