Significant Figures

by Jules Bruno
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So when we're dealing with any type of question or trying to write down the answer to a question, we need to take into account significant figures now significant figures. These are the numbers that contribute to the precision associated with any value. Now we're going to say here that there is an easy way and, of course, ah, hard way to approach significant figures. Luckily for us, we're gonna focus on the easy way. Now the hard way has ah lot of rules, and it has terms that sometimes might be confusing, such as leading zeros and trailing zeroes. We're gonna avoid all of that, and we're gonna rely on three simple rules to help us determine the number of significant figures associated with any value. Now, the first rule if your number has a decimal point, so if it has a decimal point, you're gonna move from left to write. Start counting once you get to your first non zero number and keep counting until the end. So here we have our first two examples. One is written standard notation. One is written scientific notation, but that doesn't matter if we look at the first one are moving from right. I'm from left to right. We're gonna start counting when we get to our first non zero number. So 0000 Here is our first non zero number. This too. We're going to start counting there and we count all the way into the end. So one, 23 This number has three sig figs or three significant figures for the next one. It's written in scientific notation, but that doesn't matter when it's written. Scientific notation focus on the coefficient. So this part here the base which is the 10 and the power of the exponents don't matter. It has a decimal point. So we're moving from left to right. Our first non zero number is this eight way. Start counting there we count all the way until the end. So 123 So we have 366 in this one as well. Next, if you're number has no decimal point, then we're gonna move from right, So left. So we're gonna go this way. Same rules apply. Start counting once you get your first non zero number and keep counting until you get to the end. Our first non zero number is this five. So that's one to 34 So we have 46 fix here as our number significant figures. Now, this third rule, this third goes a little bit different, So this third will deals with exact numbers. Now an exact number is a value or integer, so that means it has to be a whole number that is known with complete certainty. We're going to stay here for a exact number. There are an infinite number of sig figs or significant figures. So, for example, your lecture class has 125 students. That's something we can know with certainty, because we can literally count the number of students that we see within the room or a dozen eggs equals 12 eggs. This is something that is known with complete certainty. 12 eggs. We can count each one of those individual eggs. So 125 students within Electra Hall isn't eyes has an infinite number of sick fix 12 eggs equal one dozen that can also have an infinite number of sick fix. That's because, for example, for looking at the 125 students, it could be 125 which would have three sick fix. Or it could be 125.0. That's still 725 that has four sig figs. Or it could be 125.0 which has 56 figs. And it could go on and on and on and on because technically, that is still saying 125. So just remember, the first two rules are pretty simple that deals with decimal place or no decimal place. The third role is a little bit trickier. You have to recall, if this is an exact number, something that could be counted, that you can know for certain 100% that it's that number. Those have an infinite number of significant figures. Now that we've taken a look at these three rules, let's move on to the example question in the following video and see if we could determine the number of correct significant figures