![]() So to make it clear the our measurement is only good to the nearest centimeter, because there is more error here, then. This part of the tower I was able to measure to the nearest centimeter. The reality is that I was only be able to measure the part of the tower to the millimeter. You don't know, if I told you that the tower is 3.991 meters tall, I'm implying that I somehow was able to measure the entire tower to the nearest millimeter. it's kind of misrepresenting how precise you measurement is. And the problem with this, the reason why this is a little bit. So let me add those up: so if you take 1.901 and add that to 2.09, you get 1 plus nothing is 1, 0 plus 9 is 9, 9 plus 0 is 9, you get the decimal point, 1 plus 2 is 3. And let's say those measurements were done a long time ago, and we don't have access to measure them any more, but someone says 'How tall is it if I were stack the blue block on the top of the red block - or the orange block, or whatever that color that is?" So how high would this height be? Well, if you didn't care about significant figures or precision, you would just add them up. We have a, let's say we have an even more precise meter stick, which can measure to the nearest millimeter. Let's say we have another block, and this is the other block right over there. So let's say we have a block here, let's say that I have a block, we draw that block a little bit neater, and let's say we have a pretty good meter stick, and we're able to measure to the nearest centimeter, we get, it is 2.09 meters. And to see why that makes sense, let's do a little bit of an example here with actually measuring something. The least precise thing we only go one digit behind the decimal over here, so we can only go to the tenth, only one digit over the decimal there. only as precise as the least precise thing that we added up. But in our answer we don't want to have 3 significant figures. Then, in this situation - this obviously over here has 4 significant figures, this over here has 3 significant figures. (let me do another situation) you could have 1.26 plus 102.3, and you would get obviously 103.56. This time it worked out, cause this also has 2 significant figures, this also has two significant figures. Cause we have a six right here, so we round up so if you care about significant figures, this is going to become a 3.7. It only went to the tenths place, so in our answer we can only go to the tenths place. The least precise thing I had over here is 2.3. The sum, or the difference whatever you take, you don't count significant figures You don't say,"Hey, this can only have two significant figures." What you can say is, "This can only be as precise as the least precise thing that I had over here. When you add or subtract numbers, your answer, so if you just do this, if we just add these two numbers, I get - what? - 3.56. This is the hundredth and this is the tenth. Here this is two significant digits so three significant digits this is two significant digits, we are able to measure to the nearest tenth. If you just add these two numbers up, and let's say these are measurements, so when you make it (these are clearly 3 significant digits) we're able to measure to the nearest hundreth. ![]() How many decimal places do you go? For example, if I were to add 1.26, and I were to add it to - let's say - to 2.3. But when you add, when you add, or subtract, now these significant digits or these significant figures don't matter as much as the actual precision of the things that you are adding. That was only particular to carpets or tiles. ![]() I was just saying a general way to think about precision in significant figures. Just because you don't wanna it's easier to cut carpet away, then somehow glue carpet there. In my last video, I talked about laying down carpet and someone rightfully pointed out,"Hey, if you are laying down carpet, you always want to round up. And obviously even my real world examples aren't really real world. I just do a kind of a numerical example first, and then I'll think of a little bit more of a real world example. When we do addition and subtraction, it's a little bit different. We only limited it to 2, because that was the smallest number of significant digits we had in all of the things that we were taking the product of. Because we can have 2 significant digits. 2 times 3.5 is 7, and we can get to 1 zero to the right of the decimal. So just as a quick example, if I have 2.00 times (I don't know) 3.5 my answer over here can only have 2 significant digits This has 2 significant digits, this has 3. We saw in the last video that when you multiply or you divide numbers, or (I guess I should say when you multiply or divide measurements) your result can only have as many significant digits as the thing with the smallest significant digits you ended up multiplying and dividing.
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