I'm in year 11, and we have so far had 4 weeks of term, in chemistry class I've learnt next to nothing, that's from 4 weeks! In just half an hour I'm almost learnt all of what has been taught for the whole 4 weeks, thank you very much Prof. Dave!
I'm in the first grade of high school, and you are the first and only person that got me interested in chemistry. I was always interested in physics and biology, but not this. Thank you Dave, you just made me feel smarter.
in case anyone here is unable to go to college and is trying to self-teach themselves college-level chemistry, his videos provide you with everything you need. I'm currently in college and 90% of the curriculum is based off of his channel and his vids. i think im going to drop out because im paying tuition to a college that assigns his FREE youtube vids as homework. It is 100% possible to self teach yourself chemistry, education is truly everywhere and in our faces, its up to us to use it.
I've started chemistry learning in detail by following your practical courses. This channel provides essential information for students and other enthusiastic readers to a better understanding of general aspects of chemistry.
+Marian Iskandar I am most pleased to help teachers in the classroom! Honored to be of assistance. Stay tuned as I upload the remaining 25 or so general chemistry clips over the upcoming weeks.
Holy moly, I thought I understood sig figs, but you explained it way better than my chemistry teacher in a tenth of the time. I found you trough your debunking content and I'm glad I did. I just started the general chemistry series and I can already tell that school is about to get a lot easier. Thank you, Dave.
I'm 34 going back to school, and can't believe this stuff used to trip me up so much when I was younger. It's actually not too bad thanks to you, Professor Dave. Probably won't feel this confident the entire way through the playlist though lol.
One rarely mentioned rule is that when multiplying by an integer where no decimals are possible, such as counting, the integer has infinite sig figs. This reconciles the discrepancy that comes from sig fig rules of adding 5 identical values versus multiplying the identical value by 5.
For example, if 2.33 x 18 included two measurements, 2 sigfigs in the answer. However, if 2.33 were measured and 18 was a precise count, the answer would be three sigfigs. It wasn't as clear in the video. Don't get me wrong, your videos are great!
I have such a weird situation being an adult pursuing astrophysics and understanding a lot of science but not really the fundamentals of chemistry at all 😅 throughout grade school we kept having science teachers leave in the middle of teaching specific curriculum to my class in particular, then they’d be replaced with a new science teacher who would start with a different subject in science. I loved learning science but it was hard to be taught the fundamentals of it when we never fully covered topics. I also have trouble comprehending the way some teachers explain things as well, but I could understand this very clearly. I really liked the learning check and even though it’s intended for a class I was able to go back and reanalyze the rules for identifying sig figs. At first I was a bit confused but it really helped to have control over the video to repeat things if I didn’t get it the first time. Thank you so much for what you do, my science teacher in high school actually stayed and he taught us what he could but my class was already pretty far behind. I wanted to score better on the ACT and even asked him if he could help me prepare but he had to explain that he isn’t even teaching the curriculum, the curriculum is in AP classes. I didn’t even make benchmark. He did also explain that many public schools have more of a priority to make money than to actually teach so they’ve let kids go to the next grade who weren’t ready, they could only send a specific amount of students to special needs schools (Me having adhd, if I couldn’t focus I was just thrown in the hall and never given real solutions to my educational needs), and they wouldn’t do anything about disruptive behaviors just send kids to the hall for that too since they couldn’t give a lot of kids detention due to the school board chewing the staff out over it despite it literally being a behavioural issue. I don’t at all believe our government actually advocates for education, I’m very disappointed with the way my early education was handled. But again, I’m very grateful to have this information presented to me for free in a way that allows me to sit down and listen.
Hi there, how do we determine the sig fig of uncertainty, standard devaition , relative standard deviation and standard error in analytical chemistry? thank you very much
Hi just want to say thank you for making those videos. They are super helpful when I need to refresh my memory of some old knowledge I learned from school a long time ago. Also I learned all this in Chinese and usually have no idea what the English equivalents are. Your videos especially illustrations help me to pair them up. Thanks!
I was taught that if 5 is preceeded by an even number, round down (1.25 -> 1.2). If it’s preceeded by an odd number, round up (1.15 -> 1.2). The theory is that since 5 is exactly halfway between 0 and 10, it should be rounded up half the time and down the other half, so in the long run it will balance out. Otherwise, when rounding a large number of numbers the result will be biased if 5 is always rounded one way. which is correct?
When you say about the estimation 10000 that is anything between 9500 to 10499, it means you have two sig figs, 1 and 0. But if you say anything between 5000 to 14999, then you have one sig fig.
Cause it’s addition, only the lowest decimal place (3.8) needs to be in the answer. You’re applying the multiplication rule of sigfigs which is least amount of sigfigs, which you would be right that it needs to be rounded up to 21. The real answer is 20.672, but with addition rule of sigfigs, you need to round to the tenths place = 20.7. 👍
Surely any number between 5,000 and 14,999 would round to 10,000 in the example you gave. This should be basic maths for me; I can't think where I'm going wrong
I do not understand why 0.00004050 has 4 sig figs instead of 9. Aren't the 0's there certain? If I measure some to the precision of 8 decimal places, how can the 0's be uncertain?
Hi Dave I want to ask you a question about that. For example when I multiply 20 with cos25, should I round the result to 20? Because 20 has the least significant figures. 20*cos25=20? Could you help me?
Wow! Thankyou Professor.. I have referred many videos for sig fig, but this one really awesome.. Gives me an insight of sig fig.. One question.. If the value is 10,000.00 then is it have 7 sig fig?
@@ProfessorDaveExplains Based on the rules given in this video, I'm having trouble understanding this example. If we apply the rules one by one to the given value 10,000.00: 1. Non-zero digits are significant That's one significant digit so far, the 1 at the very start, since all the other digits are zero. 2. Zeros in between other non-zero digits are significant Doesn't change our total of 1 significant digit, since there isn't another non-zero one for anything to go between. 3. Leading zeros are not significant Doesn't matter for this example since there aren't any. 4. Trailing zeros are only significant if they are decimal zeros In my understanding, this would only make the last two zeros in 10,000.00 significant, as all the others come before the decimal point. Meaning that the final answer would be 3 sig figs: the 1 at the start and the two 0s at the end. So if the real answer is actually 7 sig figs, shouldn't rule 2 instead say that any zeros between significant digits are significant, even if those significant digits are themselves zero? Sorry if I'm not making sense, I'm pretty confused since I don't remember hearing about this particular subject in school, and while I could certainly memorize these rules, I am not sure if I understand the reasoning behind them, or even the purpose they serve.
I needed this because I STILL don't 'get' why zeros AFTER the decimal point, but before the first non-zero digit, aren't significant. If you KNOW you've got 35 millionths of an inch, 0.035000in, why isn't the tenth of an inch 0 'significant'? Accurately measure down to the millionth of an inch, by definition you've accurately measured the tenths also. It's probably just a subtlety in use that makes sense when you start doing calculations and want to keep the number of significant digits consistent, so that your measurements and figures can be reliably duplicated by others, without getting kinked up with rounding errors and so forth. I wish I didn't have this nagging little feeling that I'm missing something, but the video is consistent with what I remember being taught, and the rules are unambiguous, so it's just a little quirk I'll have to DEAL WITH!!! 🙂
leading zeros do communicate information about a number, but they are not significant because they don't convey any information about the precision of the measurement. to understand this, imagine you measure something as 5.2 cm, which has two significant figures (one measured + one estimated digit). you can also represent the same value as as 0.052 m; you've gained two leading zeros, _but the precision of your measurement has not changed,_ so they cannot be counted as significant figures.
@@cartermilan Thanx for clarification. I'm not great with math on paper, and I remember having a little trouble with this way back in my school days, so I appreciate it when I can learn or relearn something. Even when I rarely encounter this or that factoid in day-to-day life, there's no such thing as too much learning! 🙂
2:04 isn't that wrong? You're saying that 10,000 has one sig fig but 9,500 and 10,499 both approximate to 10,000 only if the first zero after 1 is also considered a sig fig. If not, then 5,000 and 14,999 both approximate to 10,000. Where am I going wrong?
2:04 looking at this 10,000 example which has one sig fig, you say that anything between 10,499 and 9,500 gets rounded to 10,000. why is the range +499 and -500 of the number? shouldn't it be +500 or -500? shouldn't the upper range be 10,500 instead of 10,499?
2:35 you said 9.365 rounds to 9.37 but It says "if it is 5 then the digit before it affects the answer by its parity (odd / even)" in my textbook. And I think 9.365 rounds to 9.36 because 6 is even.
If I should take the minimal number of minimal decimal places for an addition / subtraction, wouldn't this mean 10,000 + 1 (0 decimal places) is 10,001? This seems to contradict the example when we estimate 10,000 people in the room, and one enters.
Just for clarify the above question, if I use 5 x 3 which both have only 1 sig fig the result would be 15 which has 2 sig figs. but if the rule said use the fewest sig fig then it must show only 1 sig figs in the result, how come for this case?
that's right, if five and three were measurements taken on a device that only measures in increments of ten, then five times three would indeed be 2 x 10^1, since we can only have one sig fig! as for the previous question, it's 18, since that has two sig figs.
Ah using scientific number 2x10^1. Professor don't you think 2x10^1 have less accuracy than 15? How this rule help science as I believe this is less accuracy. I'm sorry for keep asking questions but your lesson is very interesting.
well we have no idea about accuracy, that depends on the situation. but yes it is less precise. however, as is mentioned in the video, we can't estimate beyond one digit further than is inherent in the instrument, so if you were using a graduated cylinder with tick marks for every 10 mL, and you estimated 3 mL and 5 mL for two measurements, you absolutely can't use more than one sig fig, and your calculations using these measurements must obey that degree of precision. but this only applies to measurements, if just multiplying 3 and 5 as counting numbers, sig figs don't apply.
Yes professor, I understand +/- when we use cylinder with tick marks and no questions to your explanation at all. But my problem still multiply and divide for example if the car drive at fast 5 m/s for 3 sec. how far the car can go? you could see 5 x 3 = 15 m. And it will be very odd to give the result 2 x 10^1, don't you think so? Note, all 3 things have different unit hence different measuring tools. so why we limit calculation result to sig fig? last, I agree that counting number does not apply but shouldn't all not apply?
Hi professor Dave! I really love your videos, and I have learned a lot. I have a question tho, I'm kinda confused, in checking comprehension part 1 number 1 isn't it 8 sig figs is the answer because of rule 2?P.S Prof.Dave might not notice, but if someone knows the answer feel free to enlighten me... thank you prof and to whosoever that'll notice me 02:43
how many significant figures are in 100.0 because the 0 in the decimal counts as a significant figure so do the zeros between the 1 and the zero in the decimal count as significant figures?
Hey, Professor Dave! I just want to ask, in the sample test, isn't the answer to 16.872 + 3.8 should be just 21? because the least number of sig figs is only 2? Thanks :)
1:34 Rule : Leading zeros are NOT significant. Impact : 0.01 has only 1 sig figs. 1:46 Rule : trailing desimal zeros are significant {not significant without decimal) Impact : 50000 has only 1 sig fig. 2:25 Rule : When multiplying are dividing, use the fewest number of sig figs. Impact : *Dividing* 451 has 3 sig figs. 0.01 has 1 sig fig. When dividing, use 1 (fewest number) of sig figs. ==> 451 : 0.01 = 45100 (oh no, it has 5 sig figs) ==> 50000 (1 sig fig) DONE. *Multiplying* 451 has 3 sig figs. 100 has 2 sig figs. ==> 451 x 100 = 45100 (oh no, it has 5 sig figs), let's make it 2 sigfigs..!! ==> 45000 (2 sig figs) From now on, 1/0.01 is never be 100. Don't ask me.
Shouldnt the number of sig figs be defined by the measurement method? For example, if your instrument measures to two decimal places but you get a measurment of 100. Wouldn't that cause some issues? Please tell me if i am missing something.
If your instrument (let’s say a scale here) measures to two decimal places and you have an object that weighs exactly 100g, then the scale would read 100.00g. Because the two zeros are decimals, they are significant figures, meaning the measurement has 5 sig figs. Did I understand your question correctly?
To me this seems to be standardization for dealing with estimations due to the obvious lack of perfect precision in the real world. So I was wondering why we wouldn't use the precision of the measuring method to define the number of sig figs. Though my question was erroneous, I was attempting to point out a possible flaw. So my question still stands when dealing with whole numbers. For example, if your measuring method is precise to the hundreds place but your value happened to be 100000.
@@AlphaOfCrimson if you had something that weighed 100,000g and a scale that only measured increments of 100, it would ideally have 4 sig figs if I’m not mistaken. To convey this, you could always write the measurement in scientific notation as 1.000 * 10^5.
How do we communicate the difference of an estimation and exact number. If I am wanting to calculate exact numbers to get the most precise study done of people going to night clubs. So then I record exact numbers of attendees every night and one of the nights there is 100% exactly 10,000 what would the standard way of communicating that be? I know we don't always have to follow standards but its often best practice.
In the comprehension I got answer 41.94 for the 3rd one in calculations ..there the ending number is below than 5 so should round down right..? but I can understand that 41.94 is 42 but by the rules I should round down.. prof dave or anybody reply
i'm sorry Professor, I'm a little bit confused to the rule. what if we multiply point number 3 in the calculation board into (2.33 x 17) instead of (2.33 x 18), the result would be 39.61. Now, because it should be 2 sig figs, then we must round it down first (39.6), because it still 3 sig figs then we round it up, so we get 40 right, But you said once, the trailing zero rule, if 35000 has only 2 sig figs, then 40 has only 2 sig fig, we know it contradicts to each other in that case. What should we do for that? Thank you, Professor Dave.
i mean 40 has only 1 sig fig, while the rule for multiplication and division is that the answer must have the fewest sig figs. but in this case where it should be 2 sig figs (because of 17), now it has only 1 sig fig.
so the key is that the 40 in this case cannot be seened as the way that 35000 represents, because it is an estimation, while 40 has decimal after it. hmm, i got that. Thank you very much, Professor.
I cannot understand the logics in Sig. Figures. First off, is there a logic behind it? The chem book "Chemistry by Zumdahl", 10th edition, gave the example of 2 different grapefruits being weighed on two differente balances. One balance is not very precise and give only 2 digits (such as 10g, 1.2g, etc) and the other balance gives up to 4 digits (such as 2000g, 1.758g, etc). He says that: - grapefruit 1 weighed 1.5g in the less precise balance and 1.476 in the precise one. - grapefruit 2 weighed 1.5g in the less precise balance and 1.518g in the precise one. With that in mind, he then states: Do the two grapefruits weigh the same? The answer depends on which set of results you consider. Thus a conclusion based on a series of measurements depends on the certainty of those measurements. For this reason, it is important to indicate the uncertainty in any measurement. This is done by always recording the certain digits and the first uncertain digit (the estimated number). These numbers are called the significant figures of a measurement. Therefore, he says that significant figures are used to express the certainty of a measurement. Just to refresh, certainty of a number refers to the true value of something. For example, if I have a jar that only measures 1 liter and 2 litters, and let's say I filled this jar up to about 1,5 liter. Observe that I know I have at least 1L of milk (because it has passed the 1L mark on the jar), thus 1 is a certain digit. However, the last digit (5) is only an estimated digit, since I measured it only by relying on my eyes rather than a precise instrument. Therefore, I can have 1.6 liter of milk but my eyes believe I have only 1.5. Therefore, the last digit (5) is what we call UNCERTAIN digit. If you think for a little while you will realize that uncertain digits are always the last digit of a number. Now is the thing that I don't understand. As I mentioned (4th paragraph), the book says that Sig. Fig. are the certain digits and the first uncertain digit of a number. So, the number 0,0025 has 4 CERTAIN digits (the zeros and the 2) and 1 uncertain digit (the 5, which is the last digit of the number). Thus, if the certain digits and the first uncertain one is called significant figures (see paragraph 4), why does 0,0025 has only 2 Sig. Fig. instead of 5? I mean, 0,002 are the certain digits and 5 is the uncertain one.
If 500 and 500. are exactly the same, why does 500. have 3 significant digits and 500 has only 1. Isn't 500 without the two zeros become 5 (with the same number of significant digits) and those 2 zeros after the 5 are super significant because they give you the correct place value of the 5 before them?
They aren't exactly the same, at least not in the context of scientific notation. 500 is precise only to the hundreds place, implying that it could represent anything from 450 to 549 while 500. means it is precise to the units place, so it could be anything from 499.5 to 500.4 because of the decimal listed.
Significant Figures and Scientific Notation: Significant Figures - Digits in a measurement that degree of accuracy of a measurement. - Applies to measurements written in standard or scientific notation.(technically just everything numerical :D) - Rules of SF must be followed. :) Rules of Significant Figures: Significant: - Non-zero numbers (1,625) - Zeroes between non-zeros (2,025) - Trailing zeroes AFTER decimal (14.00) - Trailing zeroes in a whole number WITH THE DECIMAL (640.) - Scientific Notation(Only the mantissa): M x 10 (2.60 x 101) Not significant ☹: - Leading zeros (0.0032) - Trailing zeros in a whole number with NO decimal (54000) - Scientific Notation(Only the base): M x 10 (2.60 x 101)
Rounding Measurements: Rounding-off measurements based on number of SF: 1. Determine the number of given significant figures in a measurement. 2. Perform the operation required. 3. For final answer, round off to the desired number of SF following the measurement reading with the LEAST number of SF. 4. Apply the “FIVE and UP Rule”(obv) as discussed in math and grade 7 Integrated Science….. actually what was discussed in primary :). Rounding-off measurements based on precision: 1. Determine precision of instrument of the used instrument of the given measurement readings. 2. Perform operation required. 3. For the final answer, round off to the decimal place of the LEAST precise measurement reading in the given. 4. …. “FIVE and UP rule”
Scientific Notation: Scientific Notations - representation of very small/large measurements. - Used when computations(especially in sciences) need to be precise Rules for writing measurements in Scientific Notation: 1. Value of base is equal to 10. 2. Exponent is non-zero integer. 3. The absolute value of the coefficient is greater than or equal to 1 but it should be less than 10. Mantissa - M x 10x - M < 10 Base - M x 10x - Always 10 Exponent - (really obvious) M x 10x THIS LITTLE GUY - ALWAYS a non-zero integer :)
Example of usage: - Standard: 1,5321 - Scientific Notation: 1.5321 x 104 1.5321 is mantissa; 10 is base; 4 is the exponent of the base I just copy pasted my notes from before
Hey professor, I wanted to ask why 1000.09 has 6 sig figs but 54700 has only 3, as you said that the zeros that we take in consideration are the zeros after decimal so 1000.09 should have only 2 sig figs I.e 1 and 9
I'm in year 11, and we have so far had 4 weeks of term, in chemistry class I've learnt next to nothing, that's from 4 weeks! In just half an hour I'm almost learnt all of what has been taught for the whole 4 weeks, thank you very much Prof. Dave!
@@amberheard2869 Take care buddy.
Wait..are you 11 years in age or grade? This very material was taught on us on the 10th grade bruh
@@martinmaxwell3508 year 11 is 15/16 years old
@@keevagrady8316 i see
@@armgord lucky
I'm in the first grade of high school, and you are the first and only person that got me interested in chemistry. I was always interested in physics and biology, but not this. Thank you Dave, you just made me feel smarter.
in case anyone here is unable to go to college and is trying to self-teach themselves college-level chemistry, his videos provide you with everything you need. I'm currently in college and 90% of the curriculum is based off of his channel and his vids. i think im going to drop out because im paying tuition to a college that assigns his FREE youtube vids as homework. It is 100% possible to self teach yourself chemistry, education is truly everywhere and in our faces, its up to us to use it.
But the point of going to college is getting a degree……? Sad to hear that your classes only show videos though :(
@@michilovr probably will get degree from private source and not college
@@swanhuri I didn’t even know that was possible wow 😧
@@michilovr in india, it is very much possible. Money-game
@@swanhuri this is pretty amazing to hear... can you explain further where they get these degrees from? I'm interested
I've started chemistry learning in detail by following your practical courses. This channel provides essential information for students and other enthusiastic readers to a better understanding of general aspects of chemistry.
damn who's dictionary did you swallow to learn how to talk like that???
Much clearer than my university level physics textbook.
The comprehension music is my jam
Got my finals grade in college for the first semester, thank you Prof. Dave, I passed my chemistry.
Found this for a chem lab and lemme just say
*SCIENCE JESUS*
I'm going to be using your videos all the time in my class! These set of videos are so helpful!!! Thank you! :)
+Marian Iskandar I am most pleased to help teachers in the classroom! Honored to be of assistance. Stay tuned as I upload the remaining 25 or so general chemistry clips over the upcoming weeks.
Time flies..
@@martinmaxwell3508 for real
@@martinmaxwell3508 indeed
@@martinmaxwell3508 yes
Holy moly, I thought I understood sig figs, but you explained it way better than my chemistry teacher in a tenth of the time. I found you trough your debunking content and I'm glad I did. I just started the general chemistry series and I can already tell that school is about to get a lot easier. Thank you, Dave.
This is probably the most useful youtube channel around.
I'm 34 going back to school, and can't believe this stuff used to trip me up so much when I was younger. It's actually not too bad thanks to you, Professor Dave. Probably won't feel this confident the entire way through the playlist though lol.
One rarely mentioned rule is that when multiplying by an integer where no decimals are possible, such as counting, the integer has infinite sig figs. This reconciles the discrepancy that comes from sig fig rules of adding 5 identical values versus multiplying the identical value by 5.
yep that's in here too!
For example, if 2.33 x 18 included two measurements, 2 sigfigs in the answer. However, if 2.33 were measured and 18 was a precise count, the answer would be three sigfigs. It wasn't as clear in the video. Don't get me wrong, your videos are great!
lawl my science teacher showed us this, and we all exploded with laughter at your intro xD
pretty good stuff, no?!?
+Professor Dave Explains 😜😜
lolol The intro was the weirdest part...In fact, he used the SAME video for the new eighth graders...what a creative teacher
woild've been hella lit
Daddy Lusa
Thank you so much professor :)! the checking comprehension part is awesome.
I have such a weird situation being an adult pursuing astrophysics and understanding a lot of science but not really the fundamentals of chemistry at all 😅 throughout grade school we kept having science teachers leave in the middle of teaching specific curriculum to my class in particular, then they’d be replaced with a new science teacher who would start with a different subject in science. I loved learning science but it was hard to be taught the fundamentals of it when we never fully covered topics. I also have trouble comprehending the way some teachers explain things as well, but I could understand this very clearly. I really liked the learning check and even though it’s intended for a class I was able to go back and reanalyze the rules for identifying sig figs. At first I was a bit confused but it really helped to have control over the video to repeat things if I didn’t get it the first time. Thank you so much for what you do, my science teacher in high school actually stayed and he taught us what he could but my class was already pretty far behind. I wanted to score better on the ACT and even asked him if he could help me prepare but he had to explain that he isn’t even teaching the curriculum, the curriculum is in AP classes. I didn’t even make benchmark. He did also explain that many public schools have more of a priority to make money than to actually teach so they’ve let kids go to the next grade who weren’t ready, they could only send a specific amount of students to special needs schools (Me having adhd, if I couldn’t focus I was just thrown in the hall and never given real solutions to my educational needs), and they wouldn’t do anything about disruptive behaviors just send kids to the hall for that too since they couldn’t give a lot of kids detention due to the school board chewing the staff out over it despite it literally being a behavioural issue. I don’t at all believe our government actually advocates for education, I’m very disappointed with the way my early education was handled. But again, I’m very grateful to have this information presented to me for free in a way that allows me to sit down and listen.
If no one can see the humor in Jesus teaching chemistry, then I don't know what to say man.
the Messiah has finally come to save my Chemistry grades
Lol the name of the lord is sacred thou shalt not put in such a humurous comment
@@rosa578 🤣
@@KJ-rc6qs 🤣🤣🤣
@@user-vo6hl8sp6b ha
In school we were taught that when you count something then the number has infinite significant figures like 20 books can be 20.00000000...... Books
correct! counting numbers have unlimited precision.
Hi there, how do we determine the sig fig of uncertainty, standard devaition , relative standard deviation and standard error in analytical chemistry? thank you very much
Bless you professor, from Los Angeles.
Hi just want to say thank you for making those videos. They are super helpful when I need to refresh my memory of some old knowledge I learned from school a long time ago. Also I learned all this in Chinese and usually have no idea what the English equivalents are. Your videos especially illustrations help me to pair them up. Thanks!
Great resource for my students. Thanks
I wish i had found these videos 5 years ago when i was taking chemistry in undergrad but its nice to relearn with all of these videos
Thank you professor dave, I struggled with sigfigs for so long
I was taught that if 5 is preceeded by an even number, round down (1.25 -> 1.2). If it’s preceeded by an odd number, round up (1.15 -> 1.2). The theory is that since 5 is exactly halfway between 0 and 10, it should be rounded up half the time and down the other half, so in the long run it will balance out. Otherwise, when rounding a large number of numbers the result will be biased if 5 is always rounded one way.
which is correct?
yeah I was wondering the same
When you say about the estimation 10000 that is anything between 9500 to 10499, it means you have two sig figs, 1 and 0. But if you say anything between 5000 to 14999, then you have one sig fig.
i love this guy so muchhhh, thanks for saving my physic class
very understandable. thank you, prof.
much better than the crash course video on this topic
*pauses video and counts people in the crowd*
I'm from Peru and i'm here because i need to learn chemistry in english, thank you very much for your videos
1:04 "We do not have access to that level of precision" after getting it spot on.
Thanks Professor Dave Explains.
Why in 3:04 is the answer to question 2 of section 2 20.7 and not 21? Considering the fact that sig figs of 3.8 are 2?
Cause it’s addition, only the lowest decimal place (3.8) needs to be in the answer. You’re applying the multiplication rule of sigfigs which is least amount of sigfigs, which you would be right that it needs to be rounded up to 21. The real answer is 20.672, but with addition rule of sigfigs, you need to round to the tenths place = 20.7. 👍
thankyouuuu Prof. Dave ! this really help me to undestand significant figures ^^ ♡♡♡
thank you Sare your videos are very useful to me
I'm rewatching to retain my knowledge from my 11th and 12th grade about gen chem and gen bio to test my knowledge and prepare for my biochem class☺️
Surely any number between 5,000 and 14,999 would round to 10,000 in the example you gave. This should be basic maths for me; I can't think where I'm going wrong
I do not understand why 0.00004050 has 4 sig figs instead of 9. Aren't the 0's there certain? If I measure some to the precision of 8 decimal places, how can the 0's be uncertain?
I used this channel when I was younger to learn stuff for fun. Now I'm using it for school...
Thank you so much Professor Dave!!
Hi Dave
I want to ask you a question about that.
For example when I multiply 20 with cos25, should I round the result to 20? Because 20 has the least significant figures.
20*cos25=20?
Could you help me?
I subscribe just because of that funny intro 😂 I laughed longer than the initial video 😝
Wow! Thankyou Professor.. I have referred many videos for sig fig, but this one really awesome.. Gives me an insight of sig fig.. One question.. If the value is 10,000.00 then is it have 7 sig fig?
that's correct!
@@ProfessorDaveExplains Based on the rules given in this video, I'm having trouble understanding this example. If we apply the rules one by one to the given value 10,000.00:
1. Non-zero digits are significant
That's one significant digit so far, the 1 at the very start, since all the other digits are zero.
2. Zeros in between other non-zero digits are significant
Doesn't change our total of 1 significant digit, since there isn't another non-zero one for anything to go between.
3. Leading zeros are not significant
Doesn't matter for this example since there aren't any.
4. Trailing zeros are only significant if they are decimal zeros
In my understanding, this would only make the last two zeros in 10,000.00 significant, as all the others come before the decimal point. Meaning that the final answer would be 3 sig figs: the 1 at the start and the two 0s at the end.
So if the real answer is actually 7 sig figs, shouldn't rule 2 instead say that any zeros between significant digits are significant, even if those significant digits are themselves zero?
Sorry if I'm not making sense, I'm pretty confused since I don't remember hearing about this particular subject in school, and while I could certainly memorize these rules, I am not sure if I understand the reasoning behind them, or even the purpose they serve.
I needed this because I STILL don't 'get' why zeros AFTER the decimal point, but before the first non-zero digit, aren't significant. If you KNOW you've got 35 millionths of an inch, 0.035000in, why isn't the tenth of an inch 0 'significant'? Accurately measure down to the millionth of an inch, by definition you've accurately measured the tenths also.
It's probably just a subtlety in use that makes sense when you start doing calculations and want to keep the number of significant digits consistent, so that your measurements and figures can be reliably duplicated by others, without getting kinked up with rounding errors and so forth. I wish I didn't have this nagging little feeling that I'm missing something, but the video is consistent with what I remember being taught, and the rules are unambiguous, so it's just a little quirk I'll have to DEAL WITH!!! 🙂
leading zeros do communicate information about a number, but they are not significant because they don't convey any information about the precision of the measurement. to understand this, imagine you measure something as 5.2 cm, which has two significant figures (one measured + one estimated digit). you can also represent the same value as as 0.052 m; you've gained two leading zeros, _but the precision of your measurement has not changed,_ so they cannot be counted as significant figures.
@@cartermilan Thanx for clarification. I'm not great with math on paper, and I remember having a little trouble with this way back in my school days, so I appreciate it when I can learn or relearn something. Even when I rarely encounter this or that factoid in day-to-day life, there's no such thing as too much learning! 🙂
Thanks professor 💜️
I LOVE THIS GUY!!!!! THANK YO A LOT. YOU ARE A LIFE SAVER FRR
thank you for teaching me what significant figures are👏👏👏👏
we're having a test on physics in a few minutes, and here i am reviewing for the last minutes 😊‼️
💞❤️Amazing way of Teaching 💞❤️
I just started his series and it's helpful but can you please how computation? thank you huhu
way better explanation for sigfigs then my chem teachre
thank you professor dave
Thank u for helping me even though this vid is before 6 years
Im thinking ill go biochem so this is really helpful thanks!
2:04 isn't that wrong? You're saying that 10,000 has one sig fig but 9,500 and 10,499 both approximate to 10,000 only if the first zero after 1 is also considered a sig fig. If not, then 5,000 and 14,999 both approximate to 10,000. Where am I going wrong?
Unit of measurement 0:18
2:04 looking at this 10,000 example which has one sig fig, you say that anything between 10,499 and 9,500 gets rounded to 10,000. why is the range +499 and -500 of the number? shouldn't it be +500 or -500? shouldn't the upper range be 10,500 instead of 10,499?
0.5 is conventionally rounded up (to 1)
Thank you professor!
2:35 you said 9.365 rounds to 9.37 but It says "if it is 5 then the digit before it affects the answer by its parity (odd / even)" in my textbook. And I think 9.365 rounds to 9.36 because 6 is even.
No, the 5 makes it round up.
@@ProfessorDaveExplains Ok, thanks.
Damn this all began 7 years ago
India's Ncert Book Has Diff Rules For Sig figs and the rules of calculations.
i learned more in this then two years of chemistry class
Does this sig fig rule apply for every word problem in any science course?
0.00024, and 20000 why are these zeroes not siginificant? They do impart some info about our calculation ... can anyone help explain this?
If I should take the minimal number of minimal decimal places for an addition / subtraction, wouldn't this mean 10,000 + 1 (0 decimal places) is 10,001? This seems to contradict the example when we estimate 10,000 people in the room, and one enters.
Thank you Dave! Very cool!
I'm inspired by this program
Yeeeh the intro's fire
This video was used for an EdPuzzle in my chemistry class. Just thought you should know.
fam i for sure got 1 right on the whole comprehension check
How do you come up to your answer in Number 4 calculation? Why it became 4.36?
Professor, when multiplying use the fewest number of sig figs. if the question is 6.0 x 3.0, the answer would be 18 or 18.0?
Just for clarify the above question, if I use 5 x 3 which both have only 1 sig fig the result would be 15 which has 2 sig figs. but if the rule said use the fewest sig fig then it must show only 1 sig figs in the result, how come for this case?
that's right, if five and three were measurements taken on a device that only measures in increments of ten, then five times three would indeed be 2 x 10^1, since we can only have one sig fig! as for the previous question, it's 18, since that has two sig figs.
Ah using scientific number 2x10^1. Professor don't you think 2x10^1 have less accuracy than 15? How this rule help science as I believe this is less accuracy. I'm sorry for keep asking questions but your lesson is very interesting.
well we have no idea about accuracy, that depends on the situation. but yes it is less precise. however, as is mentioned in the video, we can't estimate beyond one digit further than is inherent in the instrument, so if you were using a graduated cylinder with tick marks for every 10 mL, and you estimated 3 mL and 5 mL for two measurements, you absolutely can't use more than one sig fig, and your calculations using these measurements must obey that degree of precision. but this only applies to measurements, if just multiplying 3 and 5 as counting numbers, sig figs don't apply.
Yes professor, I understand +/- when we use cylinder with tick marks and no questions to your explanation at all. But my problem still multiply and divide for example if the car drive at fast 5 m/s for 3 sec. how far the car can go? you could see 5 x 3 = 15 m. And it will be very odd to give the result 2 x 10^1, don't you think so? Note, all 3 things have different unit hence different measuring tools. so why we limit calculation result to sig fig? last, I agree that counting number does not apply but shouldn't all not apply?
Hi professor Dave! I really love your videos, and I have learned a lot. I have a question tho, I'm kinda confused, in checking comprehension part 1 number 1 isn't it 8 sig figs is the answer because of rule 2?P.S Prof.Dave might not notice, but if someone knows the answer feel free to enlighten me... thank you prof and to whosoever that'll notice me
02:43
Rule 3 says leading zeros are insignificant
how many significant figures are in 100.0 because the 0 in the decimal counts as a significant figure so do the zeros between the 1 and the zero in the decimal count as significant figures?
yep, that would be 4 sig figs
Thank you, and thank you for working on those videos, they help a lot! 😃
i have a question why does 2.33x18= 42 (2 sig figs) but the 31.9/7.318= 4.36 and (3 sig figs)
Professor i have question 162.53+32 then the number of significant figure are?Please must explain professor
Thank you so much
So a good way to look at sig figs is as if they were an approximation of something?
Hey, Professor Dave! I just want to ask, in the sample test, isn't the answer to 16.872 + 3.8 should be just 21? because the least number of sig figs is only 2? Thanks :)
ah but remember the rules! when adding and subtracting, we round to the fewest number of decimal places, not significant figures.
Alex Ofina
1:34 Rule : Leading zeros are NOT significant.
Impact : 0.01 has only 1 sig figs.
1:46 Rule : trailing desimal zeros are significant {not significant without decimal)
Impact : 50000 has only 1 sig fig.
2:25 Rule : When multiplying are dividing, use the fewest number of sig figs.
Impact :
*Dividing*
451 has 3 sig figs.
0.01 has 1 sig fig. When dividing, use 1 (fewest number) of sig figs.
==> 451 : 0.01 = 45100 (oh no, it has 5 sig figs)
==> 50000 (1 sig fig) DONE.
*Multiplying*
451 has 3 sig figs.
100 has 2 sig figs.
==> 451 x 100 = 45100 (oh no, it has 5 sig figs), let's make it 2 sigfigs..!!
==> 45000 (2 sig figs)
From now on, 1/0.01 is never be 100. Don't ask me.
this video is so great and fun 😍😎
thank you sir
Heartiest Thanks
You saved my life
Thank you!
Shouldnt the number of sig figs be defined by the measurement method? For example, if your instrument measures to two decimal places but you get a measurment of 100. Wouldn't that cause some issues? Please tell me if i am missing something.
If your instrument (let’s say a scale here) measures to two decimal places and you have an object that weighs exactly 100g, then the scale would read 100.00g. Because the two zeros are decimals, they are significant figures, meaning the measurement has 5 sig figs.
Did I understand your question correctly?
@@ZSmith-yy4lvOh you are right! I forgot about the trailing zeros part of the explaination. Thank you for that.
To me this seems to be standardization for dealing with estimations due to the obvious lack of perfect precision in the real world. So I was wondering why we wouldn't use the precision of the measuring method to define the number of sig figs. Though my question was erroneous, I was attempting to point out a possible flaw.
So my question still stands when dealing with whole numbers. For example, if your measuring method is precise to the hundreds place but your value happened to be 100000.
@@AlphaOfCrimson if you had something that weighed 100,000g and a scale that only measured increments of 100, it would ideally have 4 sig figs if I’m not mistaken. To convey this, you could always write the measurement in scientific notation as 1.000 * 10^5.
Thanks teacher
How do we communicate the difference of an estimation and exact number. If I am wanting to calculate exact numbers to get the most precise study done of people going to night clubs. So then I record exact numbers of attendees every night and one of the nights there is 100% exactly 10,000 what would the standard way of communicating that be? I know we don't always have to follow standards but its often best practice.
If you mean to convey exactly 10,000 you would put a decimal point after the last zero.
put just a decimal point, without adding another 0 after it: 10,000.
or use scientific notation: 1.0000 x 10^4
In the comprehension I got answer 41.94 for the 3rd one in calculations ..there the ending number is below than 5 so should round down right..? but I can understand that 41.94 is 42 but by the rules I should round down.. prof dave or anybody reply
I certainly hope you have learned more than just Significant figures on 4 weeks!
i'm sorry Professor, I'm a little bit confused to the rule. what if we multiply point number 3 in the calculation board into (2.33 x 17) instead of (2.33 x 18), the result would be 39.61. Now, because it should be 2 sig figs, then we must round it down first (39.6), because it still 3 sig figs then we round it up, so we get 40 right, But you said once, the trailing zero rule, if 35000 has only 2 sig figs, then 40 has only 2 sig fig, we know it contradicts to each other in that case. What should we do for that? Thank you, Professor Dave.
i mean 40 has only 1 sig fig, while the rule for multiplication and division is that the answer must have the fewest sig figs. but in this case where it should be 2 sig figs (because of 17), now it has only 1 sig fig.
it would be 40. with a decimal after it indicating that the trailing zero is an exact number and therefore significant
so the key is that the 40 in this case cannot be seened as the way that 35000 represents, because it is an estimation, while 40 has decimal after it. hmm, i got that. Thank you very much, Professor.
I wanted to know the reason of these rules... That would have been a physics video
I cannot understand the logics in Sig. Figures. First off, is there a logic behind it?
The chem book "Chemistry by Zumdahl", 10th edition, gave the example of 2 different grapefruits being weighed on two differente balances. One balance is not very precise and give only 2 digits (such as 10g, 1.2g, etc) and the other balance gives up to 4 digits (such as 2000g, 1.758g, etc).
He says that:
- grapefruit 1 weighed 1.5g in the less precise balance and 1.476 in the precise one.
- grapefruit 2 weighed 1.5g in the less precise balance and 1.518g in the precise one.
With that in mind, he then states: Do the two grapefruits weigh the same? The answer depends on which set of results
you consider. Thus a conclusion based on a series of measurements depends on the certainty of those measurements. For this reason, it is important to indicate the uncertainty in any measurement. This is done by always recording the certain digits and the first uncertain digit (the estimated number). These numbers are called the significant figures of a measurement.
Therefore, he says that significant figures are used to express the certainty of a measurement. Just to refresh, certainty of a number refers to the true value of something. For example, if I have a jar that only measures 1 liter and 2 litters, and let's say I filled this jar up to about 1,5 liter. Observe that I know I have at least 1L of milk (because it has passed the 1L mark on the jar), thus 1 is a certain digit. However, the last digit (5) is only an estimated digit, since I measured it only by relying on my eyes rather than a precise instrument. Therefore, I can have 1.6 liter of milk but my eyes believe I have only 1.5. Therefore, the last digit (5) is what we call UNCERTAIN digit. If you think for a little while you will realize that uncertain digits are always the last digit of a number.
Now is the thing that I don't understand. As I mentioned (4th paragraph), the book says that Sig. Fig. are the certain digits and the first uncertain digit of a number. So, the number 0,0025 has 4 CERTAIN digits (the zeros and the 2) and 1 uncertain digit (the 5, which is the last digit of the number). Thus, if the certain digits and the first uncertain one is called significant figures (see paragraph 4), why does 0,0025 has only 2 Sig. Fig. instead of 5? I mean, 0,002 are the certain digits and 5 is the uncertain one.
I'm estimating 3000 people. 35 faces across times approx 60 lines back = 2100. Rounded up to 3k faces/people.
If 500 and 500. are exactly the same, why does 500. have 3 significant digits and 500 has only 1. Isn't 500 without the two zeros become 5 (with the same number of significant digits) and those 2 zeros after the 5 are super significant because they give you the correct place value of the 5 before them?
They aren't exactly the same, at least not in the context of scientific notation. 500 is precise only to the hundreds place, implying that it could represent anything from 450 to 549 while 500. means it is precise to the units place, so it could be anything from 499.5 to 500.4 because of the decimal listed.
2:58 Number 2 says it's
3 sig figs but I see 5 numbers, what?!
the trailing zeros are not significant
Professor Dave Explains so if that number 7 was at the end of the row then it will be significant right?
all non-zero numbers are significant, and zeros in between non-zero digits are also significant
Professor Dave Explains thank you
Significant Figures and Scientific Notation:
Significant Figures - Digits in a measurement that degree of accuracy of a measurement.
- Applies to measurements written in standard or scientific notation.(technically just everything numerical :D)
- Rules of SF must be followed. :)
Rules of Significant Figures:
Significant:
- Non-zero numbers (1,625)
- Zeroes between non-zeros (2,025)
- Trailing zeroes AFTER decimal (14.00)
- Trailing zeroes in a whole number WITH THE DECIMAL (640.)
- Scientific Notation(Only the mantissa): M x 10 (2.60 x 101)
Not significant ☹:
- Leading zeros (0.0032)
- Trailing zeros in a whole number with NO decimal (54000)
- Scientific Notation(Only the base): M x 10 (2.60 x 101)
Rounding Measurements:
Rounding-off measurements based on number of SF:
1. Determine the number of given significant figures in a measurement.
2. Perform the operation required.
3. For final answer, round off to the desired number of SF following the measurement reading with the LEAST number of SF.
4. Apply the “FIVE and UP Rule”(obv) as discussed in math and grade 7 Integrated Science….. actually what was discussed in primary :).
Rounding-off measurements based on precision:
1. Determine precision of instrument of the used instrument of the given measurement readings.
2. Perform operation required.
3. For the final answer, round off to the decimal place of the LEAST precise measurement reading in the given.
4. …. “FIVE and UP rule”
Scientific Notation:
Scientific Notations - representation of very small/large measurements.
- Used when computations(especially in sciences) need to be precise
Rules for writing measurements in Scientific Notation:
1. Value of base is equal to 10.
2. Exponent is non-zero integer.
3. The absolute value of the coefficient is greater than or equal to 1 but it should be less than 10.
Mantissa - M x 10x
- M < 10
Base - M x 10x
- Always 10
Exponent - (really obvious) M x 10x THIS LITTLE GUY
- ALWAYS a non-zero integer :)
Example of usage:
- Standard: 1,5321
- Scientific Notation: 1.5321 x 104
1.5321 is mantissa; 10 is base; 4 is the exponent of the base
I just copy pasted my notes from before
Hey professor, I wanted to ask why 1000.09 has 6 sig figs but 54700 has only 3, as you said that the zeros that we take in consideration are the zeros after decimal so 1000.09 should have only 2 sig figs I.e 1 and 9
zeros in between non-zeros are significant
@@ProfessorDaveExplains thank you so much for replying so fast :) your channel is really helpful
Very helpful video! I'm a chemistry major and lol my exam is in 3 hours