Learn the toughest concepts covered in your GOB - General, Organic, and Biological Chemistry class with step-by-step video tutorials and practice problems.

Matter and Measurements

The number of **Significant Figures** for a value affects its precision.

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Significant Figures (Simplified) Concept 1

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before you can determine the number of significant figures within a given value. You first need to understand the difference between exact and inexact numbers. Now we're gonna say the numbers you will encounter can either be exact or inexact. An exact number is a valuer integer obtained from counting Objects. Or as part of a definition, for example, there are 125 students in your lecture. This is something that you can determine by actually counting the number of students within your lecture or there are 13 objects in a baker's dozen. So this is an actual thing. A Baker's dozen is actually 13 and not 12. Now an inexact number, This is a value obtained from calculations or measurements that contains some uncertainty. We're going to see your textbook is measured at a length of 12.53 in so you've determined this by taking out a ruler and measuring it. Now you might be a little bit off because maybe you didn't adjust to the exact edge of the book. So there is a little bit of uncertainty associated with this number. That would not be the case with an exact number. I count 125 students in your lecture. I can't say there is 1 24.8 because a student doesn't count as 0.8. A student is a student. A baker's dozen is 13, not 12.8, not 12.5, not 13.1. It's exactly 13. So just remember the difference between an exact and inexact number.

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Significant Figures (Simplified) Example 1

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Here are example states determine if the following statement deals with an exact or inexact number, the combined mass of all doses of Broncho Dilator administered to a patient measure 10 mg Alright, so remember we're dealing with an exact number. We get an exact number either from a definition or by literally counting the number of objects. Remember, an inexact number happens when we do measurements or calculations within this statement. It tells us the word measure, we're measuring 10 mg of this bronchodilator because we're measuring it. That means that this is an inexact number. So there's a little bit of uncertainty associated with it. We may think we're administering exactly 10.0 mg. So maybe we're ministering 10.1 mg. Okay, so there's a little bit of uncertainty associated with this value in this case. Remember this is an inexact number.

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Significant Figures (Simplified) Concept 2

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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

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Significant Figures (Simplified) Example 2

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So let's take a look at the following example question here, it says determine the number of significant figures in the following value. While our value has a decimal point, when it has a decimal point, you move from left to write and we start counting. Once we get to our first non zero number. Our first non zero number is this three. So that's where we start counting. So that's gonna be one to three four. You count all the way to the end once you start counting. So here, this would just simply have four significant figures. So remember, just to rely on the three rules that we know in terms of determining the number of significant figures if it has a decimal point such as this one, we move from left to right. Start counting once you get to your first non zero number and keep counting until the end. If it had no decimal point, then we moved from right toe left and follow the same exact rules. If it was an exact number, then would have an infinite number of significant figures. Now that we've done this example question, move on to the practice question

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Problem

How many sig figs does each number contain?

a) 100. min

b) 17.3 x 10^{3} mL

c) 10 apples

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Problem

Indicate the number of significant figures in the following:

A liter is equivalent to 1.059 qt.

A

0

B

1

C

3

D

4

E

infinite

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