[quote=ItzPootz]@Cinnanmonny: Ah I see what you mean now. When you're just multiplying two [i]constants[/i]--just regular numbers, that weren't from a measurement--yes, you don't have to worry about sig figs. You only need to worry about sig figs when you're using a value to do a calculation that you found through measurement
The terms accuracy and precision in these regards are reserved only for when you're talking about a measurement that was done.[/quote]
I meant that both of the two were taken from a measurement (not just one)
so since I was not understanding their purpose my argument was that 6.05 and 6.1 were not accurate I was not thinking of 6.1 as a less precise way of writing 6.05, but rather I was wondering why the two numbers were so different (almost as if I really meant to say 6.05 and 6.10)
^ don't give up trying to explain this I meant what I said and that was essentially the whole point of this thread
[quote=ItzPootz]He's just being boisterous; in any case, the reason why you'd say precise instead of accurate in that case is because you only say a measurement is accurate if you have an accepted value for it.
In your example, let's say you measured with a ruler that something is 5.5 meters; The ruler only has marks for every 10 centimeters, so you can only measure two significant figures here. This means when you measured the object to be 5.5 meters, you measured that the object [i]is closer to 5.5 meters versus 5.4 or 5.6[/i]. Then, as explained before, you don't say the end product is 6.05 m; because you would only be able to measure this result up to either a precision of 6.1 m or 6.0 m
A little bit clearer on how the terms are defined?[/quote]
I'm talking about an answer after simple multiplication not just a taken measurement
[quote=iLoveKitties]if you want to talk about how many decimals you have then yourre talking about precision bad accuracy would be if you said that it was 10 when it was really 2.4[/quote]
I was using it correctly then I was saying that 6.05 is way off from 6.1 my point was that it is not the same thing
[quote=Cinnanmonny]perhaps a more specific example should be given because I do not see why you would randomly make your answer less specific ..[/quote]
It's wrong to have measurements that are more accurate than your most accurate measurements, which is why I gave the area of a square that had sides measured to 1.25," which is the most accurate number your instruments could effectively measure. It doesn't make sense for your final answers to be more accurate than your instruments.
and because you dont know its 6.05. the most precise measurement you can get is 6.1. if 5.5 is actually 5.55, then 5.5*1.1 would be 6.105 which is a whole .1 higher than what you wanted to say it was. do we know that its 5.50 and not 5.55? or 5.52? or 5.46? NO. so we cant say the answer is that precise.[/quote]
[quote=Cinnanmonny]equipment accuracy makes sense but calculations do not[/quote] Those numbers you are using in your calculations are [i]measured[/i] using equipments. The significant figures shows how accurate the equipment is. Numbers don't appear out of thin air, you need some sort of [i]tool[/i] to measure it.
[quote=iLoveKitties]if i measured that the distance is 5.5m and i multiply it by something, i cant make anything anymore precise than that because the ruler doesnt tell me wheter its 5.55, 5.49, 5.51, etc, so how can i say the answer to 5.5*x is 0.123954875853479324947543. i only know for sure to 2 sigfigs[/quote]
if you get 5.5 and multiply by 1.1 you get 6.05 6.05 is more accurate than 6.1 why would you need to make things less accurate?
[quote=nekci]holy crapencasacke im having my honors chem test tomorrow on chapter 1. god wish me luck. first of all, significant figures have a very significant point to why we use them. But im not going to answer that. why are you living? why do we learn trig? why are you questioning this? just accept what they are and lets get started.
since you are not asking for sig figs and operations i wont talk about that. just know this. If decimal point is Present, Pacific. (how the Pacific Ocean is on the left side of the US.) and if it is Absent, Atlantic (how it is on the right side of the U.S.)
few examples:
0.06201... ok since it has a decimal, go Pacific, or left. start counting from the first non-zero digit all the way to the end. 6..2..0..1. that is 4 sig figs 3.41... decimal point is present yet again, go Pacific, or left. 3.41 = 3 sig figs 3.041... ok dont be worried because of the 0 inbetween, still count it. 3.041= 4 sig figs 3,000,000... ok, the first non decimal problem. since the decimal is *A*bsent, *A*tlantic, or start from the right. this is only 1 sig fig because the other digits are ALL zero, so dont count them. if it was 3,000,001 on the other hand, there would be 7 sig figs. 1.000... ok decimal points again. go Pacific, and count till end. dont worry that all of the other digits are 0's, count because of the decimal. 1.000 = 4 sig figs as 1.0000 = 5 sig figs. 4.0450... another decimal yay! still count all digits from Pacific. dont worry that the last digit is 0 again, still count it. 4.0450 = 5 sig figs one more... 4,051,000... ok, no decimal so Atlantic (again that is right). count from first non-zero digit until it ends. 1..5..0..4.. that is 4 sig figs
so keep in mind
Atlantic = absent = right Pacific = present = left[/quote]
this doesn't have anything to do with my question though
Your instruments only measure to the nearest hundredth of an inch, however your calculations get you to the ten thousandth, which is impossible given the comparative inaccuracy of your instruments.
That is the point of significant digits/figures.[/quote]
perhaps a more specific example should be given because I do not see why you would randomly make your answer less specific ..
Your instruments only measure to the nearest hundredth of an inch, however your calculations get you to the ten thousandth, which is impossible given the comparative inaccuracy of your instruments.
Significant figures are for accuracy. Let's say you measure something on the ruler, and your ruler goes in increments of 0.1 and you read something that lands exactly on the 2 mark, and you record that as "2.00" with significant figures. The extra "0" on the end shows the uncertainty or the "guess value", it also show how good your measuring tool is.
When you're doing a scientific experiment, you're reading figures from your equipment. You don't know the "missing" decimal places (it could be as little as 0 or as much as 9). So you have to give up accuracy for significance. - If you're doing computations on figures obtained from two different machines (with different displays), the "significance" of your computations are only as good as the poorest significance supplied to you by your equipment.
19 Comments • Newest first
Let's say that I made two measurements that were 5.5 and 1.1
I most likely would not know if 5.5 would be 5.45-5.55 and 1.1 maybe could be 1.05-1.15
So the lowest possible value could be about 5.7225 and highest 6.3825
6.1 is not the middle ground, about 6.05 is
so wut da hek I still dun get it why do we like 6.1 so much
[quote=ItzPootz]@Cinnanmonny: Ah I see what you mean now. When you're just multiplying two [i]constants[/i]--just regular numbers, that weren't from a measurement--yes, you don't have to worry about sig figs. You only need to worry about sig figs when you're using a value to do a calculation that you found through measurement
The terms accuracy and precision in these regards are reserved only for when you're talking about a measurement that was done.[/quote]
I meant that both of the two were taken from a measurement (not just one)
so since I was not understanding their purpose my argument was that 6.05 and 6.1 were not accurate
I was not thinking of 6.1 as a less precise way of writing 6.05, but rather I was wondering why the two numbers were so different (almost as if I really meant to say 6.05 and 6.10)
^ don't give up trying to explain this
I meant what I said and that was essentially the whole point of this thread
[quote=ItzPootz]He's just being boisterous; in any case, the reason why you'd say precise instead of accurate in that case is because you only say a measurement is accurate if you have an accepted value for it.
In your example, let's say you measured with a ruler that something is 5.5 meters; The ruler only has marks for every 10 centimeters, so you can only measure two significant figures here. This means when you measured the object to be 5.5 meters, you measured that the object [i]is closer to 5.5 meters versus 5.4 or 5.6[/i]. Then, as explained before, you don't say the end product is 6.05 m; because you would only be able to measure this result up to either a precision of 6.1 m or 6.0 m
A little bit clearer on how the terms are defined?[/quote]
I'm talking about an answer after simple multiplication not just a taken measurement
[quote=iLoveKitties]if you want to talk about how many decimals you have then yourre talking about precision
bad accuracy would be if you said that it was 10 when it was really 2.4[/quote]
I was using it correctly then
I was saying that 6.05 is way off from 6.1
my point was that it is not the same thing
[quote=Criticism]"6.05 is more accurate than 6.1"
bro.[/quote]
I don't see how it was misused in that context bro
[quote=Cinnanmonny]perhaps a more specific example should be given because I do not see why you would randomly make your answer less specific ..[/quote]
It's wrong to have measurements that are more accurate than your most accurate measurements, which is why I gave the area of a square that had sides measured to 1.25," which is the most accurate number your instruments could effectively measure. It doesn't make sense for your final answers to be more accurate than your instruments.
[quote=iLoveKitties]omg guise accuracy=clonseness to the accepted value
precision=precise measurements and such
stahp mixing them up[/quote]
I didn't misuse them tho
[quote=iLoveKitties]@Cinnanmonny: *precise
and because you dont know its 6.05. the most precise measurement you can get is 6.1. if 5.5 is actually 5.55, then 5.5*1.1 would be 6.105 which is a whole .1 higher than what you wanted to say it was. do we know that its 5.50 and not 5.55? or 5.52? or 5.46? NO. so we cant say the answer is that precise.[/quote]
AND THUS IT HAS BEEN EXPLAINED
[quote=Cinnanmonny]equipment accuracy makes sense but calculations do not[/quote]
Those numbers you are using in your calculations are [i]measured[/i] using equipments. The significant figures shows how accurate the equipment is. Numbers don't appear out of thin air, you need some sort of [i]tool[/i] to measure it.
The only thing that confuses me about sig figs is that 1.0 has 2 sig figs while the same number can have like infinite sig figs..
[quote=iLoveKitties]if i measured that the distance is 5.5m and i multiply it by something, i cant make anything anymore precise than that
because the ruler doesnt tell me wheter its 5.55, 5.49, 5.51, etc, so how can i say the answer to 5.5*x is 0.123954875853479324947543. i only know for sure to 2 sigfigs[/quote]
if you get 5.5 and multiply by 1.1 you get 6.05
6.05 is more accurate than 6.1
why would you need to make things less accurate?
[quote=nekci]holy crapencasacke im having my honors chem test tomorrow on chapter 1. god wish me luck. first of all, significant figures have a very significant point to why we use them. But im not going to answer that. why are you living? why do we learn trig? why are you questioning this? just accept what they are and lets get started.
since you are not asking for sig figs and operations i wont talk about that. just know this. If decimal point is Present, Pacific. (how the Pacific Ocean is on the left side of the US.) and if it is Absent, Atlantic (how it is on the right side of the U.S.)
few examples:
0.06201... ok since it has a decimal, go Pacific, or left. start counting from the first non-zero digit all the way to the end. 6..2..0..1. that is 4 sig figs
3.41... decimal point is present yet again, go Pacific, or left. 3.41 = 3 sig figs
3.041... ok dont be worried because of the 0 inbetween, still count it. 3.041= 4 sig figs
3,000,000... ok, the first non decimal problem. since the decimal is *A*bsent, *A*tlantic, or start from the right. this is only 1 sig fig because the other digits are ALL zero, so dont count them. if it was 3,000,001 on the other hand, there would be 7 sig figs.
1.000... ok decimal points again. go Pacific, and count till end. dont worry that all of the other digits are 0's, count because of the decimal. 1.000 = 4 sig figs as 1.0000 = 5 sig figs.
4.0450... another decimal yay! still count all digits from Pacific. dont worry that the last digit is 0 again, still count it. 4.0450 = 5 sig figs
one more...
4,051,000... ok, no decimal so Atlantic (again that is right). count from first non-zero digit until it ends. 1..5..0..4.. that is 4 sig figs
so keep in mind
Atlantic = absent = right
Pacific = present = left[/quote]
this doesn't have anything to do with my question though
[quote=ClementZ]1.25" x 1.25 = 1.5625"
Your instruments only measure to the nearest hundredth of an inch, however your calculations get you to the ten thousandth, which is impossible given the comparative inaccuracy of your instruments.
That is the point of significant digits/figures.[/quote]
perhaps a more specific example should be given because I do not see why you would randomly make your answer less specific ..
1.25" x 1.25 = 1.5625"
Your instruments only measure to the nearest hundredth of an inch, however your calculations get you to the ten thousandth, which is impossible given the comparative inaccuracy of your instruments.
That is the point of significant digits/figures.
Significant figures are for accuracy. Let's say you measure something on the ruler, and your ruler goes in increments of 0.1 and you read something that lands exactly on the 2 mark, and you record that as "2.00" with significant figures. The extra "0" on the end shows the uncertainty or the "guess value", it also show how good your measuring tool is.
When you're doing a scientific experiment, you're reading figures from your equipment. You don't know the "missing" decimal places (it could be as little as 0 or as much as 9). So you have to give up accuracy for significance. - If you're doing computations on figures obtained from two different machines (with different displays), the "significance" of your computations are only as good as the poorest significance supplied to you by your equipment.
I agree.
Crap is stupid...
but if you don't understand them then they'll ruin your grade
Because they're significant.