Hello students welcome back to this lecture series on chemistry basic concepts and its calculation lecture 2 So in this lecture we are going to see what scientific notations are and why we use scientific notations and how we calculate with normal mathematical operations and what are significant figures we will see in detail in this lecture So, the first thing we are going to see is scientific notations. Before we see what scientific notations are, let us see why they are there. For example, in chemistry, we use very large numbers and very small numbers frequently. For example, if I take 197 grams of gold, there are so many gold atoms present in it.
So, if you look at the masses of one gold atom, So, approximately I have written a bold data mass here. So, it is difficult to write these numbers normally. So, it is more difficult to do normal mathematical operations like addition, subtraction, multiplication and division with these numbers. So, to remove this difficulty, scientists have found scientific notations. What scientific notations are?
In this format, we can represent these numbers in a short form. So, if we ask what is n, we will take it as non-zero digits. So, let us see how to write these big numbers n into 20 power of n in scientific notation.
So, I have assumed that there is a decimal point. So, what I am doing is, first I have written a decimal point for non-zero digits and then I have written it in simple form. Okay, clap and into.
10 to the power. So, we will see what will happen in power. So, first I have assumed that there is a decimal point here.
So, this decimal point should be in the center of the non-zero digits here. That is, it should be in the next questions for 6. So, see how many digits are moving. If you move here, it is 3 digits. 6, 9, 12, 15, 18, 21, 22, 23. That is, 23 digits have moved from right to left side. Okay?
So, we will write 23 as 10 to the power of 10 Since it is moving from right to left, we will write 23 as positive So, we will write 23 as a big number Similarly, we can write this number in scientific notation So, 3 is the first non-zero digit So, we will write a decimal for non-zero digits So, if you want, you can write decimal after two non-zero digits. So, what I have done is, I am writing decimal after first non-zero digits. So, 3.27 into 10 to the power.
So, we have asked what will come in power. So, this decimal point should come in the next questions for first non-zero digits. So, how many digits should be moved?
3, 6, 9, 12, 15, 18, 21, 22. So 22 digits move from left side to right side So when it moves from left side to right side So 22 So when it moves from left side to right side, we use negative quotient So what does negative mean? It means a very small number Ok? Ok, so we have seen how we represent a large number in scientific notation So let us see two examples for this So what we have done here is 4, 300 So I have given a number here, so in these numbers, I have given a decimal in the last So I am going to represent these numbers in scientific notation So from here, this digit has to move 3 6 digits So 4.3 into 10 to the power of 6 So this has to move from the right side to the left side, so I am using the positive sign So what is the positive sign? We are milling a very big number So in this, the decimal points are here, so in the same way So what I am doing at this time is writing 2, that is, I am writing the decimal after 2 non-zero digits So 34.8 is the value. So how many digits should be moved?
3, 4, 5. 5 digits should be moved. So 10 to the power of 5. So this is moving from left to right side. So we will write negative.
So we are representing scientific notation with big numbers and small numbers. Okay? So we have seen what scientific notation is. Next we will see normal mathematical operations.
Additions, subtraction, multiplication and divisions. Let us see how to do this for scientific notation So I have given multiplications I have taken two numbers from two scientific notation So I am multiplying these two So the multiplication is so simple this number and this number, first we will multiply them for example, 0.05 2.5, ok come into 10 to the power 5 into 10 to the power 8, ok come so, we will do normal multiplication like this so, 5 into 25 5 into 25 number, will it be 125 ok done, so 3 decimals are left, ok, so I have done normal multiplication like this So, how to multiply the power? If the power is in two multiplications, we will add the powers of the two multiplications So, we will add the powers of the two multiplications So, if we simply multiply it, it will be 13 So, I will keep the first non-zero digits as 1.25 x 10 to the power of 13 So, So, if it is moved from left to right, it is minus.
So, it is moved from left to right. So, we have to write 1. So, 1.25 x 10 to the power of 12. So, the answer for this multiplication is 1.25 x 10 to the power of 12. So, we have seen the multiplication. Next, we will see the division. So, the division is so simple. I have divided it like normal simplifications.
So, you can write the remaining as 0.2. 1 into 10 to the power 3 divided by 10 to the power of 5. So, if you ask me if the numerator is missing from the denominator, it will come in negative term. So, into 10 to the power of minus 5. So, if you want to understand more about this, I will just represent it here.
So, it is 10 to the power of 3 and 10 to the power of 5. So, what I am doing is, I have multiplied the denominator and numerator by 10 to the power of 5. So, these two are 10 to the power of 3 and 10 to the power of minus 5. So, we will add these multiplications. So, plus 5 and minus 5. Plus 5 and minus 5 will be 10 to the power of 0. So, anything power 0, we have said 1. So, into 10 to the power of minus 5. So, this is what I have represented here in short. So, if we see now, These two are in multiplications. So, 0.1 into 10 to the power of 3 minus 5. So, 0.1 into 10 to the power of minus 2. So, this is also non-zero digits.
So, 1.0 into 10 to the power minus 2. So, from left to right side it moves. So, I have written minus. Only one digit has moved. So, now minus 1. So, now 1 into 10 to the power of minus 3. So, this is the answer of division.
So multiplication and division is little bit easier But in addition, we have to design both the powers as common Example 6.65 into 10 to the power of 4 and 10 to the power of 3 I will change this to 10 to the power of 3 10 into 10 to the power of 3 plus 8.95 into 10 to the power of 3 is the same. So, both the powers are same. So, I will take out the powers commonly. So, 6.65 into 10. So, if we do this alone, it is 66.5 plus 8.95 into 10 to the power of 3. I have taken out 10 to the power of 3 commonly.
So, if you ask me to add these two, it is 5415. 75.45 into 10 to the power of 3 is the answer. So, the same thing happens with subtraction. So, to do subtraction, the powers of the two must be similar.
But here, 10 to the power of minus 2 is given and 10 to the power of minus 3 is given. So, what I am doing is, I am changing this to 10 to the power of minus 2. So, how do we do it? 2.5 into 10 to the power of minus 2 minus 4. 0.8 into 10 to the power of minus 3. So, I am writing it as minus 1 into 10 to the power of minus 2. So, in these two multiplications, if we add these two, it will be minus 1 minus 2 minus 3. So, I have written it like this.
So, in this, 10 to the power of minus 2, 10 to the power of minus 2 is common. So, I will take that out. So, 2.5 minus 4.5. 4.8 into 10 to the power of minus 1. So, what is the meaning of this? 4.8 divided by 10 is the meaning.
So, if we put this, it will be 0.48. So, what I am doing is directly 0.48. into 10 to the power of minus 2 so if we simplify this 2.02 into 10 to the power of minus 2 so in addition and subtraction we have to check if the powers are common if they are common then we have to take them out and write them in multiplications ok so we have seen scientific notation next we are going to see precision accuracy so let us see a small example For example, I have measured x as 2.00 grams I have given the measured mass to 3 students and asked them to calculate the mass and give the results So, they have measured it twice and gave the results So, we will learn about accuracy and precision with this Before that, we will see the definitions of precision and accuracy Accuracy refers to how closely a measured value This is measured value This is correct value How closely a measured value agrees with the correct value So, if measured value is closely related to the correct value, we call it accurate measurement What does precision mean? Precision refers to How closely individual measurements agree with one another So this is an individual measurement and this is an individual measurement So the relationship between these two is called precision So if these two are closely related, we can say that it is precise So we will find out which is precise and which is accurate So this is measured reading and this is the correct value So these two are closely related This is 1.94 grams and this is 2.00 grams So, more or less means that it is not that closely So, what we are saying is Not accurate So, we are saying that this is not an accurate measurement If we ask that it is precise, both of these are very closely This measurement and that measurement Both of these measurements are more or less same So, if we say that both of these measurements are same We are saying that these values are precise Or we are saying that it is precision Note these two readings We are relating the correct value of the reading measured by the students When we relate the readings, the distance between the two readings is not the same So, we are saying that the measurement is not accurate If we ask if the measurement of these two readings is close, we are saying that the measurement is not accurate So, in the readings, this is the measurement and correct value so these two are more or less closely so these two readings are also closely so these two readings are accurate measurement so these two readings are more or less closely so we say accurate and precise ok? so I think you have understood what is precise and accurate so let us see another example so in this example I have fixed a board so in this board you have I will give you 3 chances, and you have to hit 4 bullets in each chance So, if you ask what your target is, this is your target But if you ask what you have done in the first attempt, you have placed your target behind the target So, your 4 bullets are here So, these 4 bullets are more or less near each other So, we can assume that they are in the same place So, if you see the target, it is precise but Your you have not achieved the target so what we will say is not accurate but precise ok so what does precise mean how repeatedly how can you place the bullets in one place that is what we mean by precise in measurement in one reading no matter how much you measure same readings that is precision So, in the second chance, this is your target.
But you have placed the bullets around the target. If you see, it is not near to the target. It is here, here and here. Since, all the targets are at a distance, we can say that it is not precise and not accurate. So, we can say that it is not accurate and not precise.
You cannot place the bullets in the same position repeatedly. So, you have achieved your target. But, all 4 bullets are in the same place. So, what does this mean?
Accurate and precise Okay? So, you know what is precise and what is accuracy So, what are we going to see today? Significant figures Before we see what are significant figures So, first we will see few definitions What are they? Numbers obtained by counting For example, I have asked how many fingers are in my hand We will count 10 fingers 1, 2, 3 So, counting like this we can say 10 fingers.
So, the numbers that come in counting like this and from definitions. If you ask what definitions mean here, So, 1 hour. How many minutes is 1 hour?
60 minutes. So, these are the definitions. These are the numbers that come from definitions. If you ask what to say, 1 inch is equal to 2.54 cm. So, numbers like this by counting and from definitions are exact.
numbers but numbers obtained from the measurements are not exact so what is the meaning of this? let us see in an example so what I have done is I am measuring the length of an object so I have placed the length of the object and I have drawn a line so we are going to measure this line with this scale and how much it is approximately so I have placed 0 here and 10 cm here so the length of the object is more or less half half of it feels like half of it so what I am doing is I am saying that it is 5 cm ok? so I am measuring the length of the same object using another scale so in this measure I can see that it is 5 cm so the length of the object is 5 cm but I am not sure if it is 5.1 cm or 5.2 cm so what I am doing is I am saying that it is approximately 5.2 cm ok? ok So, I am measuring the same thing again but on a different scale.
So, when I am measuring in a different scale, I know exactly that it is 5.1. So, what I am doing is, I know exactly that it is 5.1. So, it seems like the 5.1 and 5.2 are connected in the center. So, what I am doing is, 5.4 or 5.14, 5.15, 5.16.
So, it can be anything. So, what I am doing is, I am taking 5.14. So, all these are measured.
So, numbers obtained from the measurement are not exact. Now, we will see how to do that. So, we have just said that this is an approximate number.
We have said that it is approximately 5 centimeters. So, we know exactly about this number. But, we have said that this number is estimated.
So, it can be 5.1 or 5.2 or 5. So, we know exactly what number is in between the numbers. So, we know that the number is above 5.1. So, in these readings, it can be 4, 5 or 6. So, in these 3 values, it can be anything. So, the first two numbers are known digits. The last one is estimated digits.
So, if we say that significant figures are short, All known digits plus one estimated digits. We should say this. Okay? So, if we ask to say the definitions, significant figures are meaningful digits which are known with certainty. Certainty means definite.
That is, the numbers that you can definitely say are what we call certainty. And plus one which is estimated or uncertain. We should say this. Okay? So, let us see what this means in a small example.
Okay? Let us see. So, I have placed a liquid in a graduated cylinder I will measure the measurement of that liquid So, here it is 30, 35, 36, 37, 38 So, it is in the center of the 38 and 39 lines So, I have placed 38 in the center 38.6 ml is placed in the cylinder It can be in 5 ml also So, it is 5.5 ml, 0.6 ml, 0.7 ml So, it can be in any of these 3 numbers So, we have calculated 38.6 ml as the estimated amount So, we have 2 definite digits plus 1 estimated digit So, 36 is the estimated digits So, in 38.6, this is the definite digits and this is the estimated digits So, if we ask how many significant figures are there, it is all known digits plus one estimated digits So, there are two known digits and one estimated digits, so we can say that there are three significant figures Similarly, we have filled another example in a burette In a burette, the top reading is zero and the bottom reading is So, we have 38 here and 39 here So, we can take 38.5 as the number So, 38.5 and 38.6 are in the center So, 38.5 is the number we can say as definite So, it is more or less in half ranges So, we can take 6 or 7 or 5 So, we can take any number in these 3 numbers Because it is like that when we estimate So, I have 38.6 So, these are known digits and the last one is estimated digits So, we call known digits plus estimated digits as significant figures So, if we ask how many significant figures are there? We can say that there are 4 significant figures So, significant figures are meaningful digits which are known with certainties So, we call these 3 numbers as certainties And one which is estimated or uncertain So, we call the last digit as estimated So, that's why uncertainty ok done so we have explained how to calculate significant figures so we have given a set of rules that is to find out how many significant figures are there we have given a set of rules so let us see what are they all non zero digits are significant figures so i have given an example so 24.5 ml so all these are non zero digits So, all non-zero digits are significant figures. So, now, there are 3 significant figures in this.
Okay? Okay, done. So, now, zeros. We have said that all of these are non-zero digits. Now, we are going to see the rules for zeros.
So, zeros between non-zero digits are significant figures. That is, if there are zeros between two non-zero digits, they are significant figures. So, if we look at the significant figures of this, we will say 4. Okay?
So, why I am telling you all these is because, when zeros are in a particular place, sometimes they are significant figures and sometimes they are non-significant figures. So, please be careful with zeros. So, next rule is, zero presiding to the first non-zero digits are not significant figures. So, zeros are in front of non-zero digits. So, if you see zeros like these, we will not consider them as significant figures.
So, how many significant figures are there? 1, 2, 3 So, there are 3 significant figures So, if we want to give an example So, I am saying 0, 0, 2 So, before non-zero digits there are zeros So, we will not say significant figures So, if we want to know the significance of these we will say 1 Ok? So, next rule 0 at the end of the number that contains a decimal point or significant figures So, there are numbers like this and there are zeros and non-zero digits. But, these zeros are on the other side of the decimal point. The zeros after the non-zero digits are on the other side of the decimal point.
So, we call all these zeros as significant figures. But, if it is like this, we will not consider these zeros as significant figures. We will consider the remaining zeros as significant figures.
because the previous rules said that the zeros before non zero digits are not considered as significant figures next rule is that zero at the end of the number does not contain a decimal point may or may not be significant so for example, look here there are zeros after non zero digits so there is no decimal point in it so if there is no decimal point then those zeros may be significant significant ilaamalam irukulam adhavati enna solraang abdina idhukku significant figures padhinga abna 3aabam irukulam, 4aabam irukulam, 5aabam irukulam adhavati enna abdina we need much more information to explain how much significant figures are there abdina dha solraang ok glab so adhia nana information sipe babbu so 24300 kilometers iruku so adhila padhinga abna plus or minus 1 abdina solri kuduthana so abdina enna meaning panudha abdina kedinga abdina 24300 an so 99 km or 24301 km So, these two are equal to 24300 km So, the values we measured are the same as the values of the three digits So, what does this mean? Only the last digit changes So, we know that these are estimated digits The remaining four digits are known digits So, known digits 4 one estimated digits, so how many significant figures are there? 5 significant figures, okay? okay done so, in this example, they have given 24300 km but they have given plus or minus 10, okay? so, I will explain this so, 24000 290, I have written minus 10 in the first digit and in the readings, so 24300 kilometers and plus 10 is 24310 kilometers so the last digit is not changed but the digits before that are slightly estimated so in all the 3, the readings before that are there so these are all definitely known digits This is called as Estimated Digits So, the zeros are just for the representation So, how many significant figures are there in this?
3 plus 1 So, 3 plus 1 is 4 significant figures So, the same is the case in this example So, 24300 plus or minus 100 So, 24200 can be 24300 can be 24400 So, these two numbers are just All the numbers are same but the last digit is changing So, these digits are estimated digits and these are known digits So, 2 plus 1 is 3 So, this number has 3 significant figures So, we can say that these numbers have 3 significant figures But, these numbers do not have any such numbers So, we cannot say that these numbers have 3 significant figures Okay? Okay then. So, next rule is, number in the scientific notations, then the power should be negligible.
That is, there is a number in the scientific notations. So, if we want to get the powers, we have to neglect it. Okay? So, there are zeros after decimal points.
What do we say after decimal points? We say that they are significant figures. 1, 2, 3. So, there are significant figures. There are 3 significant figures. Okay then.
So, next rule. Exact numbers can be considered having unlimited number of significant figures. these applies to definite quantities so we know definite quantities counting means we have to count that we have 10 fingers so to measure that we have 10 fingers exactly we will write 0, 0, 0, 0, 0 in infinite times so all the zeros after decimal are significant figures so for counting numbers, decimal point means 0 infinite number of zeros after decimal points we will consider as significant figures so if we ask how many significant figures are there we will say unlimited number of significant figures so this is not only counting but also for definite quantities so 1 liter is 1000 ml so if we want to say 1000 ml correctly we will write infinite number of zeros So, after decimal there are zeros and all of them are significant figures. So, for this too, we can say that there are unlimited number of significant figures. So, next time I have given you few examples.
So, in these examples, there are zeros after non-zero digits. So, non-zero digits and zeros are also in decimal. So, we can say that there are three significant figures.
So, for this, there are zeros and there are no decimal points. So, if we ask how many significant figures are there, the answer is information is insufficient or 1, 2, 3. So, we can say that there are significant figures in these 3. So, there are zeros after decimal, so how many significant figures are there? If we ask, 3, 4. 4 significant figures. So, if we look at this, 5 significant figures.
So, in scientific notations like this, we will neglect power. So, if we neglect, it will be non-zero digits. All non-zero digits are significant figures.
So, we will say 4. Next, I have given you few examples In the first example, there are zeros before non-zero digits We will not consider them as significant figures So, if we ask how many are there in this, we will say 2 significant figures If we ask how many significant figures are there, we will say 208 km So, the number of significant figures is 3 Because, there is 0 in the center of non-zero digits So, we can see 2 non-zero digits in this So, we will consider them as significant figures. So, 4 significant figures. So, in this, 3 significant figures can be there, 4 can be there, 5 can be there, 6 can be there. So, in all these, anything can be there.
So, we need much more information. Okay, come. Okay then.
So, in this, 4 significant figures. Okay, come. Okay then. So, the next rule says that, we have to represent significant figures in addition and subtraction.
That is what it says. Okay? So, the rule says that, in addition and subtraction, The last digit retained.
So, in this, the answer is clear. So, in this, which is the last digit? position of first doubtful digits so first doubtful digits position is we have to consider as last digit so first doubtful digits are in second position after decimal but here first position is after decimal so doubtful digit is here after decimal there is third digit ok, so if you ask where is least digit after decimal point first numbers are doubtful digits so we will use first decimal digit So, we have 31.1 So, how many significant figures are there? 3 significant figures So, let us see few examples in this role So, on this side, we have additions and subtractions So, in this, doubtful digits are after decimal There is only first point So, the first point after decimal is doubtful digit So, we have to take 2.6 So, we have to say 2 for significant figures Okay done So, the first doubtful digit is after decimals.
So, we will start with 4.8. So, the significance figure is 2. So, note down the first doubtful digit. For example, if we ask for the significance figure, it is 5 and 1. So, we will start with the doubtful digit.
So, in multiplications, the answer contains no more significant figures. So, we count the number of significant figures. So, the least number has two significant figures and the other has three significant figures.
So, the least significant figures are the answer's significant figures. So, how to represent this? We have to stop the answer with two significant figures. So, we will say that the significant figures are 2. So, in this answer, there are 3 significant figures.
For this, there are 4 significant figures. So, the answer is 2954. So, we have to stop the least significant figures with 3. So, what we will do is, we should not stop the answer with 295. Why? Because... The values are 295 but here it is 2954. So, we should not change the value of the position. So, if we write 0 here, 0 means there are no significant figures in some positions.
So, here 0 means we will not count as significant figures. So, if you ask how many significant figures are there, it is 3 significant figures. So, next rule is round off. So, let us see how to round off a number. So, it is normal.
We do it in normal mathematics. So, we are going to remove all the last digits and round off them. So, the last digit is above 5. So, if it is above 5, what we do is, we add 1 to the next number and write the answer.
So, it is 1.39. So, here, 5 is... So, if it is less than 5, we can update remaining numbers. 4.33 So, here it is 6.35 So, here it is exactly 5 If it is more than 5, we can add the previous number.
But, if it is exactly 5, what we have to do is We have to check the previous number. So, the previous number is odd number. So, what we have to do is We have to add the odd number. If it is exactly 5 If the previous numbers are odd numbers, we can add them If the numbers are even numbers, we can keep them I have given few examples of round up and how to do it For example, there are 3 numbers I am telling you to write round up in 3 significant figures So the point after decimal is 5 So the number before is an even number So what we have to do is write the numbers like that So this number is in two significant figures So this is the only significant figure So I wrote 34 The value here is 34 but here 342 is there, so the value of this is also changed so in any situation, we have to add 2 so what I am doing is adding 0 so the significance of this is, I have rounded off 2 the value of this is also not changed here also 342 is there and here also 340 is there So, the next value is, I have told you to write in 4 significant figures So, 4 significant figures means we have to write only these numbers So, the next number is less than 5, so we will write these numbers So, now we will write 10.47 So, next I have told you to write these numbers in 2 significant figures So, this number is 2878 So, if I write these 2 numbers, the value will be 28 So, this is wrong So, what we are doing now is, 7 is above 5. So, what we will do if it is above 5? We will add the number next to it.
If we add 1 and add 0, it will be 2900. So, the significance figures are 2. At the same time, the value of that number is not changed at all. Okay? Okay then. So, next, I have given an example. So, what they are saying in this example is, If the value of Avogadro number is this much and the value of Boltzmann constant is this number.
Boltzmann constant is also given to us. So, then the number of significant digits in the calculated value of universal gas constant. So, universal gas constant is represented by R. So, Avogadro number is represented by NA and Boltzmann constant is represented by K. So, these values are given to us.
So, what I am doing with these values is I am substituting them. So, what they are saying is that we have to find out the significance of the figures in the universal gas constants So, what we have said in the multiplication rule is that we have to find out the least number of significant figures That is what we are saying is that we have to find out the significance of the answer So, if we see the significance of this, it is 4 So, if we see the significance of this, it is 4 0 is after the decimal So, that power should be neglected So, we have seen that in a rule So, the least significant figures are more or less 4. So, we have to round off 4 digits in the answer. So, here we have 4 digits. But, the digits after that are above 5. So, we have to add the previous number. So, we have to add 8.312.
That is joule per mole per kelvin. So, this is the answer. So, the significance figures are 4. So, next we will see an example.
Which is the most accurate measurement? So, to know which is the most accurate measurement, we need a large number of significant figures. So, the significance figures are 1, 2, 3 and 4. So, the more significant figures, the more accurate measurements. So, next in our example, in the example, 18.72 grams of X occupies 1.81 cm3.
What will be the density measured in a correct significant figures? So, density means mass by volume. So, mass is given here.
Space occupied is called volume. So, we substitute these two numbers. So, we can find out the least significant figures in the division and multiplication rule So, why are there significant figures in these two? This has 4 and this has 3 So, this is 3 and these are the least significant figures So, the answer will be like this So, we have to round off the answer with 3 significant figures So, 3 significant figures are these 3 numbers So, I will write 10 points So, the next digit is less than 5 So, I will simply represent these digits So, what can we do?
correct way measured correct significant figures so this is the correct answer okay okay done okay done so next one example so in the examples which is dimension analysis okay so in the examples express 1.47 miles in inches okay so 1 mile is this much and 1 feet is this much okay so how we solve this first we convert feet from miles and then inches one point seven miles is equal to 1.47 x 5280 feet so we will take this number and take this as 1.47 x 5280 x 12 inch so these are the answers and we will solve the easy problems like this But, if we look at these problems, what are they saying? 1.40 into 10 to the power of 10 seconds. We have to convert it into years So, we know that 1 year is 365 days So, 1 day is 24 hours So, 1 hour is 60 minutes 1 minute is 60 seconds So, if we calculate all these, it will take some time So, for that, we will see about unit factor method So, unit factor method is called as label method And we will call it as dimensional analysis Ok, let's go So, 1 mile is equal to 5 to 8 zero feet. So, what we will do in this unit dimension is, we will first convert this into a unit factor.
How? First, we will divide by 1 mile. And, divide by 1 mile. Okay?
So, these two will be cancelled. So, if these two are cancelled, we will have 1. So, 1 is equal to 5 to 8 zero feet divided by 1 mile. So, this is what we will call unit factor. So, if we ask another value, if I divide by 1 mile, I will divide by 5 to 80 feet and if I divide by 5 to 80, both these will cancel and we will get 1. So, 1 mile divided by 5 to 80 feet.
So, this is also the unit factor. So, both these are unit factors. So, we will understand the difference between these two in the next step. So, if I convert this to 1 mile, If we divide by 1 feet, it will be 12 inches divided by 1 feet So, if we divide by 12 inches, it will be 1 feet divided by 12 inches So, we can say that these two are the unit factor So, what I am going to do is, I am going to multiply both these two So, if I multiply both these two, it will be 1 divided by 1 So, I am going to multiply both these two and write it down So, we have to multiply both the numbers So, in the questions, we have to convert 1.47 miles into inches So, I have already told you the answer to the previous question So, I am multiplying 1.47 miles into inches by multiplying both the sides So, I am multiplying 1.47 miles into inches by multiplying both the sides So, we have to multiply 1.47 miles into inches by multiplying both the sides So, this feet is cancelled.
If you multiply the remaining numbers, we get the answer of 1.47 miles. This problem will be easy for you. But, we have discussed the second hour problem. These problems.
If we solve these problems, it will be a little easier. So, first we need to find the unit factor. So, 1 year divided by 365. days is equal to 1 so in the next one days divided by 24 hours is equal to 1 hour divided by 60 minutes is equal to 1 so next one minute divided by 60 seconds is equal to 1 so what we are going to do is we have found 4 unit factor If I multiply that, it will be in this format.
Okay? Okay then. Okay? Okay then. So, next what we will do is, we will multiply both sides because 1.40 into 10 to the power of seconds.
So, if you see, seconds cancel, minutes cancel, hours cancel, days cancel. So, if we simplify these numbers, the answer we get is 444 years. So, if you see very big numbers like this, it will be easy to solve in this method.
But, if you ask the correct way of solving, this is the correct way of solving. Okay, come. Okay done.
Okay, that's it. Okay, so what we saw today is, we saw what scientific notations are and what significant figures are. And, we saw what dimensional analysis is in detail. Okay?
Okay, that's it. All the best. Thank you.