Significant Figures - A Fast Review!

This video will be a quick

review

of

significant

figures

. The first thing you need to be able to do is determine how many

significant

figures

there are in a number. For example, let's say if we have the number 846, how many significant figures are there? Every non-zero number is a significant figure, so there are three significant figures in this number. Another example, 3546 has four significant figures. Now let's say that if we have a zero between two non-zero numbers, that zero is significant, all zeros between two non-zero numbers. The numbers will be significant, so 704 has three significant figures. 5006 has four significant figures.

Now, what about the zeros to the right of a non-zero number like 500? How many significant figures are there in this number? It all depends on whether there is a decimal point or not. If we don't have a decimal point, the zeros to the right, which are called trailing zeros, are not significant, so this would just be a significant figure. In this case, the trace and the zeros are significant, so they would be three significant figures in the same way if we had 500.0. this would be four significant figures now, what about the zeros to the left of a number like this point zero seven five are these zeros the leading zeros are significant the leading zeros are never significant so there are only two significant figures seven and five so let's say that if we had the point zero zero eight three six only these three numbers will be significant, so to

review

, let's try with this example .0050830 how many significant figures there are in this number, so looking at the leading zeros remember that the zeros initials are not significant, the zeros that are between two non-zero numbers, those are significant and the final zeros are only significant if there is a decimal point that we do have, therefore, these five digits are significant, so we will have five figures significant, so what am I going to do about this?

The point is to give you a test and I want you to determine how many significant figures there are in the following numbers, so the first one will be 42.50 and the second will be 7080 and then one thousand fifty with a decimal point and then point zero zero seven. zero three then we have point zero eight zero six zero and then 5030.0 and finally 750.064080 go ahead and determine the number of significant figures in each of those numbers, by the way, for those of you who want more difficult examples or maybe just more examples, I have another. Video on YouTube that is about an hour and a half long but really goes into depth on this topic, so for those of you who want to master the concept of sig figs, you can check out that video.

I'll post the link in the description section of this video, so feel free to check it out when you get a chance. Also, if you're going to subscribe to this channel, be sure to click the notification bell if you want to receive updates on any new videos I post. I'm going to post in the future, so let's go ahead and start with four thousand two hundred and fifty, how many significant figures does that have? The zero on the right, do we count it correctly? It's a trailing zero and there's no decimal point, so we're not going to count it, so we can only count these three non-zero numbers, so we have three significant figures in the first example.

Now what about the second example? How many significant figures are there? Well, once again, we don't have a decimal point. So we can't count that zero, but what about the zeros between non-zero numbers? So those zeros we can count. Therefore, in this answer I mean that this problem also has three significant figures. Now for the next one there is a decimal point, so the trailing zero is. are counted and all zeros between 3 and 5 are also counted, so this example will have 5 significant figures for the next one, we have a decimal point but no trails and zeros, we have some leading zeros but those will not be counted , so only these three digits will be counted, so there will be three significant figures in that number, for the next one we have a trail at zero that will be counted, the leading zeros will not be counted, so now there are only four significant figures in the next number 5030 we have a decimal point so all trailing zeros will be counted and the zero between three and five is always counted, so we have a total of five significant figures for the last example, all zeros among the non-zero numbers are counted and since we have a decimal point, the zero to the right is also counted, so in this example everything is counted, so let's look at one, two, three, four, five, six, eight, nine, so now we have nine significant figures for that problem.

The next thing you need to be able to do is be able to round a number when multiplying or dividing. For example, let's say that if we are multiplying 4.6 by 3.52, how can we round our answer to the appropriate number of significant values? figures well the first thing we need to do is do the calculation so 4.6 multiplied by 3.52 if you type it into your science device your calculator will give you 16.192 now how should we round this answer to the appropriate number of significant figures , What would you say? The first thing we must do is determine the smallest number of significant figures in the first two numbers that we have already multiplied, so in the first number 4.6 there are two significant figures, in the second number 3.52 there are three significant figures, so when Al multiply or divide, you need to round your final answer to the smallest number of significant figures in the original numbers you used to multiply to get your final answer, so basically we need to round this answer to two significant figures, so we write from left to right.

Well, we have the first digit which is one and then the second digit is a six. Now it's two significant figures, so the last number we need to look at is six, should we keep it at six or should we round it up? to seven, then we must look at the next number, if it is five or more, then we must round the six to seven, if it is four or less, then we will round down, we will keep the six and since it is four or less it is one that we are going to round down, so our answer is 16 rounded to the appropriate number of sig figs.

Now let's work on some other examples. Let's multiply 5.64 by three points or rather, let's choose a number greater than twelve point four five eight. and let's divide ninety-six point seven five two by three points, go ahead and try those two examples, round your answer to the appropriate number of significant figures, so first let's type this into the calculator, so 5.64 multiplied by 12.458, The calculator gives us 70.26312, now the first one. The number has three significant figures and the second number has five significant figures, so we have to round our answer to the smallest number of significant figures, so that's three.

So how can we round seventy point two six three one two to three significant figures, so we're? We will need the first number, the second and the third. If we keep it at two or round it to three, looking at the next number to the right of the two, it definitely falls into the category of five or more so it tells us that we need to round, we need to round two to three, so the answer for this example it is 70.3 and has three significant figures. This answer has a total of seven significant figures. Now let's try the following example, so let's start by dividing 96,752 by three point five four one, then you should get twenty seven point three two three three five four nine eight.

Now the first number has five significant figures and the second number has four, so, as always, when multiplying or dividing you must round your final answer to the smallest number of significant figures in this case four, so looking at the fourth digit or the fourth significant figure from the left, should we keep it at two or should we round it to three? So looking at the next number it falls into the category of four or less, so we're going to keep the two, so our final answer is 27.32. Now let's talk about addition and subtraction, but mainly about addition, so let's say that if we want to add 2.36 plus 12.1, how can we round our answer to the appropriate number of significant figures, so if we add these two numbers, we will get 14 .46, but what should we do here for this type of problem?

It is better to write the problem like this. Now you need to round your final answer to the minimum. number of digits to the right of the decimal point, so what I like to do is draw a line because for 12.1 there is no number to the right of one, so we are not going to have any number to the right of this line. but now, if we add the two numbers together, we will get 14.46, so what we are going to do is keep this number significant, but we need to determine if it should remain 4 or if we should round it up. to 5.

Looking at this number, it is greater than 5, so we need to round this number up, so our answer will be 14.5 and this is how you are supposed to do it when adding or subtracting. Let's try another example: 4.328 plus 13 plus 5.45. Go ahead and try that problem, first we have to add so that we have eight, two plus five is seven, three plus four is seven and then four plus three plus five is twelve, we take the one and one plus one is two, so we get twenty. two point eight now, what should we do next? How can we round it out?

So what we need to do now is determine which number has the fewest number of digits to the right of the decimal point and that's the second number, so let's draw the line here because it doesn't have anything on the right side of that line , so our final answer should only contain these two digits, but we'll use the 7 to determine what we should do with the 2. Should we keep it? a 2 or round it to 3, well seven is more than five, so we'll round the two to three, so our answer will be 23 and that's basically it for this video, so once again if you want more.

Problems with significant figures. Please see the link in the description section of this video to see the other video that goes into more detail on this topic. Thanks again for watching.