 How we note down or can we introduce percentage and relative error also then we can take all the numerical that is better okay write down percentage or relative error next relative error write down relative errors are used relative errors are or can be used to compare two sets of the readings suppose you have to compare between the accuracy of one set of the reading and the other set of the readings fine suppose one set of reading is to calculate your distance from your home other set of reading is to calculate the distance of moon from the earth you have to compare the accuracy which one is more accurate then you can't compare the absolute errors okay you have to compare the relative error okay and the way relative error is defined is this how do you think it should be defined any idea the absolute error is what this this is your absolute error the ratio error should be this divided by the coefficient of the coefficient of this this is your relative error okay if you are measuring one lakh kilometer and the error is one kilometer then one divided by one lakh is the relative error okay so let's write down this example if you are measuring one lakh error is one relative error is one divided by one lakh if you are measuring ten and the error is one the relative error is one by ten so clearly this is lot lesser than this okay you can't compare one with one this one is for the measurement of one lakh this one error is for the measurement of ten of course this is more accurate but we know it is more accurate but we should also know how to quantify it this is how we what is the percentage error into 100 into 100 is percentage error okay so percentage error is relative error into 100 simple any doubts we'll take up a numerical now okay we can take up this write down we are measuring the time period of oscillation for the simple pendulum and these are the readings we measure the period of oscillation of a simple pendulum in successive measurements the readings turns out to be these 2.63 2.56 2.42 2.71 and 2.80 okay you need to find out the absolute relative error and percentage error absolute relative for whatever it is written here we do find out for these readings he got the answer tell me absolute relative error percentage error no you cannot increase the accuracy of the readings the readings are up to 2 decimal place how can when you calculate suddenly comes accurate three decimal places if you're getting third decimal place discard it we'll talk about rounding off and all later on right now you can just discard okay the things are 0.01 0.06 0.09 0.09 oh shit there's one more after that yeah 0.5 4 divided by 0.1 0.8 0.5 point 0.1 it's 0 when I one one 1 1 1 1 very so they one one one point yeah 0.1 1 is the absolute error and then relative 0.1 1 how many of we got 0.1 1 2 1, 2, 3, 4. I think it is straight forward. Entire chapter is straight forward. First you have to take the mean. That is a true value. Mean is how much? Some of these values, 2.62. Discard the third doesn't point. 2.62. So this value will be treaty to find out the error in the measurement. First error rate at which is 0.01 percent. How much? 0.04. Minus of 0.06. 0.04. This is 0.04. Minus of 0.2. 0.11. Yeah, 0.9. 0.04. This is how much? 0.09. 0.09. Then this one? 0.18. 0.18. Okay, take more of this and then take the average of that. You get the absolute error. Which will be 0.01 plus 0.06 plus 0.2 plus 0.09 plus 0.18 divided by 5. That is 0.11 seconds. 2.62 plus minus 0.11. This is the actual heading. This is how you should write. It can be plus 0.11 or minus 0.11. Your actual value will lie between these two. Okay, so this is the absolute error. What about relative error? 0.04. 2.62. 0.11 divided by 2.62. Which is how much? 0.04. 0.04. So percentage error is? 4 percent. 4 percent. 4 percent error is? Yeah. Understood all of you? Yes. 0.11 divided by the true value. 0.2 divided by the absolute value. Yes. Not a nearest percentage. Delta a m divided by a is 0.04. 0.02. 2 you have to discard. Third decimal point. Now see we are talking about something which we are directly measuring. For example length you can directly measure. Mass you can directly measure. And you will get the error in that. Now suppose you are measuring the mass. There is some error. And then you are measuring the acceleration. There is some error. Force is mass into acceleration. You are not measuring the force directly. Suppose I ask measurement and acceleration measurement. What is the error in the force? Using the, you are not calculating force. You are not measuring the force. Are you getting it? So we need to understand what will have our multiplied. What will happen to the error? Right. What will happen if two quantities which we are measuring are getting added up. Getting subtracted, getting divided or raised to power. Right. So next we will be discussing. See right now suppose 2 pi under root L by g. Okay. Length of the pendulum. There is a value of g. Suppose I ask. G is not measuring. I am not measuring g directly. See g have to measure it right. Okay. So this is what we are trying to do now. To find what will happen to the combination of errors. Right now. I can hear that thing. Right. Combination of errors. For some or a difference. Class tenth. We had this habit of you know. Learning theory in the class. And then going back home. Again revising theory. And then start solving the problems. Okay. You need to first solve the problems. If you are stuck then read the theory. And anyway you will not be able to solve all the problems. I am talking about depression for j. Okay. If your score is 60% doing very very good. So 60% you might not have seen in your life till now. It will be soon less than that also. And tell you frankly 60% is very good score. Right. So if you are aiming to get around 60-70% or 80% max 80%. Okay. Then you are not aiming for a perfection. Right. You are aiming to get better and better in problem solving. Okay. So that will only happen when you solve. Okay. Don't go back home and start reading the chapter again. This strategy will not even work for your school exams going forward. This used to work in 9th and 10th. No longer now. Okay. Solve problems only when you go back home. Alright. Errors of a sum or difference. Okay. Suppose you have an expression like this. Y is equal to A plus B. Okay. You are measuring A. So there will be error in A. So there will be error in B also. But we are trying to find. Okay. So when you measure A, how you write A as A will be equal to A mean plus minus delta A mean or delta A mean. Plus minus is there. We will take care of it. Okay. Similarly B you can write as B mean plus minus delta B mean. Similarly if I also, Y should be written as Y mean plus minus delta Y mean. Okay. Now let's substitute all these values in this expression. Okay. What will happen to delta Y plus minus delta Y? This will be equal to AM plus minus delta AM. Plus B plus minus delta B mean. Okay. So Y mean plus minus delta Y mean is equal to A plus minus delta AM plus minus delta B mean. Okay. Is some of the, like the way the formula is. Okay. Then the error in Y should be what? Y mean should be equal to? Plus minus. Delta AM. Yeah. Plus minus will come when you put it. Okay. So delta AM is delta AM plus delta B mean. Like this. Understood? Yeah. So when you measure quantities, the error gets added. Office. Yes or no? Suppose you have to subtract. Suppose Y is equal to A minus B. Try to do that minus B. Then can you derive and tell me what is delta Y mean should be equal to? Delta. It's the same thing. It's the same thing. No, it's the same thing. It's the same thing. Yeah, it's the same thing. Guys. Done? Will it be delta A mean minus delta B mean? No, it's not. Why? It's because it's plus or minus and it's plus or minus. Yeah. But it becomes plus minus and it becomes minus plus? Yeah. That's the same thing. See, the thing is that when you subtract, you will get it like this. Y plus minus delta Y to A mean minus B mean plus minus delta A mean. You can say minus plus delta B mean because you have put minus sign. Okay. But it's basically the same thing. But you don't know the maximum possible error. The same thing. Whether you add or subtract, as you remember this thumb rule, maximum possible error. You can write it down. It can be used in lot of problem practice as well. You should not get confused. The way numbers are getting added or subtracted, it's not the same as the errors are getting added or subtracted. Errors will never ever will get subtracted. They will always add up. Minus. Both can be plus together. Both can be minus together. They're random. Like this, you can take care of a difference. Okay. So you have a lot of formulas where you have plus sign. For example, B is equal to U plus AT. Term whatever the displacement. Time period is first measured time period plus next measured time period. Attraction. Changing any variable is final minus initial. Delta t is final time minus initial time. Okay. So addition and subtraction happens quite a lot in physics. So you should know that both the cases, the error will get added up.