Okay everybody get the plethora of emails I sent out about 24 hours ago. That answer most lingering questions. Do you have any lingering questions at the moment that I should answer now But again okay I chose this as my thought for the day or a number of reasons. One is I used to have a beard so that fellow up there the white board used to look something like. This is taken from a long ago issue. You the student newspaper here at the University of Delaware. And I was fascinated by the fact that when the cartoonists that that you do something that would be great and the students in the front row. They tell somebody that looks not only a lot like chemistry but a lot like some chemistry that we'll be talking about later on this semester. Income went through. I mean why is the capsid which says students for their part should question anything they don't understand. So if you do have questions either about the course material or the administration of the course. Please don't hesitate to ask at any point. Alright reminder lab this week. No lab next week because its labor day Monday is anyone. And I've been getting a few questions about the Thursday 5-7 segment that's blacked out at your schedule. And they answer those questions is you have nothing to do or that block that day this day Because the only time this group is going to be using that Thursday 5-7 slot is for exams and your first exam is not until October three. So enjoy football separated. Since your first lab is coming up in about ten days Clearly talking about some aspects of making measurements in the laboratory looking specifically at section 1.5 in your textbook. But let's start from scratch and I'm thinking that a good chunk and what I'm going to be talking about today should look familiar to you already. By the way and he supports the duct. When you work in the lab this semester and scientists in general and they do laboratory work and write up the results in journals. Work with the metric system. Why Yes okay to give reasons right there. What is most sensible with the notable exception of the United States is a metric system are everything. And so and scientists and other companies go to the laboratory they use the metric system because why not that's what we use when we go to the food store. But not this country however we decided at some point that we would like to be able to communicate with our coworkers and other countries. And therefore we decided to use the metric system itself. By the way the metric system is sometimes referred to as the SI system Yes I stands for System International which is French for the way sensible countries do it. And the other good reason that was just given was that conversions between units are based on powers of ten as opposed to what we do in this country where we have all kinds of different numbers that we have to remember. There are 12 inches in a foot three feet in a yard therefore quarts in a gallon there are 5,280 metric. You don't have to remember all those number here. One number. I'm sure you're aware of the following metric prefixes. The prefix kilo means 1 thousand which is ten to the third of whatever the base unit is. Centi means 1 100th or whatever the base unit is. So that's ten to the negative two power because you're dividing by a 100 not multiplying by a 100. And milli means 111000 or whatever the base unit is ten to the negative third. For right now these are the only three we're going to ask you to know. We will introduce others as time goes on and as we need to you may be familiar with some of them already Such as micro Greek letter mu is the symbol for one millionth of the basically Nano as in nanotechnology one billionth of the base unit and so forth and so on. But the point is the macrosystem is considerably easier than what we've got going on in this country. And we'd like to be able to communicate with our colleagues around the world. So we're going to use the metric system and lab which means you're going to use the metric system. Okay that doesn't come as a big surprise tray. I'll give you a couple. It's the finished for this slide. Actually related Alright so I agree with the eighth and his life. Here's a semi trick question. But I'm willing to bet a lot of you know the answer what is the fundamental metric or SI unit of mass say m gram is actually not the right answer. The kilogram is however I don't blame anybody for saying ramp because the prefix kilo suggests that Graham is somehow more more fundamental than kilogram is. And actually the basis for saying that the kilogram is fundamental A unit of mass is going to be changing sometime very soon if it hasn't already. This was based on the idea that there was an object somewhere in France under a bell jar with a side of a bell jar that says this thing weighs one kilogram. However people notice in recent years that that object is starting to rust or road or whatever. And so the chances are pretty good that it doesn't weigh one kilogram anymore. So the kilogram or gram maybe in the process of being redefined but not tremendously differently from what they were. And by comparison to American units the closest thing we have the kilogram is the pow1 is about 2.2 pounds at one kilogram And the closest thing we have the grams the outs but even that's not all that close. There's about 28 grams in one and else. What's the fundamental metric unit of length or distance yes the meter. What America unit comes closest to being a meter. Does a yardstick it's actually more than that because 36 interested AR is a little over 39 meter And I was called a on a few volunteers before class today and make a few measurements on the cigar box that I brought along. We'll share those results with you before the end of the class period today. But the point is the meter stick is divided up into centimeters. So the meter is a little bit more than a yard and the closest thing we have to a centimeter is an inch an inch is actually about 2.5 centimeters. Again probably no big surprise. What's the fundamental metric unit of volume Yes very good. Technically there is no metric fundamental unit of volume because meters actually define a volume if you think of it in three dimensions. So you can certainly talk about the cubic meter. We saw what a leader looks like and you gotta match that Q. One meter wide one meter tall one meter deep. That defines a volume which turns out to be approximately 1000 liters. However I think most people are familiar with leaders and milliliters as common everyday units for measuring volume and these things actually made it into this societies cultural that people buy sodium to leaner models and things of that nature The leader is slightly more than a word 1.06 ports. Here closest thing we've got to the milliliter is a teaspoonful. A teaspoon of oil is probably about five milliliters. And also the term cubic centimeters sometimes is a cubic centimeter is the same thing as a milliliter. Point is when you go into the laboratory before too much longer and start making measurements. You're gonna be using metric units like this. And we'll talk later on about how to make conversions metric units already units if that's necessary to do. But again hopefully most of what's on this slide if not through any questions so far okay we'll give people another minute on this one bit Everybody good. I assume you all noticed what kind of a lovely day today. So I appreciate the fact you gain a chemistry class anyway. But I guess it's about 80 degrees out there. On what temperature scale Fahrenheit course it's what we use in this country. It's probably about 27 degrees out there today on what other temperature scale Celsius and what's the third one elements degrees Fahrenheit degrees Celsius and technically Hellman's not degrees Kelvin. Although if you put a degree sign before the k that won't be the worst thing you ever did. What's the boiling point of water a Fahrenheit scale to dwell on what's the freezing point of water at scale 32 somewhere between there is a temperature frequently divide as room temperature roughly 77 degrees Fahrenheit Little bit cooler than what we have out there today but okay what's the boiling point of water on the Celsius scale freezing point southeast. Zara room temperature Celsius scale typically translates to about 25 degrees Celsius. Right away just from that. See two things that are different between the Fahrenheit to Celsius again. What is the meaning of 00 on the Celsius scale that's where water freezes. 0 Fahrenheit scale somewhere below the point at which water freezes The other thing that's different is the size of that agree. The difference between these two physical phenomena the freezing of water at the boiling water is a 100 degrees on the Celsius scale but a 180 degrees on the Fahrenheit scale. So the size of the Celsius degree and the size of the Fahrenheit degree are different. You probably seen that equation that looks like this. This is equation that's commonly used to convert back and forth between Fahrenheit and Celsius. Temperature scales. The 32 comes from the fact that 32 degrees Fahrenheit scale is 0 degrees on the Celsius scale That corrects for the difference between what's 0 means. And the 1.8 is what you get. You divide these two numbers a difference of a 180 Fahrenheit degrees is the same as a difference of a 100 Celsius degrees. So 180 divided by 100 is 1 a. Some people further write that as nine over five. And that's okay it means the same thing. Some years ago about this time of year. I attended a chemistry conference in Toronto. Ontario Canada a civilized metrics be. And so I got the runaway airport. I got my luggage I got my rental car can down the road. You go to my hotel and I put on the radio and the first thing I hear is a weather report and the guy says it's gotta be a lovely evening in Toronto tonight with lows around ten. And I was thinking maybe I should've brought the long underwear. And then I realize oh wait I'm at a civilized country. He's talking about the ten Celsius. Fahrenheit. 50 times you get the answer. Multiply this by 1.8. You get 18 Add 30 to 50 Fahrenheit. Just see there's a little bit more palatable than ten Celsius but they're the same thing. Like sets. Okay there is a temperature known as absolute 0. That is the coldest possible temperature. Later on this semester we'll talk about why it's not possible to have a temperature lower than that. But for the moment we will simply say that translates to 459 below 0 fahrenheit scale 273 below 0 on the Celsius scale. It's absolute 0 on the Kelvin scale 0 the Kelvin scale is basically just like the Celsius scale except for the meaning of 0 the Kelvin scale is sometimes called the absolute scale because 0 is absolute 0 the coldest possible temperature. And therefore there is no sense in trying to talk about anything below that temperature because it's not physically possible. So all kelvin temperature's must be positive numbers. The freezing point of water and the temperature on the Kelvin scale. 273 the boiling 0.373 room temperature to 98. A lot of people just ran off to about 300. And the point is to convert Celsius temperature to Kelvin temperature Simply add 273. Everybody still comfortable any big surprises so far today. Section 1.6 in your textbook. It's titled mathematical treatment of measurement results. That's a fancy way of introducing the concept. Some people call it using conversion factors other people call it using dimensional analysis. That's the next thing we're going to be gotten better. What we mean by a conversion factor is simply a fraction that has a value of one. And the reason it has a value of one because the numerator and the denominator of the fraction or the same thing just expressed in different units. Here's a problem that should be easy to solve. What's the answer 100 and you get answer. Your feet there helps to know that. Why is the answer not diner How did you know to divide by three instead of multiply by a very simple answer to that question is because 900 doesn't make any sense. That's because you have an intuitive understanding having grown up in this culture But how many feet there aren't a yard how big a foot is how big a yard is. Obviously the answer involves dividing by three. There will be times later in the semester when we do calculations that don't involve units that are quite as commonplace as f0 and yards. But you might know how many whatever there is and whatever else. But where it gets interesting is do you multiply or divide that's where conversion factors come in come in handy. Obviously to solve this problem you have to know that there are three feet in a yard. Having said that there are two possible conversion factors you can write based on this equation Three feet over one yard or one yard over three feet. So they're both fractions that are equal to one. But only one of those is going to be a useful conversion factor for solving this particular problem. Suppose we try to solve the problem using the first conversion back. Well if we take 300 feet which is what we have to start with. And if you want you can write as a fraction 300 feet. And then multiply by this conversion factor well punch the number up on the calculator. The calculator says 900. But And the answer is wrong for two reasons. 1900 doesn't make any sense. But to even if you don't recognize that look at the units feet times fi square f0 and then the denominator you have yards. Well you want the answer to come out in yards not square feet per yard. And so this must be wrong because you haven't cancel out the units that you don't want. But if you try solving the problem using the second conversion factor Then it comes out right and you can be confident that it comes out right because starting with 300 feet and multiplying by one yard over three feet. Well the calculator says 100. But more importantly feet in the numerator and feet in the denominator cancel out. And what you're using conversion factors like this any units that are the same in both the numerator and the denominator can be cancelled out. And so in this case the only units left are guards which is good because that's what you wanted the answer come out. So we can be reasonably confident that 100 yards is the right answer. And of course it is So the moral of this particular story is when in doubt write out the conversion back. Even if you think you know what you're doing it's still a pretty good idea to write out the conversion factors include the units cancel out the units that you don't want to keep the units that you do. By doing that you will rarely make mistake. And show you another example in a moment before we do does anybody need more time with this one okay going back to my experience in Toronto. But I first The highway of my rental car the first thing I saw was a sign that said speed limit 100. And I think it okay finally at least where I could drive like I want until I realized that's not miles per hour that's kilometers per hour. And then you have to look at the other dialogues but the other interesting experience wasn't buying gasoline or petrol as they call it in Canada. Even given the economic situation at the time when you're pulling to a gas station and see a sign that says Gas. $0.50 you're thinking hey that's a pretty good deal. Until you realize two things One it's Canadian money. And more importantly they sell it by the leader not the gallon. My rental car from the Toronto Airport got 12.5 kilometers per liter of petrol. But I'm an American and so I think in terms of miles per gallon how many miles per gallon is that given these two pieces of information. Now I'm not asking you to actually solve this problem. I'm just telling you to tell me how we would solve this problem. In other words to solve this problem that you multiply or divide by 1.69 the multiply or divide by 3.76 Yes divide by 1.6 so nine and multiply by 3.17. That's correct. You divide by this when you multiply by this one. Now that's not immediately obvious. That's why you set up the conversion factors. 12.5 kilometers per liter or you can write it this way. If you wish. Anytime you see per as in kilometers per liter whatever follows the pert can go to the denominator that makes it more convenient. But the id in solving this problem is first you want to get rid of kilometers and replace that by miles. So when you set up your conversion factor you want kilometers in the denominator miles in the numerator. That's why we wind up dividing by 1.6. So dy because 1.609 kilometers is the same thing as one. Likewise you want to get rid of the leaders and the denominator and leave yourself with garlands down there. So your conversion factor should have liters over gallons or liters over liters cancels out. This like kilometers over kilometers cancel out. And that's why you multiply by 3.76 because this 3.76 liters in one go. So if you do these things and punch up the answer on the calculator. You find that my repo Gaga at 29.4 miles per year Any questions about the use of conversion factors. Some people call it dimensional analysis because you cancel out and you don't want and keep the dimensions the question. Use this part. Can you just write it out this way shortly but the point is OK. We're starting from here. Drill point bump. The 12.5 kilometers over one liter. And the point is it's we want to cancel out kilometers kilometers in the denominator that typically what I do is I just write the units first and then put in the numbers. So I put kilometers down here because And cancel those out miles on top. And I look at this how many kilometers are either a mile 1.6 so nine so 1.09 goes next kilometers. One mile on top. Same reasoning over again cancel out meters in the denominator. So liters goes on top gallons goes on bottom. 3.7 86 goes next to the leaders and we cancel out the units. We don't plot or left with miles over gallons and that it's just doing the arithmetic makes sense. It sense whoever. Okay is this a valid conversion factor Some say yes some say no somebody defend their answer. Yes. This is not a valid conversion factor because 1000 kilometers is not the same thing as one meter. But this sort of mistake is very very easy to make. How could you make this a valid conversion factor yes over then. You get either switch the units. 1000 meters over one kilometer or yes See see this isn't as easy a lot is when you try to do it I was thinking the easier way to go would be to just switch the numbers one over at the house but you could do 0.01 kilometers equals one meter that would work also. Main point is for it to be valid conversion factor the numerator and the denominator must be equal to each other. If that's the case then it's not a valid conversion factor. And for some reason when people need to multiply or divide by a thousand it's a very common mistake to make to get the numbers upside-down. And so you're either multiplying And when you meet and divide by 1000 or vice versa and then your answer is off by a factor of a million. So you just gotta be careful about things like that. There are similar problems to these in your textbook for additional brands. Alright. Let's talk about scientific notation. How would you write this number in scientific notation Go ahead. Correct. Then there's only me by scientific notation. Even though he didn't write the decimal point it's right there. The idea in scientific notation is to move the decimal point. However many places you have to until you arrive at a number that is between 110. If we move the decimal point here 12345678 places to the left we now have 3.21 which is a number between 110 So I write down 3.2 times ten to the eight means the way I have to multiply 3.21 by 108 times to get back to this number. The exits. How would you write this number in scientific notation Okay. Here's the decimal point move it 1234567 places. We're at 6.56. To get back to this number we have to take 6.56 and divide it by 107 times. The negative exponent means you're dividing more orderly. This number Large number or small number large this number small large numbers positive exponent. When you write the number in scientific notation. Small numbers negative exponent when you write the number in scientific notation. Scientific notation is often useful when you don't want to write a whole bunch of zeros will see plenty of cases where we're working with either very large numbers or very small numbers in this course. So scientific notation will come in handy. That's not a difficult concept but I think most people understand that where it gets interesting is how calculator's deal with this Now I'm hoping that long before your first exam probably before you go to lab you should be choosing what calculator you are going to work with this semester and stay with it. And hopefully it's a calculator that can handle scientific notation. Having said that since different calculators do this differently you need to make sure you understand how your calculator anvil scientific notation. Many calculators have an E for that purpose. I recommend using that wherever necessary. Some calculators don't have that but they haven't EXP day that would work. Some calculators have a times ten to the x key or a little character a phone it whatever. But you need to figure out how your calculator does. That's the point is if I have a calculator that has an E key and I want to enter this number in scientific notation into the calculator. I type in three decimal points you want E H. And here's what comes up on the gap when you'll see the 3.21 and then way over on the right sides of ways you'll see the 08 which tells me that the exponent on the ten should be pete. Now one problem that some people have sometimes when you type this in and you see this I'm going to split. People will write down the 3.21. They will ignore this part altogether That's a problem because that's really the most important part of the number. And if you think otherwise I have a business proposition for you I will happily give you $3.21. If you give me 3.21 times $78. That go a makes a big difference. Some calculator displays have a D for the exponent. Whatever again make sure you know how to use your calculator to do this. If I wanted to enter this number in scientific notation I typed six decimal blank 567 and then I have to use the sign change are key. It has plus and minus. You get a negative exponent. But again you'll see something that looks like this on the display with a negative sign in front of the seven or the exponent negative seven whatever. But the main point is once again you need to figure out how your calculator does this. And if you're having any problems figure it out how your calculator handle scientific notation Bring me your calculator will figure it out. However let's make sure we do that before the first exam not during the first day saying Sal reasonable. Okay For the rest of our time together today we'll be talking about what's in Section. 1.5 the title religious measurement uncertainty accuracy and precision. And on the next page significant figures in measurements. That before class today. You bought hears to use the meters to measure dimensions this cigar box. We thought they were. Let me share the results with. So I asked people to measure the length in centimeters away centimeters depth in centimeters and ask for what I got for volunteers and we'll just call them A B C and D The results are going to be a no particular or person. A 21.5613 person B. 211 is so-called that roughly 21.113.6 Person C 21.513.76.6 and person B got 21.713.86. Right off the bat. One thing is obvious. For volunteers could agree on what the length of the box was. Within limits which we'll talk about shortly. I'm not going to criticize my volunteer because this is normal. I been doing this kind of thing for a long time and we typically get results that look like this. Where it gets interesting is when you try to figure out what the volume of the boxes. Now you have permission to laugh at this point but I like my iPhone for person a if we multiply the three dimensions of the box together to figure out the volume comes out 1701 that's a great number. Any Star Trek fans here. Yes no. Serial number. The enterprise SEC. 1701. Moving at 21.1 times 13.561709.1. C 21.7 points 19.0344. And finally person me 21.7 times 13.8 times 6.761796. Okay Question Will 1800 milliliters of water fit in the cigar bucks birthday says No person B says nobody person thesis almost Person C says Sherwin. Well there's an obvious point that we're trying to make here. The only variable here was the people making the measurements with the same box saying meters thick. But it's not at all unusual or different people to come and get different results when they are using the same instrument to measure the same artifact. And that's where we get into the realm of Significant figures. This is what we mean by uncertainty in measurement. The point is when I ask my volunteers to do is make a few measurements that involve numbers. And the point is whenever you make any measurement that involves a number and write down some number representing that. You're actually making two statements. One is what you believe the value of that measurement b. And the other is how precisely you think you've measured it The concept of significant figures or sig figs for short are the digits in any measure quantity that are known with certainty plus one digit that is unless sir. So for example when person D here measure the length of the box to be 21.7 centimeters. What that person was saying whether or not they realized it was I'm pretty sure about the two in the tens column. I'm pretty sure about the one in the units column is the seven in the tenths column where I might be off a little bit maybe it's actually 21.6. Maybe it's actually 21 pointing However the same person when measuring the depth of the box just wrote down six. So again whether or not they realized what they were saying was I might be off by as much as a centimeter. Maybe it's actually five maybe it's actually seven. If that's not what they met they should've written now the decimal point and some other digit after the decimal point even at that digit happens to be a 0. So the point is when you write down some number that represents a measured quantity you should write that number with the correct number of sig figs or significant digits. Now what I'm gonna do is show you a bunch of numbers. And we're going to assume that all of these numbers represent some quantity that somebody measured. And the question I'm going to have for you is how many significant figures how many sig figs are there in each of these measured quantities what start with 6.3 to three sig figs event. No any non-zero digit is always significant. Next 1.306 hacker and two different answers on that. One. For the right answer is three. Because if the person who measured this only intended to show two significant digits. They should have written it this way. If you write down 6.3 you're saying I'm sure about the six but it's the theory and the tens column that might be off by a little bit maybe 6.2 maybe 6.4. But if you're pretty sure about the number in the tens column then you should write down some number in the hundreds column that you don't happen to be quite so sure about that number happens to be a 0. So in these two different representations of what may or may not have been the same measurement. This person is expressing a little bit more confidence in their ability to read whatever the measuring devices than this person is How many sig figs at this number and for any NET 0 that's located between a two non-zero digits is significant. How many sig figs on this number three bring the zeros in front here serve no purpose except to show where the decimal point is. Zeros whose only purpose is to show where the decimal point is are not significant. And a very easy way to figure that out. If you're not sure what's going on right the number in scientific notation. I want to write this number in scientific notation She's the magnet. Okay thanks that raise your hand. So I know which direction I'm supposed to look. But yes. 6.32 times negative two the point is you wouldn't write zeros zeros 6.32 times ten to the negative two. Because those zeros in front don't make any difference anymore. And they didn't make any difference here either except to show you where the decimal point is and now you're using scientific notation to show you where the decimal point is. Then that these concepts make sense so far. Okay how many sig figs in this number 33 Is one possible right answer or four or five. That number is written. To me it's not obvious how many sig figs there are. There are certainly at least three. Now again if this number was written in scientific notation would make a whole lot more sense. I have no idea what was being counted here. But if whatever was being measured here if the person thinks making this measurement they might be off by about a 100 or so. Then they should write the number this one. In scientific notation the show three sig figs The problem with the way this number is written. It's not really obvious whether those zeros after the two are significant or if they're just showing you where the decimal point is if they really are significant if whoever counted the 63,200 or whatever things it is thinks they're only off by one. Then they should write it that way. 6.3 to 00 times n to the four. Clearly shows five sig figs there. So I think this is a little bit ambiguous but writing scientific notation like this. It's not questions about any of this Last example a lot of and spree 0.0060. How many sig figs five is the originates. The zeros in front are not significant because they only show you where the decimal point is. Everything else there is significant. The 0 between the two and the six is significant. As last 0 is significant otherwise it wouldn't emit rhythmic. You'll be dealing with this concept a lot in the laboratory. So again problems in the textbook for additional practice here Generally figuring out how many sig figs you have in some measure quantity. It's not that difficult where it gets more interesting is in doing calculations using those quantities that you make. There are different rules for handling sake things. Depending on what particular arithmetic operation you happen to be doing. Let's talk about what happens when you multiply and divide first. The key question to ask yourself there. How many sig figs are there at each number that I'm working with. Suppose you go into the laboratory and you want to measure the density of some sample in a liquid. So the first thing you do is weigh the sample. Turns out to have a mass of 6.03 grams. And then you figure out its volume to be 7.1 milliliters. And since density is an object's mass divided by its volume we simply divide those two numbers. And you punch those numbers up on the calculator here's what the calculator sense. How many of you think you know the answer to this question to seven sig. Figs see any hands go up. That's good because you don't. Here's today's take-home. Never forget. It. Lesson. Calculators lie to you about say say it with me calculators lied to you about. I didn't hear you out debaters to you about. How many sig figs in Islam bring money in this number to how many in the answer For both answers are several answers actually. The rule for multiplying and dividing is the answer should have no more sig figs then whichever of your measured quantities as the smaller number and saying things. Three versus two that means the right answer should have to that. Here's the good news is. You can look at this number and you say okay I should write this number down but I should only have two sig figs here. First of all to 0 and fraud is not significant because it's just showing you where the decimal point is. Then you say okay eight and then it's followed by a four Now some people just say okay that's where as a nine after it. So 09 is almost the whole number we rounded up and it comes to be five. And that's fun. There's nothing wrong with you. And then there's another school of thought that says well wait a minute. If what we're saying is there's an uncertainty you have the four then everything that comes after that is completely uncertain. And he says that those are what the digits are the calculator huh calculators like Team. So maybe that's a nine. Maybe it's a six maybe it's three maybe it's someone who does. So some people rather than rounding it off to 0.85 would just say chop it off and write it as 0.84 For purposes of what is the right answer I would accept either one of these. Because the whole concept of sig figs as exemplified by our little exercise with the cigar minds says that reasonable people might reasonably disagree about what the value of the uncertainty digits. So we should agree on the eight and attempt Scala. But if there's a little bit of a variation on whatever the number is in the hundreds column. That's the last digit is uncertain which means different people might not agree him up. Wouldn't it make sense ok. That's the rule for multiplying and dividing. Here's a multiplication problem using the same two numbers same problem bunch it up on the calculator. You get this. Calculator's lie to you about seeing things three sig figs here two sig figs here. Answer should only have to say things. You can either round this off to three or chop it off really do whatever you're most government. So the point is multiplying and dividing. Ask yourself which of my measured quantities has the fewest sig figs that's the number of sig figs. There should be the answer and don't expect a calculator to do sig figs for you because it doesn't. So if the rule multiplying and dividing adding and subtracting there's a different. And the problem is that when you add and subtract numbers what you're doing is adding and subtracting columns of numbers. The question to ask yourself or an addition problem or subtraction route is which column contains an uncertain digit. Using our same two numbers and this time either adding them or subtracting them. You punch the numbers up on the calculator. Here's what you get. But hopefully by now you know you get dressed the calculator to do sig figs. Here's the thinking. In 7.1 the uncertain digit is in the tenths cough. As opposed to the 6.03 were the uncertain digit is in the hundreds column. If there's an uncertainty in the tenth column then it makes no sense to write down some number in the hundreds column because you're only allowed to keep one uncertain digit. So the right answer over here is 13.113.13. Because this digit in the hundreds column should not decaf because there's an uncertainty. Scholar. Calculator says 1.07 for this But we shouldn't go to the hundreds column we should stop and the tens column. So once again you can either round this off to one whitewater or chop it off to 1. Either one is okay as long as you don't go beyond the tens column for the answer. So since you're only allowed to keep one uncertain digit that means the right answer over here is the 0.1 to the right answer over here is 1.1. You buying all this. Again it's frequently the case that people get the rules for multiplying and dividing mixed up with the rules for adding and subtracting. That's why there are problems in your textbook for additional practice Welcome back to this slide just a moment. I'm going to go back to one earlier slide for a second. Because so far we've been talking about measured quantities. And the rule for sig figs apply to measure quantities. But they do not apply to quantities that are known by definition. Quantities called exact numbers are numbers that are known by definition not by making them. For example the 12812 inches in one foot is an exact number Because if you say that it's not you say that this is a number that only has let's say two same things. Well then what you're telling me is that there is some feed that have 13 inches and other feat that have eliminations. Is that true of course not a foot is exactly 12 inches. A kilometer is exactly 1000 meter as I'm sure you can think of other examples. And so the way to think about this in terms of sig figs an exact number as an infinite number of sig figs. In other words they are not 12 inches in one foot There are 12 inches in one foot. And that does come into play sometimes when you're doing calculations like the one we were just looking at the exact numbers have an infinite number of sig figs. Suppose we want to convert 365.24 feet into yards. What do we do guess divided by three said I'm a conversion back. One yard over 3V. Bunch it up on the calculator calculator says one-to-one link 74666. How many sig figs should there be an incorrect answer yes. Five is the writing. Because how many sig figs are there in this number five and many other and this number an infinite number. Because there are not three feet in a yard there are 3 Xunzi thinks they are. So five sig figs here an infinite number of sig figs here. Okay the rule for multiplying and dividing is whichever one's smaller. Five is smaller than infinity. So we keep 5C things and the answer which means make either round this off to 121.75 or chop it off. 121.7 for either one is okay as long as you don't go beyond five sig figs questions about any aspect of this. Again. Okay convenient stopping place Enjoy the football game and joined the Labor Day weekend. Also we work with. We have got. He was a class that big a deal because you can always watch the video later with Agile. Hopefully those things will not conflict with exams or laboratory. As long as they die. In a lab you have Siri Davidson. Anyways every whatever office hours are basically right before this class 1230 to 130 on Tuesday but they also have office hours for 1015 or there's. None of that works for you to send me mail and say. That's 90. Students typically anyways. Because well I sent out the one email yesterday about So let's do that and then you'll see what the exams look like last year crease and we're all looking me up. Well obviously can't what else read your settings you go up to the one of the three should be followed by some number like three or something like that. You went with algebra. Where particularly understand the wonderful times. Okay well that's your alleged that where do you lack in their eyes that day that time there should be a lab section numbers. Appears to be something. I'm not seeing your lab section. You realize there should be some lately to pull out from Moody's. Maybe my laptop or something like that. And it should have a number like say like 93 lives around those reset your website integrate that. Dividends are basically different labs. It's pretty much the same style. Same everything. Same exam dates. Or missing bias is not that they can watch them. Later switch advancing it. I would have is a bit involved missing Xavier overlap. But we'll cross that bridge. I'd like to find out something or you have you know ahead of time. Just reading that. Yes. Yes very good example of a tool. Why is it that we say because why Could you actually measure it at 7.37.1 that last digit one is uncertain. That means there's an uncertainty that temps commented. That means if you're adding and subtracting there's always going to be I certainly have a tents go. Alright that means anything that comes after the tenth mealtime. So that's why I'm so if you're like me numbers we know in other words when somebody writes down. 7.1 yeah what they're saying is I'm confident about the seven. It's that one in the tens column that I'm not top or why we accompaniment. Well that's just a judgment call by the person. Okay and that's because readers thing overview Now I asked you to use this meter stick debate favorites. Well you think you can read this bitter steak is up to you. I think most people get read into at least a set of irritability et cetera centimeter. Some people are going to interpret and interpolate between those tens of centimeters bakery and dwelling ruthless enemy depends on how well you think you could use the beaters. I guess that's the point different people using the same device to measure the same object may come up with different numbers that I've just different number of sig figs to question how well they hated. Peter books 41 flat. We use 105 last year because I had published a lot of threes yet because that was my first time teaching can one I'm sorry. But now that we have either 105 anymore brightness my healing through red tag ways. I think yesterday. Well okay camera through the lab manual looks good. Now this is doctor when Graves lecture make. Your daddy is glass. I would say that you're not taking mine. So I recommend purple thing here looks like. So this you probably won't need but this you should be okay. Okay. Yeah. I think so I'm just trying to make sure I'm not sure it can handle scientific notation to kind of figure out how it does its thing. There maybe a couple of times that of the x-coordinate was talking about before. So for example 6.02 times ten to the x three like that okay that should work just fine. Alright. Second ohmic return changes. Okay fill out the gave it back next time. And the rest you have any questions don't be afraid. And there is a small correction which we want to watch that you recapture money has to catch up. The one that listed here as early nineties actually listed under that case that would change that to me was that doesn't put an S 70 Hg. Then we should be able to get the videos right. Now that Labs out they did until not next week but the following week Dr. Berg was going to be your next presentation just pair up most questions about lab. You're getting a nice preaching. So with the labs. So Wednesday is not Monday is that not the only think I was saying is that labs Begin September died in a sense a week of September. So obviously you don't go to lab and they'll shut them out of the lab this week in the lab. Next. Thank you Hi class you're charging guy who that's up to you. Now the textbook has a big heavy thing. If you feel like getting work down you're going to read the textbook around a glass with you. Sometimes what I'll do is I'll say 123 textbook we see in this table and some people like to have with them just so they can look at that table right then and see whether there's other people to say Here's invade 123 than they look it up like University of Washington. We just need to pretty much this electrical watching captioned videos. Next question on y axis and the link should be in the well okay the link should be in the syllabus that you get the email I sent out yesterday yes okay the update because in that evening I just got that you should also ESS. They sent me an email for tacitly competencies or they take an arbitrary tests. That's why accommodations are there. That's why they sent me emails. Don't you know that's. Okay. So we have to do is go to the DSS office and said that up with them. Alright. Okay yeah so forth. Alright you make yourself you're ready. You can only read this to the nearest centimeter. Zoom I my dad 30 probably reasonable and it interprets it one. Little lie to your baby would say every one that's related links between them. Maybe it's 31.5. What is going to be our well-being whatever the measuring devices. But the point is that a right that should only have one uncertainty by that point high. But that's if you're right at 31 here say I can't read any farther somebody else by right at 31.55 because they think they can read it tonight. So that's something which you have to say Okay this is as well as I can read the instrument. I'm going to write down some number that represents. The last digit is answer. More than one answer. Unlawful measure. Like you said these exact numbers as advocates for that 121212 inches or foot exactly here. For purposes of thinking about things. Okay the daily sheets of paper and everybody thought that over the last year tell me something I said I got to visit friends. Name. You're battling. Trainees. Wow. A bunch this up on the calculator says this. But that's wrong because you have an uncertainty in the tens the hundreds column it makes no sense at all. You should even include huh The calculator doesn't know to do that. It's just putting the numbers in because the calculator doesn't know what digits are. Certain are uncertain. You have to make that yet when herself. So in this particular case since we haven't certainly in that sense the answer should go beyond the ten scope. So despite the fact calculator says this you write down on your lap and that's what I mean when I say calculate multiple samples it will turn out to be 13 because you go beyond that. It's gone. Completely just when you're writing what you're measuring is just SegPhrase. Okay that's the rule for multiplying and why not. But when you add subtract subtracting numbers that's why the column manage promoted why you're dividing lighting doesn't. Sense yeah. Daily the bumps in the textbook and the end of chapter one and that had to do with things like this and see if you're getting the right answers. I just know I mean I guess we could sit here and have this conversation. The abstract I think it'll make more sense to you if you're actually tries it and see how they come out. And if you disagree with the books answers that we can talk about how that plays out in the context of entity. For private drop straight down thinking. Okay. Thank you for your herself. Oh yeah

chem103-080-20190829-140000.mp4

From Dana Chatellier August 29, 2019

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Video Created by UD Capture Classroom Recording in Smith 120 on 2019-08-29 14:00:00.

Appears In: CHEM-103 Chatellier

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