Significant Figures ?
 

Hi everyone !

Well, I have this big issue in my head and I think for the most part I am like overthinking the problem...

My actual problem is the understanding of significant figures IN calculations.

For example...

The correct results WITH the correct sig. figs. for: (angles are in degrees)

1314.459 + 3.01
23.15 * 5.2
29.87777 / 2.0
31.7 * sin(76)
pi * 2.3
( 2.765 + 4.1 ) / ( squrt(3*sin(55)))

I think you get the idea... I get confused whenever I start to mix up angles and many digits from different COMBINATIONS of arithmetic operations.

I really hope someone could clarify this for me b/c its killing me and it's taking a LOT of points from my exams :(

Thanks a lot in advance.

DEJHAN

Re: Significant Figures ?
 

You should round your results to the below expressions to the stated sig figs:

1314.459 + 3.01: 3 sig
23.15 * 5.2: 2 sig
29.87777 / 2.0: 2 sig
31.7 * sin(76): 2 sig
pi * 2.3: 2 sig
( 2.765 + 4.1 ) / ( squrt(3*sin(55))): 2 sig

If a number is like 0.0001, that's 5 sig fig, but 0001 is 1 sig fig. If it's 2.32340 that's 6 - the 0 at the end counts if it's there. If it's 3.0, it's two, but 3. is also two - the decimal signifies that (though normally no one writes it like that). A number such as a constant like the speed of light is considered to have infinite sig figs. You should do all problems without rounding. Then at the end, round to the # of sig figs of the value in the problem with the least # of sig figs.

Re: Significant Figures ?
 

I think for number 4 it would be 3 sig figs since the sin(76) = .970295.....

Re: Significant Figures ?
 

Thank you but I still have something unclear; since the first calculation would yield a result of: 1317.469
How am I supposed to report that ? As 1317.47 ?

Could you please type ALL the results for the calculations I posted so I can see that and also that will help me to figure out things a bit quicker.

Thanks a lot !

Re: Significant Figures ?
 

Yeah the addition one are wrong.

Answers:

1. 1317.47 , 6 sig figs
2. 120 , 2 sig figs
3. 1.4 , 2 sig figs
4. 30.8 , 3 sig figs
5. 7.2, 2 sig figs
6. 4.9, 2 sig figs

For addition the sig figs are determined by the least amount of decimal places.
For multiplication they are determined by term with lowest amount of sig figs.

Re: Significant Figures ?
 

No. If a problem gives you 76 as the measure of an angle, then you must round your result to the # of sig figs of that given angle. sin(76) would need to be rounded to 2 sig figs if that's the only calculation - 0.57

Heh, I looked at #1 too fast and thought it was multiplication: "1314.459 + 3.01: 3 sig"

For addition and subtraction, you take the least # of digits after the decimal and make sure your answer has that # of sig figs. 1314.459 + 3.01 would equal 1317.47 (rounding to 2 sig figs after decimal).

If you had to add 0.000000001 to 1.1, you'd get 1.1. Because the limiting sig fig is from 1.1.

Re: Significant Figures ?
 

1314.459 + 3.01=1317.47
23.15 * 5.2 = 120 (2 sig digs)
29.87777 / 2.0 = 15
31.7 * sin(76)=30.3
pi * 2.3=7.2
( 2.765 + 4.1 ) / ( squrt(3*sin(55)))=3----1 sig dig(the 3 is only one sig dig)

for multiplication and division it is the total number of digits in the smallest number

for addition it is the highest place value (1200 would be 2 where as 1200.1 would be 5)

you do all arithmatic first then either round or truncate to correct digits

i am absolutly sure about this, i was the only one in my class (gifted) who could even understand why this is so.

Re: Significant Figures ?
 

You actually meant 4 in your last calculation right ? (1 digit)

And what would be the result for 23.15 * 5.9 ? Would 137 be correct ? (3 sig figs? -- but look that 5.9 has only 2 sig figs.)

Re: Significant Figures ?
 

So it's 140

Re: Significant Figures ?
 

"23.15 * 5.9 = 140 in sig figs"

That is why I hate sig figs. They are only cause for error in your answer. I have yet to be told by my school's teaching staff what purpose they have or how they are beneficial to our society.

Re: Significant Figures ?
 

If anyone wants a super detailed very correct way to understand and count significant figures I will copy it out of my Chemistry book for you. Just let me know.

Re: Significant Figures ?
 

It shows how accurate you measure to. When ever making a measurement you are suppose to only make the measurements you can. You don't measure to micrograms. You measure to milligrams at best. But it doesn't mean that when you measure to 1 milligram you measure to 1.000000000000000 or exactly one to the infinite significant digits. It is impossible. You may measure to 1.0 and leave off .04756345694351 of it. 1.05 of it is your sig fig. The last digit is understood to be uncertain. If When you make multiplications and additions you get decimals places you shouldn't have or are not accurate to what measurements you took. Sig figs get rid of these innacurracies. It give you the answer for the accurateness of measurement you took.

Oh yeah, and the 3 is understood to be 3.0000000 (infinite zeroes) so there is 2 sig figs on the last one.

Re: Significant Figures ?
 

So, if I do the following:

29.87777 / 2.0 = 15 (2 Sig. fig.)
and
29.87777 / 2 = 10 ( 1 Sig. fig. )

Is that correct ?

Re: Significant Figures ?
 

No, two would be understood as 2.00000000 to infinity so the answer would be 14.93889 to seven sig figs. This at least what my chem book says.

Re: Significant Figures ?
 

Is that true ?? So, not 1 sig. fig. but 7 !?!? (for the division by 2)

And also, for ( 2.765 + 4.1 ) / ( squrt(3*sin(55))) what is the correct result to the correct number of sig. figs. ??

Thanks a lot for the help so far guys, I am really putting some concepts together in my head :D

Dejhan