Significant Figures in Combined Operations

Covers how to determine the significant figures in problems containing a combination of addition/subtraction and multiplication/division.

[@marklandau365]

again, needing a refresher, i wish i could remember it as clearly and calmly as you tell it, but a million thank yous for this!

[@jessicajordan6906]

THANK YOU. I'VE BEEN TRYING TO FIGURE THIS OUT FOR WHAT FEELS LIKE AN ETERNITY, AND NOW I FINALLY UNDERSTAND!!!!!

[@Philosjutsu]

7:00 I have no idea how you jumped from having 3 sig figs to having 2 during the subtraction. For me the final answer should be 5.39 instead of 5.4. What happened?

[@XMostaxX]

0.0033557 (3sf or 5dp) - 0.00316456 (3sf or 5dp) = 0.000191147, if this was the final operation we would have to round at the 5th dp (because it's subtraction), but this isn't the final operation so we should put an underscore under the 5th dp (which happens to be the "9") making it 2 sf and not 3. Now since the last operation is multiplication, we need to round to the least number of sf which is 2 sf.

[@salmat0712]

Use this calculator www.omnicalculator.com/math/sig-fig

[@marklandau365]

o my god. this helped me so much! am freaking out abt quiz #1 tomorrow and i'm gonna watch this a couple times. good job/thx!

[@robertbryan6485]

Thank you, my teacher went over this in class way too fast so I didn't understand it. Your video was very helpful!

[@Paulakoala]

I greatly appreciate this video!!!! Keep up the good work.

[@cartoonpeach9208]

THANK YOU THIS MAKES SO MUCH SENSE

[@jeongaugustine3209]

wouldnt 1 divided by 298 be 1 sigfig only? since 1 has 1 sigfig?

[@flowerzzzzzzzzzz]

Hi, for 10.51 why is it 3 significant figure?

[@ecpchem]

Thank you for answering that question.

[@edrod8807]

you're a real one Eric

[@hassanz96]

great job brotha

[@OmarGarcia-xt1df]

Great video!

[@purplepineapple117]

Thank you so much.

[@mrprofile101]

2.84 is correct. It threw me for a loop too. With multiplication and division you use the answer with the least number of sig fig's to see how many sig fig's your final answer will be rounded to. 0.91+1.2+8.4=10.51 has only 3 sig figs in our case because of the addition performed beforehand, and 3.700 has 4 sig figs. When multiplying or dividing, our answer can only have the least number of sig figs, which in our case is the 3 sig figs that came from that 10.51, which means the answer is 2.84, and not 2.8.

[@risingstar6100]

Hi Eric, can you help me with my confusion for this situation where 2000 - 32.43. Is the solution 2000 or 1968?

[@ahmadandaleeb1781]

helped alot thanks

[@NickDuMortier]

@ minute 6:40 you say, "1/298, this had three significant figures." How does that work out to be three significant figures considering that "1" has one significant figure and "298" has three significant figures? I can't tell if this is a mistake or an exception.

[@JoshRogers]

+Nick DuMortier I am wondering the same. I thought this would be sig of 1.

[@arestes]

+Nick DuMortier well, he should've mentioned this: numbers that are there "exactly there to help writing" such as mathematical exactly defined constants (those that don't carry experimental uncertainty) are considered to have an infinite precision, that is, they don't influence the number of sig figs of quantities you multiply /divide/add/ etc them with. For instance, "pi" which appears in formulas, or in this case, this "1" , which is there just to help you write down the inverse of the measured value 298. You could as well have written "298^-1". Of course, there is a possibility that that 1 came from some measurement (say 1 gram or something and the 298 is given in cm^3). In that case he should've considered 1 sig fig for that 1.

[@arestes]

+arestes Other cases where numbers don't have sig figs are definitions such as 12 in=1 ft when converting units and used as a conversion factor ( 4.9875 ft = 4.9875*(12 in) should be computed with 5 sig figs becase that 12 doesn't have sig figs). Also, definitions such as the speed of light in meters per second (it is interesting to know the speed of light is not measured now, it is defined). the other case I know is when we have whole numbers that come from counting things carefully. They have infinite precision too.

[@hughg.rection3628]

+arestes I thought that we DO know, the number of sig figs for exact numbers, like for example 325000 here we have 3 sig figs but the the 3 zero's are ambiguous. So we would just say 3 sig figs ( unless a decimal is expressed, of course). But I can agree with you that number 1 could be just considered a non affecting number as just the inverse of a number, so it doesn't affect the sig figs. Good points. Very complex

[@arestes]

+TheNecromancer What you say about the ambiguous zeroes is true. They are significant but only if those zeroes came from a measurement, then you would have 6 sig figs in your example, but only three if those zeroes are only there to avoid using decimal places (3,25 times 10^5) and FINALLY, if that number 325000 came from COUNTING, none of the figures are significant.

[@cptdrscientist1]

Thank you. Seriously, this really helped me a lot. I was wondering though, doesn't 2.82 x 10(-16) x 1.91148 x 10(-4) come out to be 5.4 x 10 (-20) -- not 5.4 x 10(-19)? Or am I missing something else?

[@treevs]

it's 28.2 x 10^-16, not 2.82

[@arestes]

What textbook did he say they use?

[@sergioguevaramiller4108]

The ending was confusing both were in the -5 places but you said one is -3. How did you just get 2 sig figs in 1.9 this is so confusing!!!

[@andrearyan1350]

Please explain how you got 573.694? I added 459.44+144.25 = 603.7 Did I do something wrong, or did you add wrong?

[@PrideofPitchers]

after doing the first calculation you must have rounded. 459.444+114.25 = 573.694 but 459.44+114.25 = 603.69

[@blink7777777]

whys the 9 in 1.91148 the sig fig? minute 7.20

[@rubixcubesolve]

confusing on the last problem, but good video.

[@ecpchem]

You are going have to be more specific. I teach analytical chemistry at the university level. These are essentially the rules as outlined in every general and analytical chemistry book I have seen. You would not necessarily get the same answer when propagating uncertainty.

[@suhailanaura3051]

Second problem is wrong, you have 10.51/3.700 but only 1 spot to the right of the decimal is significant. So you'r eanswer is 2.8 not 2.84

[@HarrisZheng]

exactly

[@tonyhuang2594]

I don't get your explanation. I see it as this. The problem is division, and 10.51 is accurate to tenth place so 3 sig fig. You divide it and get 2.8405. You round 2.8405 to the least sig fig of 10.51 -3 sig fig- and 3.700 -4 sig fig. You round it and you get 2.84. Unless I am missing something.

[@suhailanaura3051]

With addition you can only have as many sig figs past the decimal point as the one with the least sig figs. So example is if you have 10.5 and 6.201 And you're told to add them together. You get 10.701 but you are only allowed ONE sig fig past the decimal, So your answer would be 10.7 because the 10.5 only has 1 sig fig past decimal. In his Second problem, he added up THREE terms. .91 1.2 and .84 So that means you're answer is only going to have 1 SIG FIG past the decimal because the 1.2 is the lowest sig fig past decimal. He got 10.51 which is fine, but after he divided he kept 2 sig figs when he completely forgot to apply the 1 sig fig past decimal rule. The answer should be 2.8 not 2.84

[@tommyw5332]

He did it correctly, I just don't think he adequately explained it. He did underline the 5 in 10.51, using the addition/subtraction rule correctly. Knowing 10.51 is only accurate up to 1 decimal place, you can count the numerator as having 3 significant figures (1, 0 and 5). When the last step (division) is done, the numerator is accurate to 3 significant figures and the denominator is accurate to 4, which means 3 significant figures is the most accuracy you can use in the final solution, making 2.84 correct. If this is still confusing, just know that what you're doing is trying to take the addition/subtraction rule to the final answer, when in fact it should only be applied to the portion of the problem utilizing addition/subtraction. Since addition/subtraction is not the final step, and division is, then you need only use the addition/subtraction rule to determine the amount of significant figures in that portion of the problem, which is all that is required by multiplication/division.

[@KingChristo]

Suhaila, zeros are only non significant when a decimal is not present. Because those zeros are after a decimal, they are significant.

[@berrie7098]

why do you round to 570 and not 574? are we going by decimal places for addition/subtraction or just # places in general (i.e. 10s, 100s, etc.)?

[@optikalillusion777]

your second problem is WRONG? is it?. i thought when adding/subtracting you only pay attention to right of the decimal place. You dont necessarily count significant figures? clarify?

[@angelikakwak6284]

+optikalillusion777 I agree.

[@seanc.reynolds8829]

+optikalillusion777 Actually, no (if it's the problem with 570 as the answer). Because of the division operation, you only know 459.44 to two significant digits which means the answer is only precise to the tens place, where the 5 digit is. On the other hand, you know 114.25 to the hundreths place, making it more precise. Since 459.44 is the least precise measurement in this specific problem it affects the result of the addition operation, so you can only report 573.694 answer to the nearest tens place as 570. There would be more error in your result, otherwise. You can actually go further and report the answer in scientific notation as 5.7 x 10^2 to make it clear that only two significant digits is your level of precision in the answer. This is one reason why scientific notation is used in general.

[@ryanschmidt7530]

+optikalillusion777 I believe the second problem is wrong. 1st, it is not in correct scientific notation. 2nd, when you're subtracting the two numbers in parenthesis after turning them into decimals, you end up with 4 sig figs. You are then left with the first value (28.2) having 3 sig figs and the second (.0001911) having 4 sig figs. After you multiply these two figures you end up with .0005390148x10(to power of -15 when you put the first value 28.2 in correct scientific notation). The your final answer is 5.39x10 (to power of -19) containing 3 sig figs. and correct scientific notation.

[@suhailanaura3051]

Nope. Second problem is wrong

[@samhall8876]

So many contradicting comments. Are the answers right, or are they wrong? I'm so confused

[@Theterrydaniel]

Why couldn't the teacher just say that? Thanks Bro!

[@ARMYALEX1869]

dont make ur answer "more fun" that just confuses us as to whether we should also add zeroes when the denominator has decimal places

[@maame8282]

The second problem is correct the way he did it. He's just not explaining it well

[@92Kleann]

I'm sorry but can you explain why you got 570 from 573.694? were you trying to make an ambiguous number? i just don't understand your reasoning.

[@01107345]

+Kara Burns He did it to put the answer in two significant figures.

[@salmat0712]

Thank you but according to this calculator there is alto of mistakes you have, this calculator is amazing for sig figs try it www.omnicalculator.com/math/sig-fig Oh This is ten years after the video was published

[@optimusprimo]

please remove this video, people cannot learn from incorrect examples until much later. this video is very misleading

[@shagunthakur665]

Last 2 example explanation is wrong 😡😡😡

[@hasanozbey1013]

you've got too many wrongs out there