HOW MANY SF SHOULD I USE?! | Rant with Mo Ali

Added: 2026-05-12

[00:00:00]Assalamu alayikum. Hello. Hello. And welcome to a very unusual rant video. And the reason why I posted this video, and you probably looked at the title, is because of this. That didn't happen because of this. Wait, I'm covering stuff up. Let me scoot aside. Okay. And maybe just a little bit more. Lately, because exams are coming up, I've been getting a lot of questions about these messages over here. I'll be pointing in the wrong direction all the time. This video because of these messages over here. So, for example, the first one says, "Hi, sir. I have a quick question because I don't think you've ever clarified before." I'm sure they're being sarcastic cuz I have. But how many significant figures should I round my final answer to? Two or three? If you look at the second guy, he's like, "Or girl, mister, do I have to round my answers to two significant figures?"

[00:00:54]That's what SF is short for, I'm sure.

[00:00:56]And honestly, third guy gets the cake goes, "Greetings and salutations." He sounds like a British like monarch.

[00:01:03]Greetings and salutations. I've been solving exams of old. But when I open the mark scheme, answers always are rounded up. Are my answers okay? The only problem with this is the okay. like you you sounded all like regal throughout the messages and then you like ended with okay come on keep up the bit and then even got a message like this like with a full I love these kinds of messages cuz they're like super meticulous this individual is like really meticulous in detail it's like hi when I'm solving a calculation question and your answer is uh 102 45.6 39.4 four and you don't round will you get the mark even if the answer in the mark scheme is rounded and they showed me like an example from their solution and mark scheme and their answers are fine like and if you're usually accepted significant figures how much did you round to so clearly clearly there's an issue with what with how many significant figures should I write my final answer to [sighs and gasps] I'm not going to give you the TLDDR now I'll give you TLDDR in the end but let me prove how how many significant figures you should write your answers to because I'm pretty sure there's going to be a bunch of people online and maybe stuff on Reddit, maybe stuff on Tik Tok is going to advise you to only write your answer to two significant figures or maybe something else. Who knows? Some of the advice will be right. Some of it will be a bit bit mis misguided. But before I show you, I want to show you what exactly the mark scheme says because this is all in your mark schemes. Mark scheme says when it comes to this kind of stuff. So step one, want you to relax. Okay. So, calm down.

[00:02:36]Let's take a look. Oh, I'm I'm covering stuff up. So, I'm just going to scoot myself down just a bit more. Ah, there we go. Good.

[00:02:46]Okay. So, let's read this. It says for question. This is from the numeric scheme about couple of things. You'll find this under calculation specific uh advice. So, stuff about just calculations. Okay. for questions in which the number of significant figures required is not stated. So that's all up here. So I'm reading all the way up here. So it's not stated up here.

[00:03:09]Credit should be awarded for correct answers. Hold on. Hold on. Read this again. Credit should be awarded for correct answers when rounded by the examiner to the number of significant figures given in the mark scheme. What does that mean? This means that if the mark scheme says an answer is like 64, but your answer is actually 63.8 and you wrote that down, if the examiner rounds it up to two significant figures, it'll be 64, which means you're okay.

[00:03:45]But to further prove my point, this next giant like blob of blob of text is also in the mark scheme and lately in more recent mark scheme. This is honestly instructions for examiners and students really don't need this but it'll help you understand how many significant figures you need to write. So first numerical answers are expected to be to be given to the number of significant figures given in the final answer in the mark scheme. And then you go like oh my god mister this means that all my answers need to be two significant figures and you're no hold on calm down let's cut you all wrapped up relax chill take a chill pill and read the next bullet point. Yes, the examiner expects you to write your answers through most of the time, especially if you're in IGCSE physics, two significant figures, but read the rest of it. Answers given to more significant figures than expected are awarded the A mark. A mark means answer mark in the mark scheme.

[00:04:48]So, you're given the full answer mark when rounded to the correct number of significant figures and the answer matches the mark scheme allowing for ECF. like this is still considered an error carried forward but not really.

[00:05:01]It's fine. If you write your answers to more significant figures, you're a okay.

[00:05:06]Okay. So, what does that mean? For example, let's say you're calculating something like force and as I said the mark scheme says the value of the force should be 64 newtons.

[00:05:25]And then your answer was F= ma.

[00:05:31]And then you wrote down the working is you know let's say the mass was 10 kg and the acceleration is 6.4.

[00:05:38]Uh actually let's say the acceleration was 6.38 cuz you got that from a previous part.

[00:05:46]So obviously your answer is 63.8.

[00:05:49]And then you've got your f equals dot dot dot dot dot dot dot. You should write everything down. And you decide to write down 63.8 newtons.

[00:06:00]Is this okay? Yes, it is. Absolutely.

[00:06:04]Why? Because if I, as the examiner, am reading this answer, I'm going to have to round this up. So, I go like, oh, does this round up to 64? Oh, yeah, it does. So, you're okay. Good. You get all, let's say this was like a two mark question. You get all two marks. Good.

[00:06:21]Move on with your life. However, what I'm often concerned about is writing too few significant figures. And here's why.

[00:06:30][sighs] Where a final answer is given to too few significant figures.

[00:06:36]And here's a condition. And the mark scheme answer has been seen in the working to at least the expected number of significant figures. This is penalized only once. Okay, the whole paper for the whole entire paper with the SF annotation. This is like more you know examiner kind of speak. Okay. And the A is not awarded. Subsequent occurrences of this are ignored and the A mark is awarded which means if you have a habit of rounding down too much sorry rounding up too much. So you're rounding up to a very small number of significant figures. So instead of 64, you round it up to 60 for some reason. Like I don't know why we do that. You're like, um, no, but you kind of showed your answer in the working and it's fine. So you lose a mark here. But if you keep doing this again, you don't lose a lot of marks. And why would you want to lose marks for something as silly as rounding up to a very small number like one significant figure? Don't do that. And even worse is the next bit like read this next section where a final answer is given to too few significant figures and the mark scheme answer has not been seen in the working meaning which which is what most people do they just go like oh yeah f= ma that's 10 * 6.38 so f is equal to 60 for some reason that's completely wrong why because I can't even the examiner hasn't even seen what the value should be which is 63.8 8 rounded up to 64 in your working this wasn't there. So you lose marks because the examiner didn't see the proper number of significant figures. So do you see and obviously this is treated as an arithmetic error and the A mark is not awarded. So the examiner treats you like not being you know you don't know how to calculate stuff and I'm sure you do. I'm sure you do know how to do your math.

[00:08:34]Right. Right. Right.

[00:08:36]So, long story short here, how many significant figures should you write it down to? Should you write it down to two? Well, yeah, why not? Can you can you write it down to more? Yes. And is that safe? Yes. Obviously, as long as your calculation is correct, that's absolutely safe.

[00:08:54]Okay. So, I want you to take a look though at why do we have to write our answers to two significant figures? Because that's not always the case.

[00:09:05]That's not always the case. Oh, I'm not filling up much of the space, so let's pull myself up. Okay, cool. Hopefully, I don't cover up any parts of the video.

[00:09:14]Uh, this is a question from November 25.

[00:09:17]So, I'm using recent exams, so nobody argues. I'm not going to solve the whole question. I just want you to take a look at this. In this question, he gave us the uh velocity of the train.

[00:09:27]So, this is 56 m/s. And the mass of the train is 440,000.

[00:09:35]kilogram. These are both written to two significant figures. This is two and this is two. Look at the acceleration down here. That's also two. So if most of the raw values given in the question, we're doing this so I can explain why do we write our answers to two significant figures or sometimes more depending on the question. Okay. So again most of the raw values here are already given to two significant figures. So if you check the mark scheme for all of the answers, the first one is 6.9 10 ^ of 8 or 690,000 or 6190 mega. All of these are two significant figures.

[00:10:11]If you check for CI, which is the next thing that you calculate, uh the final answer is 5.3 or 530. And the next bit which is CI, that's 1,300 or 1.3. These are all two significant figures because the raw values are all to two significant figures. But if you try to work out something like you know the kinetic energy if I just like smack the numbers here really quick. Half mv squ. So half I'll even use the working in the mark scheme. What's the working?

[00:10:42]Look at this. Half * 440,000. So 440,000 times 56^ squar the mark scheme answer or like the working should actually give you 689 920 0 0.

[00:11:02]So it's not 690 million like the exam says. No, it's a lot smaller. If you round this up to three significant figures, you will end up with 690.

[00:11:14]No matter what you do, if you round this up to three significant fig, the examiner and if you leave this answer as is, even though I wouldn't recommend it because I don't like writing numbers with lots of zeros, I prefer standard form. So, I'd rather type like tap shift mode 7, which is s on my calculator three. So, I get all my answers to three significant figures.

[00:11:34]That's 6.9 10 the^ of 8. You get the answer right anyway. Okay? So, be comfortable. Write them down two significant figures or more. Now here two significant figures is absolutely safe because most of the raw values were written to two significant figures. So the examiner expects you to write your answers to two significant figures.

[00:11:56]Let's take a look at another exam. I won't I won't calculate much again now.

[00:12:00]But here's a number. Here's a value.

[00:12:02]This is a P1 V1= P2 V2 question. And all of the values are given to two significant figures. 240 is 2. 1 * 10^ 5 is 2. 1.4. Like look at him. He even writes this down as 1.0 10 ^ 5. Like why? Because he wants to keep this to two significant figures. So he expects your answers to be two significant figures as well. 170. And for the next one it's 270 cuz everything is to two significant figures. But are there scenarios where you shouldn't write it to two significant figures? Most of the time in IGCSE no not really. But paper six is a bit different.

[00:12:41]Okay. Obviously, obviously I don't have to write everything like because this is the question. Should you write everything two significant figures? No, not necessarily. In the previous questions, yeah, why not? Take a look at this next question. It's going to be a paper six question. I know because I prepared these. See, uh I can tell the future. No, I don't. I can't. This is a paper six question.

[00:13:04]The exception to the rule of oh yeah, you should write things two significant figures would be three things. One, if there is a measurement in your question. So, if you're measuring something, you're asked to measure something. Well, yeah, significant figures isn't the issue here. Decimal places are, and I'll show you why. Or if the question forces you to write to a certain number of significant figures or decimal places.

[00:13:29]For example, here, uh, this is a very classic like balancing experiment. They ask you to measure X like the distance between this and there or they just ask you to calculate something. So the pivot is at the 50 cm mark. The center of the load is at the 90 cm mark. So how do you get the distance between the two? So you go like oh yeah 90 minus 50 gives you 40. And you write this down to 40. So see this is fine right? 40 or technically it should be 40.0. Why?

[00:13:58]Because this is a ruler and measurements need to be written to the correct number of decimal places of the instrument being used. Which is why in the mark scheme it says given to the nearest 0.1 cm because measurements need to be written to the correct number of decimal places as the instrument being used.

[00:14:20]Nothing more nothing less. So taking that value and moving forward with the rest of the value she places a 2 Newton load that's two significant figures but you know that's a limitation of the small value itself and then she measures the other distance and it's 21.5 like you don't you're not doing anything and then they ask you to calculate a value called W using X which is three significant figures Y which is technically three significant figures as well because it's one decimal place and two which is two significant figures. So what should the value of W be? Like the question even prompts you give your answer to a suitable number of significant figures for this experiment.

[00:15:02]If you're calculating something and the values are all three significant figures given to you, then use three. But if I have a mixture of significant figures like this, I have three and I have two.

[00:15:12]Look at what the mark scheme says. It says W is given to two or three significant figures. Do they accept two or three? Heck look the mark even says like four but I don't like four like it doesn't work for me and I would use three why because most of the values are written to three so why not the next bit is also the same they change the value of x because they change the load essentially and they ask you to calculate the new value of w the mark scheme doesn't even give an answer it says the new value of w should be given to the same number of significant figures as I why because you have to be consistent so three is a very safe number. All right. However, things are slightly different when it comes to Alevel physics because the previous ones were IGCSE questions. Paper 4 and paper six.

[00:16:01]When you go into Alevel physics, especially if you're doing AS's or A2s, specifically A2s, okay, some questions require a very high degree of precision, which means I need more decimal places or significant figures. For example, the numbers here. If you take a look at these numbers, and if you're an IGCSC student, don't get scared. This is just this is really simple. But we're talking about the masses of, you know, nuclei here, like of an atom or a nucleus, which means I really need to make sure my decimal places are right. So even the values given to you have like an absurd number of decimal places. Okay? Heck, even the energy given to you in mega electron volts here is in four significant figures. Three decimal places. But here the question forces you. It says give your answer to five decimal places. Some questions will do that. Some questions will force you into how many decimal places or significant figures you should direct your answer to. And if that happens, writing anything other than what the examiner asked for is a mistake. Don't say, well, but Mr. Muhammad said like if the values are all to two significant figures, I should No. If the question asks you to and forces you to write an answer to a certain number of decimal places or significant figures, for the love of God, please write it to what the examiner wants, not what what you want.

[00:17:25]Okay? It doesn't happen very often, but please just do that. Okay? Okay, we're clear. We're good. Let's look at this.

[00:17:32]Like this value looks absurd. 273.920U.

[00:17:38]But 5, dozen places because the dude asked for it. like bro asks you for five decimal places just give him five okay but if the question doesn't ask you this is another A-level question because in A level we often deal with like much larger numbers and need to be a lot more precise the raw values here are all to three this doesn't happen in every question by the way most questions still go through with the two decimal place two significant figure thing most of them still prefer to use two significant figures. But the raw values in this question were given to three.

[00:18:18]So when you calculate something like luminosity and you use the equation, look at what the answer in the mark scheme even in standard form is written to three because the raw values are written to three.

[00:18:33]When you get the you know temperature of the star using your basic equation, look at this. What is this? Still three.

[00:18:43]Even though throughout most of the exam the values were two significant figures.

[00:18:50]Do you see the issue here? Like do you see where or how you're supposed to use significant figures correctly? It's not just a matter of, oh, it's supposed to be two or three, right? So, TLDDR should I use two or three? Yeah, go ahead, use it. But you need to understand something. You need to understand why we write things down to two or three or even more significant figures. Usually not less because less means you lose a lot of the precision and accuracy of the measurement of the calculation. So more is usually okay. Okay. So TLDDR you want to write it down to two or three significant figures. Be my guest. Oh, am I taking up too much space? So uh this way.

[00:19:26]No, no, no, no, no. Oh, there we go. I'm good.

[00:19:30]That was not funny. Anyway, two or three significant figures are fine by default.

[00:19:34]Especially if you're an IGCSE, it'll it'll all work out unless the question asks you to write your answer to a certain number of significant figures.

[00:19:43]You listen to the examiner. Okay? Or unless especially in paper six, you measure something. So there you don't worry about significant figures. You write it down to the number of decimal places of the instrument. Whether it's an instrument drawn in a picture that you just like make measurements off of or you're asked to use your ruler or protractor to measure something on a sheet of paper especially in paper six for IGCS paper five in you know uh A level physics you write it down to the correct number of decimal places okay so I hope I hope that answers the question of how many significant figures that you want most of the time. I personally when I calculate stuff I just go for three.

[00:20:30]However, a lot of the time two is safe.

[00:20:32]Two is fine. Especially if you're copying the value from one answer to the next. Two is okay. Unless I physically notice that every single given raw value in the question is to three significant figures or more. I and then I worry. I was like should I write them to two? I should probably write them to more.

[00:20:48]Okay.

[00:20:51]I have an extra bit. Okay. So, if you look up there got a bunch of text here.

[00:20:55]A lot of time, uh, especially in IGCSE, not so much in A level because in A level, they usually give you the units.

[00:21:01]Something's gotten to my eye. Anyway, in A levels, they usually give you the units because you've got a lot of other things to worry about to lose more time.

[00:21:09]But for IGCSE specifically, you must write your units down. So, you've written down the correct number of significant figures. Good job. But you forgot the unit. Bad job. Why? Because take a look at this. It says a numerically correct final answer without a unit is awarded the final answer mark if the unit is shown correctly in the candidates working. What does that mean?

[00:21:36]This means that a numerically correct answer with a missing or incorrect unit is not awarded the final answer mark.

[00:21:49]What? What? So if you if you don't write the unit, you don't get marks. You do.

[00:21:56]C or B marks are awarded from the candidates working. Oh, good lord. Do you know what that means? This means if you write a final answer like the same like 64 Newtons for example that were writing it was like 64 and you forget the newtons, you get zero even though the answer is right. Why? Because there's no unit. And since there's no unit, you do not get the answer mark. So they go back to your working to give you compensation. I was like, "Oh, you didn't write your working."

[00:22:24]Obviously, previously I did, but let's assume you didn't, right? You were like, "Oh, 10 times." You didn't even need your calculator. 10 times 6.4 is 64. And you move on. Fine. Fine. Just don't forget your units, please. Don't forget the units. It's terrible. Imagine losing marks for units. Like, you're doing absolutely fine. You forget every single unit in the exam.

[00:22:46]Good job. Good job. You lost everything.

[00:22:51]Okay. [sighs] No aura for you.

[00:22:56]A unit a unit with incorrect use of uppercase or lowerase symbols is PA or PA. What should you do? Make sure you write it down correctly.

[00:23:12]You will lose marks for them. Okay?

[00:23:15]Because small p capital A could mean something like pico because that's an actual prefix by the way. Pico and pair.

[00:23:25]This isn't really clear, but it's basically saying, "Hey, make sure you use the correct uh like capitalization for the letters of a unit." So, Newtons and a capital N, kilograms, a small K, small G, etc. So, make sure you use the correct A sizing.

[00:23:42]And then finally, unless the mark scheme asks for a specific unit or ask a specific question states otherwise, the only permitted derived units, derived units meaning not SI, are jewels per second for instead of watt. If you forget the watt and you just say jewels per second, that's fine. If you forget Pascal, which is the units for pressure, that's Newton per meter squar. That's fine. Momentum is either Newton second or kilogram m/s because momentum and impulse share the same units. Since change in momentum is impulse and their units are often the same. So you can interchangeably use the units for each and jewels is Newton meter. But for moments you must use Newton meter or Newton centimeters or Newton you know millimeters cuz it's force times perpendicular distance to the pivot. So you got to use it right. Okay. Cool. Now one final thing.

[00:24:36]Take a look at this very fine little sentence up here. It says fractions. An answer expressed as a fraction is not numerically correct as a final answer unless the fraction is explicitly stated in the mark scheme.

[00:24:49]Huh? So fractions are not are not are not numerically correct. Please write your answer in decimals and write it down to the correct number of significant figures. Don't write your answer as a fraction unless the question literally says calculate the fraction and even then like let's say I calculate a fraction and it's like 3 over4 you you're still allowed to write it as 0.75 as your answer. So even a fraction question can be written in decimals but you cannot write decimal answers as fractions. That is not allowed. That's enough for the extra steps. Hope that made sense. Okay. I hope you understand and everything's okay and that you're feeling comfortable with the subject now and doing your stuff. Go do your exams properly. Oh, and uh you know like subscribe and if you want to check my website out. We've got a bunch of videos there uh courses that you can I always keep them updated probably add a few more in the future like at Excel and everything else. But I'll stop rambling and end the video here. Thank you very much for watching. Have a lovely day.

[00:25:58]Good luck with your exams. I'm praying for every IGCS student just get the grades they want and that they deserve.

[00:26:04]Just remember to work hard, study, practice, lots and lots of practice, deliberate practice. Okay? So, solve your past papers, correct the marks, correct them from the marks, try to understand what you got wrong, make sure you understand the basic concepts, especially with physics. But I'll rant about like how to study in a future video. Have a nice day. Bye.