Understanding Significant Figures in Measurements

Hello everyone, here is another video with OrgTube channel. In this video, I'm going to talk about significant figures. When we use a measuring device or when we measure something, we show the level of certainty in our measurement by significant figures. More significant figures we have more certainty we have in our measurements. First, I'm going to explain how we can find number of significant figure in each number. Then I explain the application of significant figure in calculation. The first rule for significant figure is all non-zero digits they are significant. For example, here we have five non-zero digits. So we have five significant figure or sig fig. The second number it has three significant figures because it has three non-zero digits. And the third one has four significant figures. The second rule is for zeros in between. The zeros between non-zero digits they are always significant figures. So in this case d0 and d0 they are significant same as d0 and same as d0. So the first number has five significant figures, the second one has three significant figures, and the last one has four significant figures. Leading zeros, the zeros that come before the first non-zero digit, they are not significant. In these examples, these two zeros, they are not significant. These three zeros they are not but this zero is zero in between so it is significant and these zeros they are not significant. So the first number has three significant figures. The second one also has three significant figures and the third one has only one significant figure. The next rule is for trailing zero or the zero comes after the last non-zero digit. They are not significant unless we have decimal point in our numbers. For example, this zero in the first one is not significant because it's trailing zero and we don't have any decimal point. So this number has only two significant figures. But the next one because we have decimal point the zero is also significant so we have three significant figures and in the last one this zero is trailing zero but our number has decimal point so this zero it is a significant so in total we have four significant figures if we have number in the scientific notation forms we normally ignore these parts and we take a look only to our number not to the 10 exponent. So in this case this number has three significant figure 5.10 it has three significant figures and 9.36 also has three significant figures. Because significant figures referring to them certainty and accuracy of measurements, when we use this number in calculations, we need to follow some specific rules. If we have addition and subtraction, we always looking for least decimal place in our answer. And if we have multiplication and divisions, our final answer should have the least significant figures. For this reason, I would like to explain round-off rules before explaining the calculation rules for significant figures. Here are some examples. We would like to round off all these numbers to four significant figures. So this is the last digit we need to keep. For rounding off the number, we take a look to the next digit after the last certain digit. It's 3. If this digit is less than 5, we simply remove these digits so the answer in this case is 134.4 and we don't put zero instead of these three digits we just remove if we put zero the significant figures will be more than four but if we need to remove the digits at the left side of decimal point like this example then when we remove the digit we put zero instead if we want to rounding off these numbers to four significant figures this is the last digit we should keep so the next digit is three instead of removing three we should put zero So it's 13440. Then the digit after decimal point we don't put 0. This number right now has 4 significant figures. The 0 is trailing 0 and it doesn't count in significant figure rules. If we don't write this 0 and we write just 1344, then we change the value of our number. which is wrong for the next example the last digit we should keep is 6 if we take a look to the next digit it is 7 when we have more than 5 when we remove this digit we need to add one number to the last significant digit so the answer is 1 1 2 then 6 plus 1 will be 7. for the next example here is the last digit we should keep and then the next digit is five if it's five and we have other digits after that the rule is the same thing we need to add one when we remove these digits so the answer is two eight six point instead of four we write five but there are numbers that the five is the last digit like these two examples. If we have this case or if we have 0 after 5, it's the same thing. When the last non-zero digit is 5, we take a look to the preceding digit. If it's even, we don't change it. If it's odd, we add 1 to that digit. In this case, 6, 1, 2, then we keep 6 because it's even but here 791 the last significant figure is 7 when we remove 5 We add 1 to the 7. These are the rules for rounding of the numbers Then let's see what are the calculation rules for significant figures in addition and subtraction Our final answer should have the least decimal places from these numbers. For example, for this addition, 2.04 plus 4.476. The answer from calculator is 6.516. Here we have two decimal places and here we have three. So our final answer should have two decimal. So the last certain digit we have in our calculation is this one. And we need to round off this answer. We have to take a look to the next digit is greater than five. So we need to increase this last digit by one. So when we remove six, one converts to two. So the number we should report. is 6.52. We have the same rule for subtraction. When we perform the calculation, the answer is 56.7. But based on the significant rules, here we have one decimal place and here we have zero decimal place. So our final answer shouldn't have any decimal digits. so the last digit we should keep in our final answer is this digit so we need to remove 7 7 is greater than 5 then we need to add 1 here so what we report is 57 when we have multiplication or division the rule is different we take a look to the whole significant figures not only decimal the first example is multiplication the answer for this multiplication is nine point five five six five six this is the answer we get from calculator this number has three sig fig and this number has four so our final answer should have three significant figure so the last digit we keep is this one or we can also separate the digit by this line so we should keep the digit at the left side and we should remove the digit on the right side the first digit is here six it's greater than five so when we remove these digits we need to add one to the preceding digit so what we supposed to report is 9.56 we have the same rule for division the answer we get from calculator for this division is 22 0.5860696517 this is what we get from calculator here we have three significant figures and here we have five so our final answer should have the least significant figure this means three so we supposed to have three significant figure so we should keep the digit at the left side of this line and we should remove the digit on the right side the first digit on the right side is greater than five so when we remove this digit we need to add one to the preceding digit so the answer is 22.6 please keep in mind that we should keep all digits until the very end so if we have more than one type of operation in our calculation we should not round off our numbers after each step here is the first example and because we have these two numbers inside the parentheses we need to have addition first in this calculation so 3.12 plus 4.476 is equal to 7.596 then we need to multiply this by 11 but we need to identify how many significant figure we should have here but we should not rounding off this number here we have two decimal places and here we have three decimal places so our final answer should have only two decimal places so the last digit we should keep is this one but we're not going to remove six right now we should do it at the very end then the next step is 7.596 times 11. the answer is equals 8 3.556 right now we know This number should have three significant figures but 11 has only two significant figures. So we need to round off our final answer by two significant figures. So it means we should keep this digit and we should remove the digit on the right side of this line. Because it is 5 and after 5 we have other digits. When we remove this we need to add one digit to the tree. so the final answer is 84 with only two significant figure let's have more examples here is the next example we don't have any parentheses and we know always the priority is with multiplication and division so first we have to multiply these numbers and the answer is equals to 31.25 1 3 9 because this multiplication we take a look to the whole significant figures this number has three significant figure and this one has four so the answer for this part should have three significant figure then 31.25 1 3 9 minus 3.702 3 the answer for this subtraction is equals to 27.54909 Now we can run off our final answer. Here for first number, based on the significant rules for multiplication, we should have only one decimal place. And here we have 4. So we supposed to keep only one decimal digit. And we need to remove this. When we want to remove this, this digit is less than 5. so when we remove this digit we don't change the last significant number the answer is 27.5 here again we don't have any parentheses so the first calculation should be division then we need to add 2.34 to that answer the answer for this part is 12.471797 0 7 65 this is what I got from calculator and based on the significant rules here we have 4 and here we have 6 so our answer for this part should have four significant figures 1 2 3 4 then we add this number to 2.34 the answer is equals to 14.8117970765 Here we have the addition rules. We have two decimal places and here also we have two decimal places. So we need to round off our final answer to two decimal places. The first digit after the line is 1 so it's less than 5. so we can just simply remove all these digits after this line so our final answer is 14.81 thank you for watching this video to watch more video please make sure to subscribe to our youtube channel

Then I explain the application of significant figure in calculation. The first rule for significant figure is all non-zero digits they are significant. For example, here we have five non-zero digits. So we have five significant figure or sig fig. The second number it has three significant figures because it has three non-zero digits.

And the third one has four significant figures. The second rule is for zeros in between. The zeros between non-zero digits they are always significant figures. So in this case d0 and d0 they are significant same as d0 and same as d0.

So the first number has five significant figures, the second one has three significant figures, and the last one has four significant figures. Leading zeros, the zeros that come before the first non-zero digit, they are not significant. In these examples, these two zeros, they are not significant.

These three zeros they are not but this zero is zero in between so it is significant and these zeros they are not significant. So the first number has three significant figures. The second one also has three significant figures and the third one has only one significant figure. The next rule is for trailing zero or the zero comes after the last non-zero digit. They are not significant unless we have decimal point in our numbers.

For example, this zero in the first one is not significant because it's trailing zero and we don't have any decimal point. So this number has only two significant figures. But the next one because we have decimal point the zero is also significant so we have three significant figures and in the last one this zero is trailing zero but our number has decimal point so this zero it is a significant so in total we have four significant figures if we have number in the scientific notation forms we normally ignore these parts and we take a look only to our number not to the 10 exponent. So in this case this number has three significant figure 5.10 it has three significant figures and 9.36 also has three significant figures.

Because significant figures referring to them certainty and accuracy of measurements, when we use this number in calculations, we need to follow some specific rules. If we have addition and subtraction, we always looking for least decimal place in our answer. And if we have multiplication and divisions, our final answer should have the least significant figures.

For this reason, I would like to explain round-off rules before explaining the calculation rules for significant figures. Here are some examples. We would like to round off all these numbers to four significant figures.

So this is the last digit we need to keep. For rounding off the number, we take a look to the next digit after the last certain digit. It's 3. If this digit is less than 5, we simply remove these digits so the answer in this case is 134.4 and we don't put zero instead of these three digits we just remove if we put zero the significant figures will be more than four but if we need to remove the digits at the left side of decimal point like this example then when we remove the digit we put zero instead if we want to rounding off these numbers to four significant figures this is the last digit we should keep so the next digit is three instead of removing three we should put zero So it's 13440. Then the digit after decimal point we don't put 0. This number right now has 4 significant figures.

The 0 is trailing 0 and it doesn't count in significant figure rules. If we don't write this 0 and we write just 1344, then we change the value of our number. which is wrong for the next example the last digit we should keep is 6 if we take a look to the next digit it is 7 when we have more than 5 when we remove this digit we need to add one number to the last significant digit so the answer is 1 1 2 then 6 plus 1 will be 7. for the next example here is the last digit we should keep and then the next digit is five if it's five and we have other digits after that the rule is the same thing we need to add one when we remove these digits so the answer is two eight six point instead of four we write five but there are numbers that the five is the last digit like these two examples. If we have this case or if we have 0 after 5, it's the same thing.

When the last non-zero digit is 5, we take a look to the preceding digit. If it's even, we don't change it. If it's odd, we add 1 to that digit. In this case, 6, 1, 2, then we keep 6 because it's even but here 791 the last significant figure is 7 when we remove 5 We add 1 to the 7. These are the rules for rounding of the numbers Then let's see what are the calculation rules for significant figures in addition and subtraction Our final answer should have the least decimal places from these numbers.

For example, for this addition, 2.04 plus 4.476. The answer from calculator is 6.516. Here we have two decimal places and here we have three.

So our final answer should have two decimal. So the last certain digit we have in our calculation is this one. And we need to round off this answer. We have to take a look to the next digit is greater than five. So we need to increase this last digit by one.

So when we remove six, one converts to two. So the number we should report. is 6.52. We have the same rule for subtraction.

When we perform the calculation, the answer is 56.7. But based on the significant rules, here we have one decimal place and here we have zero decimal place. So our final answer shouldn't have any decimal digits. so the last digit we should keep in our final answer is this digit so we need to remove 7 7 is greater than 5 then we need to add 1 here so what we report is 57 when we have multiplication or division the rule is different we take a look to the whole significant figures not only decimal the first example is multiplication the answer for this multiplication is nine point five five six five six this is the answer we get from calculator this number has three sig fig and this number has four so our final answer should have three significant figure so the last digit we keep is this one or we can also separate the digit by this line so we should keep the digit at the left side and we should remove the digit on the right side the first digit is here six it's greater than five so when we remove these digits we need to add one to the preceding digit so what we supposed to report is 9.56 we have the same rule for division the answer we get from calculator for this division is 22 0.5860696517 this is what we get from calculator here we have three significant figures and here we have five so our final answer should have the least significant figure this means three so we supposed to have three significant figure so we should keep the digit at the left side of this line and we should remove the digit on the right side the first digit on the right side is greater than five so when we remove this digit we need to add one to the preceding digit so the answer is 22.6 please keep in mind that we should keep all digits until the very end so if we have more than one type of operation in our calculation we should not round off our numbers after each step here is the first example and because we have these two numbers inside the parentheses we need to have addition first in this calculation so 3.12 plus 4.476 is equal to 7.596 then we need to multiply this by 11 but we need to identify how many significant figure we should have here but we should not rounding off this number here we have two decimal places and here we have three decimal places so our final answer should have only two decimal places so the last digit we should keep is this one but we're not going to remove six right now we should do it at the very end then the next step is 7.596 times 11. the answer is equals 8 3.556 right now we know This number should have three significant figures but 11 has only two significant figures. So we need to round off our final answer by two significant figures.

So it means we should keep this digit and we should remove the digit on the right side of this line. Because it is 5 and after 5 we have other digits. When we remove this we need to add one digit to the tree.

so the final answer is 84 with only two significant figure let's have more examples here is the next example we don't have any parentheses and we know always the priority is with multiplication and division so first we have to multiply these numbers and the answer is equals to 31.25 1 3 9 because this multiplication we take a look to the whole significant figures this number has three significant figure and this one has four so the answer for this part should have three significant figure then 31.25 1 3 9 minus 3.702 3 the answer for this subtraction is equals to 27.54909 Now we can run off our final answer. Here for first number, based on the significant rules for multiplication, we should have only one decimal place. And here we have 4. So we supposed to keep only one decimal digit. And we need to remove this. When we want to remove this, this digit is less than 5. so when we remove this digit we don't change the last significant number the answer is 27.5 here again we don't have any parentheses so the first calculation should be division then we need to add 2.34 to that answer the answer for this part is 12.471797 0 7 65 this is what I got from calculator and based on the significant rules here we have 4 and here we have 6 so our answer for this part should have four significant figures 1 2 3 4 then we add this number to 2.34 the answer is equals to 14.8117970765 Here we have the addition rules.

We have two decimal places and here also we have two decimal places. So we need to round off our final answer to two decimal places. The first digit after the line is 1 so it's less than 5. so we can just simply remove all these digits after this line so our final answer is 14.81 thank you for watching this video to watch more video please make sure to subscribe to our youtube channel

Transcript for:Understanding Significant Figures in Measurements

Transcript for:
Understanding Significant Figures in Measurements