02 - Learn Unit Conversions, Metric System & Scientific Notation in Chemistry & Physics

Hello, I'm Jason and welcome to this section of the

chemistry

tutor. In this section we are going to talk about

unit

s and

unit

conversions

, so don't forget that

chemistry

is a mathematical science, so yes, we will talk about reactions. and molecules and things like that, but mostly we'll be interested in calculating how much something happens, how quickly a reaction occurs, whether it's a violent reaction or whether it takes years to happen, so we're going to deal with numbers. and so as a preface, we need to get comfortable with the SI

system

of units, which is the standard

system

that we use when we talk about chemistry and also

physics

and other branches of mathematics and science, and in order to do that we need to I'm going to talk about units and then I'll teach you a little thing here at the end, which is probably the most important thing you can

learn

when starting out with chemistry or any study of any science.

It's the most important thing. I know it saved my life in terms of solving a problem many, many times and that's how to convert units correctly. It's incredibly important. I can't emphasize how important it is. Now let me go ahead and tell you right now that this section right here is going to be a good primer for you to look at, understand what you need to understand, and start solving your chemistry problems, but I will say that for those of you who don't know, I have already created one, I think there are four. hours of unit

conversions

, a unit conversion to tour DVD that you can check out on the website and get and that has everything I'm talking about here expanded in even more detail with a lot more problems to give you practice, so if there is?

Is there any confusion about

scientific

notation

SI system of units unit conversions? Get yourself a copy of the unit conversion tutor because it extensively teaches you that stuff and I can't stress how important it is because when you

learn

how to convert units correctly you can almost solve all your problems without really thinking about what to do if you know how to do the units correctly, so let's start here from the beginning for those of you who don't know that we have the proper SIS unit system, as far as duration goes. Here in the US we often talk about miles and inches and feet and things like that, but when you get into science, you just throw out the idea of ​​miles and inches and feet in cubic feet and things like that, you just throw them away because you never do them. use in engineering sciences or anything like that, we are always in the SI system, which is called the

metric

system, so the unit of length that we are going to talk about in chemistry, the basic one, I should say, the base unit of length.

It's called a meter and I know you've heard of it before and we abbreviate it with the letter M, a meter is pretty close to a yard for those of you who need something to help you visualize what it is if you stretch out your arms like This is approximately a meter, it's just to give you kind of a rough estimate of how big it is and this is the base unit here, right now, the unit of mass, which is the amount of something that we have, you know, in your hand. and how much of an amount of anything you have, the base unit that we'll always use is the kilogram, which is K G, which we'll talk about how it relates to the gram here in a second, but basically it's grams kilograms.

We're all in the same family, they're talking about mass, well, finally, something that doesn't change, we use the second one, so the letter s and for temperature, the SI base unit of temperature is actually something called Kelvin, which is symbolized by the Letter K now later in chemistry we will use Kelvin quite extensively, I mean Kelvin, just so you know it's interesting: zero degrees Kelvin is when all atomic motion stops. When you say something has a temperature, it means that the atoms are vibrating. that's what it means when you heat something the atoms vibrate even more when you cool something the atoms vibrate less so the Kelvin temperature scale is the absolute temperature scale when you say zero Kelvin you mean everything stops, no atom moves at all. not even shiver, not even a small zero Kelvin is impossible to reach, it is impossible to get there, even deep space is not zero Kelvin, but that is the absolute temperature scale.

Now we will use it. You know, sometime later in chemistry, but mostly. Now we'll use Celsius, which is the letter C and Celsius is something you're probably more familiar with. Celsius is the scale we are on. One hundred degrees Celsius is the boiling point of water. Zero degrees Celsius is the freezing point of water. I will never use Fahrenheit. I shouldn't say never, but it's rare that we ever use a Fahrenheit temperature scale in chemistry,

physics

, or any other math and science, so these are the base units we'll use: meter for length, kilogram for mass. seconds for time and we'll mainly use Celsius for temperature, but the current SI system of units calls for Kelvin to be the base, so just so you know let's talk a little bit about

metric

prefixes now, let me change the colors a little bit here. a little bit let me talk about metric prefixes now let me give you a little secret everyone has heard of a meter I think everyone has heard of a millimeter everyone has heard of a centimeter everyone has heard of a kilometer right, look, the base word it has meter but all these things on the front are just prefixes that change a little bit of what you're actually talking about, that's why the metric system is so powerful and so useful because all the base units have the same distance, length, time And everything else. but we have all these prefixes that change in some way what we are talking about here, so when we talk about kilometers, we are talking about a large unit, a kilo of something is a large unit, right, we talk about milli, micro or nano.

Think about yourself, you know, a tiny nanometer, a tiny little thing, which is very, very, very small, so let's talk a little bit about these metric prefixes because they're really the secret to understanding the metric system. the prefixes, so we have the kilo, which is a metric prefix and what kilo means is 10 to the power of 3 and for those of you who are a little rusty on your algebra, 10 to the power of three means 1000, so it's a thousand of something like that. If the base unit of length, let's talk about meters, is approximately this distance, it is a meter, then a kilometer is 1000 meters and that is the unit of what we call a kilometer, so a kilometer really far is a thousand of these meters , right, and that's it. another unit we call kilometer, so in the English system in the American system it should say that we have miles and we have inches and we have feet and we have all these other things we know that these different units have different lengths we know that an inch is that big, We know that a foot is that big and we know that a mile is, you know, on the way to the store, it's pretty big, right, but they're all different words and they're not connected and they're not multiples. one from the other very well, this is a good 1,000 is a good power of 10 multiple, so it's really good to have, we'll talk about that later when we talk about unit conversions, but in the metric system everything is going to be a power out of 10 related to each other, so it's really easy to work with, so take the time to understand it because when you do it will make your life easier, so to give you an example here in terms of kilo, we say that a kilometer is equal to 1000 meters, so when you read the word kilometer, this kilo here just replace it in your mind with 1000, so instead of reading it as a kilometer, read it as 1,000 meters, that's what you should say because kilo means 1000 , it's like you substitute it or something and then you put this here in your mind, you're reading 1000 meters here a unit of 1000 meters that's what a kilogram is equal to 1000 grams a gram is a pretty small unit of measurement, right , but we We're talking about a kilogram, it's 1000 grams, so again in your mind you can take kilos and replace them with 1000 so that in your mind you can say a unit of 1000 grams if you're going to do that, let's move on. here and let's talk about instead of kilo, this is a pretty big unit, kilo is big, right, it sounds big, even what about senti, which is another, another unit or another prefix and senti is 10 to the power of minus 2, look, this is 10 to the power of 3 times 1000 10 to the power of negative 2 is the same as 0.01, which is the same as 1 in a hundred, so for those of you who are not sure about algebra when you have something raised to a negative power like this, it's exactly the same. thing like saying 1 over 10 squared that's what it means 1 over 10 squared is 1 over a hundred so when we say felt it's the same as 10 to the power of negative 2 which is the same as 1 over 100 which is the same as the point In 1, these are all the same.

I'm just writing them down to show you here, so when we say 1 centimeter, which you probably already know, is much smaller than a meter, it's 1/100 of a meter, so it's a unit that's much smaller than a meter because many times it is convenient if I am measuring something so big to talk about centimeters, it would be cumbersome to talk about kilometers or even meters if I am talking about something small, okay, so just to give you an example, if I were to measure something that big here , it would make a lot more sense to me to talk about centimeters than kilometers because that's a smaller unit there, so here it's 1/100. now continuing with the progression here let's talk about millimeters or milli, let's talk about mili the prefix milli means 10 to the power of minus 3, which is the same as 0.001, which is the same as 1 over 1000, so if I were to use this type, It would be you know, 1 millimeter is equal to let's say 1 over 1000 of the meter, that's what this says, we can read this millimeter, you can read the milli as one in a thousand, which is the same when we talk about kilometer replacing kilo with 1000, so you can see, there are different prefixes, some of them like kilo mean large multiples because we are talking about something very far away, maybe we want to talk about the distance to another planet, we would talk about kilometers or even something bigger. but if we measure the width of a human hair we will not use kilometers or whatever, we could use millimeters or we could even use nanometers or micrometers which are even smaller divisions, but you see how everything is done, everything is beautiful. the power of 10 kilos is a thousand senti is one over a hundred milli is one over a thousand so everything goes like this now let me write a little table for you just to help you, you will probably find this in your book but just to help you, 10 to the power of 9 is Jig.

Okay, so we represent that with G you may have heard of gigawatts, gigawatts of electricity, which is a huge unit of power, which is 10 to the power of 9, right, there's a lot of zeros here, it's like a billion of something that is Giga, so you have 10 to the power of 6, which is mega, which we abbreviate with M, so here we could give an example, we could have a Gigagram of something or here we could have a megagram of something right here. we have 10 to the power of 3, which is 1000, we talk about that being a kilo and we appreciate it with K, so we could be talking about kilometers right now, if we get smaller, then we could have 10 to the power of minus 1, which is deci, which is d so you could have a decimeter, for example, now, honestly, you don't use it much.

I'm just putting it here for completeness, you'll probably see it in a book. 10 to the power of minus 2 centi, we talk about C. for something, so you could have centimeters as an example, then we go from 10 to minus 3 for Milli, we could have a millimeter, so we've talked about that, but I'm still talking in terms of meters, but this could probably be milliseconds. Many of you have heard that when you time a swimmer, you can measure his results in milliseconds because you are really interested in how fast he crosses the line correctly, so you can have the minutes, the seconds, and maybe the milliseconds. after. that's kind of a fraction between seconds, so these things can be applied to any of the units, that's why we're talking about them here in general, if you make it even smaller, you get to 10 to the power of negative 6, which It's micro. now micro you can't use them again a small M this is capital M this is small M you can't use them again from micro so you actually have this little symbol which is a Greek symbol all right so you go up and then get it I put a little U on it , that's basically what you have here, so you could talk about micrometers or microns.

The way we talk about that 10 to the power of minus 9 we call it nanometers and we use the letter n, so they are nanometers. and this is kind of popular culture nanotechnology, what does that mean? It doesn't mean anything big. Nanotechnology means incredibly small or maybe an iPod nano that is really very small, so the prefix and nano actually means very small. One billionth of a meter is what it is. and finally, the last one I'll put in here is 10 to the power of negative 12, which is pink, we use the prefix P, maybe you have a picosecond.

The picosecond is incredibly small, you even know, it's even less than a billion, it's 10 to the power of negative 12. so these are incredibly small fractions of a meter per meter, being what you know about this big right, so I don't think that hasSo this is the metric system in a nutshell this is the cliffnotes version of the metric system we have prefixes like giga and mega and kilo to represent large units of a meter or a second or a gram or any kilogram megagram Gigagram okay, I can do that and then once you reduce the divisions of your base unit, you have deci, which you don't use much, and then you have I felt centimeters, millimeters, micrometers and nanometers, picometers, but they all apply to seconds, they all apply to the duration of time. mass anything in the metric system, now that we know what the correct metric system really is and now you know how to interpret it if someone tells you it's two centimeters or so many centigrams or two milligrams of something if you get a pharmacy tell you two milligrams of a certain drug every hour, you will know that that is a fraction of a gram, that is what it is now that we understand that I am going to teach you sincerely from the bottom of my heart, seriously, one of the most important things that I have learned in all my I studied mathematics and science and learned them, you know.

I guess I was in high school. I had a very good teacher who taught us this and honestly it has saved me throughout engineering. grad school is something that I use all the time and here's the deal when you're trying to convert units, you can go from kilometers to micrometers, you can go from Giga, you know, Giga meters to Pico meters and if you're not sure what to do, it's possible You may know what the conversion factor is between these two things, but until you practice a little you may not know how to set it. Do you multiply by a thousand to get what you're looking for or divide by a thousand now?

Do some mental gymnastics and figure it out, but early on, when you're getting used to these things that are a little complicated, they can easily lead you down the wrong path, so what we're going to do here are some quick and simple examples. of unit conversions to show you how this works, let's go ahead and do that. What if you wanted to convert 500 meters to the unit of kilometers so we know what the unit is? What do we know how far away we are? Here we have 500 meters of something, but we don't want to express it in meters.

I want to express it as how many kilometers I have, so what you need to keep in mind is that you know the conversion factors in the metric system, that's really it. The good thing is that many times you know what the conversions are, you don't have to memorize what it is, if you were in the English system, maybe you would need to know how many feet there are in a mile, you know there are 5,280 feet in a mile, that's a number weird, it's nothing, it's a nice magic round number, how many inches are in a foot, there are twelve inches in a foot, okay, cool, that's not a nice round number, you have to remember a lot of that stuff correctly, the metric system, everything is a good multiple of ten, so it's easy to remember that a kilometer is equal to a thousand meters, how do you remember that?

Because the prefix kilo means 1000, a kilometer, 1000 meters, that's what it is if you memorize these prefixes what they're going to do. Naturally, as you study any of these things, this becomes important so that you know what the conversion factor is to go back and forth, but at first you're not really sure if I multiply or divide by a thousand and this is super. I'm going to give you a simple problem so that many of you can look at this and know what to do, but I guarantee that as you progress through chemistry and start working with density and grams and then with moles and molarity and cubic feet and other things and meters cubic as we start doing these things, then what I'm about to show you how we convert these two things will be really very useful.

The first thing to do is write what you know, 500 meters, that's what you know, so write that, always start with what you know, don't start with the conversion factor, so you write what you know, you draw a line horizontal here and a vertical line here, so you're making it like a little bit, almost like a tic-tac-toe or something, so you draw this line here, on this line here, the next thing you want to do is write down your conversion factor which You have here, this is something like a fraction bar, a giant fraction bar. we'll talk about that here in a minute now what we know is that a kilometer is equal to a thousand meters so what we want to do is write it like this we want to write it like this a kilometer is equal to a thousand meters now we want to write it this way because what we're going to do is to treat this as a fraction because it's actually a fraction, this is like a fraction bar, so you see how we have meters at the top and meters.

Also at the bottom, what this allows us to do is cancel the meters with the meters, in effect what they are doing is dividing, it's like if you know at any time a fraction, if you have five divided by five, they divide. They give you one, well, here we have meters divided by meters, so the units cancel out like this, they kind of disappear, so the final unit that we are going to have will not be meters because these have canceled the final unit that we are. we're going to have kilometers, which is what we want, we're trying to convert the kilometers, so what we do here is again, we treat it as a fraction, so what we have is five hundred times one, we're multiplying by one because they're both At the top we take the result of what is 500 and we divide it by one thousand five hundred times one divided by one thousand, it will give you a zero point five zero point five, which is the only remaining unit it has.

I didn't cancel anything it's kilometer so we have kilometers this is the answer now this is something you could do in your head because if you know I made up an easy problem on purpose so you could follow it 500 meters if you know that a thousand meters is a kilometer then 500 meters It should be half a kilometer that's very easy but I guarantee you it could create a problem that when it comes to nanometers or picoseconds and it would confuse you on what to do, but if you set it up this way where your units cancel out leaving you with the unit at the that you are trying to convert, you will always get the correct answer and you won't even have to decide to multiply or divide, that is your true power, you don't even have to think about the logical thing to do to multiply or divide, all you need to do is set it up correctly so that in the end you get the unit you want.

Now let me show you one more thing real quick before we move on to the next problem, what happens if we set it up the other way around? 500 meters. Now the next thing we need to do is write our conversion factor. Let's say you guess and you wrote it this way. 1000 meters is equal to one kilometer. You're getting ready to do your thing here and you'd look at this and try to cancel it. You would notice K meters and kilometers do not cancel because they are different units. Now these guys are the same at the top, but they just cancel each other out. if they are at the top at the bottom they only cancel if they are at the top at the bottom, so if you accidentally wrote it this way you would immediately catch your mistake because you would look here and say kilometers don't cancel with anything else, so I can't do anything, so this is totally wrong, so I would discount it right away because you don't have the unit you are trying to convert to right now.

What if you were trying to convert? centimeters to meters correct so you would do it exactly the same way you start with what you know four centimeters they draw a small horizontal and vertical bar and then you have to write the conversion factor you know how many centimeters there are in a mirror there are 100 centimeters in a meter , then you write it this way 100 centimeters in a liter, why do you write it that way? It's because when we write it this way, unlike if it were flipped, the centimeters will cancel out with the centimeters, so they disappeared. the only thing I'll have left is meters, which is what I'm actually trying to count to convert it to 4 times 1 is 4 4 divided by 100 will give me 0.04 the unit is meter because that's the only thing left over, that's what I'm going for trying to convert and we'll do some more simple little problems, but I guess I'm going to cut to the chase here, this little method works for anything, any unit, anything, physics, chemistry, math. biology, anything with the unit, if you're talking about meters per second and you're trying to convert it to kilometers per day, you can if you're trying to take grams per cubic centimeter and convert it to kilograms per cubic.

Kilometer, you can do all that with this method here and you don't have to think about what to do. Simply set the unit to cancel everything. Make sure your conversion factors are correct. I'll spit out the correct unit because that's the way. You've set it up now let's say we're going to do something a little more complicated, not really complicated but a little more. What if you were to convert centimeters instead of two meters? What if I wanted to know how many? millimeters that was right so a lot of you watching this may not know what to do some of you probably do know what to do but a lot of you I bet you don't because you're four centimeters and unless you're good with the metric system you may not know how many centimeters or how many millimeters are actually in a centimeter, many of you may know that by looking at this right now, but some of you don't, so I'm not going to tell you because I'm going to pretend that we don't know but we don't know how many let's pretend we don't know how many millimeters there are in a centimeter but what we do know is how many we know um but write down what we know, what we do know is that 1000 millimeters are equal to a meter and also We know that 100 centimeters are equal to one meter, but this is not exactly what we are trying to do because we are actually trying to go from centimeters to millimeters, but we don't actually have a conversion factor, you may know that.

Okay, right now, looking, you might know how many are there, but let's pretend we don't know, but we do know. is how many millimeters are in a meter and how many centimeters are in a meter, so let's use what we actually have here and I'll show you the power of this method if you write it this way, 100 centimeters in a meter, right? Continue this guy as many times as you need and I can write it like this: a meter is 1000 millimeters now, why did I do that? Because here centimeters cancel with centimeters and meters also cancel with meters.

Anything at the top will cancel out with the same unit at the bottom and you can extend this unit conversion as long as you need to have the units cancel out in a way that you need them to cancel out, so that you have canceled out the units. centimeters, you have canceled the meters, everything you have. The left is millimeters, so the way you do this is 4 times 1, which gives you 4, 4 divided by 100, multiply that by a thousand divided by 1, so basically what you're doing is multiplying everything on the top and then divide it by everything. at the bottom that's all you're really doing here the answer you'll get is 40 millimeters 40 millimeters now for those of you who knew 4 centimeters how many millimeters are in a centimeter many of you probably already knew 1 one centimeter contains 10 millimeters .

This is not something I have told you. It's something that some of you may know simply because you may have worked with the metric system a little more and that's okay, if you know that's your conversion factor. And you know that's a fact then and look what I've done. I have turned it wrong. It's a good example of how you can spot your mistakes correctly. So what we know is that 1 centimeter is 10 millimeters. The reason I realized my mistake is because I looked down to cancel my units and I couldn't do it, but now I can cancel centimeters with centimeters, so all I have to do is do 4 times 10, divided by 1 .I'm going to get 40 millimeters but you see the power of this.

I mean, I don't know if you realize it yet, but you should because it's so powerful. I have solved the problem in two different ways. In a way I knew the direct conversion factor between the two things. I was trying to do it and I get the correct answer here. I really didn't even know the direct conversion factor. All I knew are two different conversion factors; In other words, I connected centimeters to meters and then connected meters to millimeters so you can sort. Think about it because it connects the dots. If I'm trying to convert from one unit to another, I don't need to know a direct conversion factor between the two.

If I know, it's great, use it, but if you don't know. As long as you connect the dots with your conversions from point A to point B, you will always get the correct answer. Here we go from centimeters to meters, from meters to millimeters, and we get the correct answer. I'm telling you, the more you do this, the more you know in chemistry and other classes, it will save you on many occasions because it really keeps you from getting into the mental mess offigure out what to do now, what if I gave you a problem and said one inch is given? equal to two point five four centimeters right, that's something I haven't told you until now but it's true if you measure one inch it's 2.54 centimeters and if I asked you to convert two inches to centimeters how would you do it right?

We've given you the conversion factor so all you have to do is start with what you know two inches and now we apply our conversion factor one inch is equal to two point five four centimeters the way I write it is one inch is 2 .54 centimeters. I don't turn it over because if I turned it over I wouldn't have canceled units anywhere, but here I have inches. cancel with inches which leaves me with just centimeters two times two point five four divided by one obviously it's five point zero eight centimeters and that's the answer and that's basically it.

I'm just giving you some really easy examples here. I'm not going to go into density calculations. I'm not going to go into other things because we're really going to use this in this technique throughout the course, in almost every problem that we do, you'll see something like this because We'll be setting up our units and I'll also tell you if you want more information about unit conversions. SI system units, things like that, check out the unit conversion tutorial. It's four hours of all this that gives you many different units. different examples I think what I have shown you here is good enough to prepare you and as we go through the course we will do it together and you will learn and I think it will be fine but For those who want a little more, check it out because now it's all there.

One more thing I want to talk about before we leave here is

scientific

notation

, it's something that many of you will have seen before, maybe it's totally new to you here, but it's a very simple concept, don't let the name scare you. Scientific notation, oh my gosh, it must be incredibly difficult, it's so easy, actually, well, it basically amounts to numbers being cool. I can represent, you know, 127 apples. If I want to and that's easy, it's only three digits one hundred and twenty-seven apples, but what if I had five billion apples? What if I had five billion three hundred forty-two million five hundred ninety-two thousand three hundred ninety-four apples?

Well, you could write down all those digits, but that gets really annoying after a while. What if I'm doing something bigger? What if I am measuring the number of meters or kilometers to the nearest planet or to the Sun speaking millions or even billions of kilometers away? so it's just a lot of digits to write over and over again, so there is a shorthand way to write very large numbers and also very small numbers. If you're looking at the size of a molecule, you might be talking about ten to the power of minus nine or very micrometers or something like that, so we use a different way of writing very large numbers and very small numbers and that's called scientific notation.

The easiest way to explain what it is is to just show you what happens if I have the number two three. seven six 2376 and I wanted to represent that in scientific notation the way I would keep the digits the same two point three seven six digits are the same but I put a decimal point after the first digit and multiply by 10 to the power of three why do I multiply by the power of three is because if I put the decimal here then when I multiply by 10 to 3 you basically move the decimal as many times as indicated in this exponent so I move the decimal three times one two three 2376 so it's basically a shorthand way of writing that and you can look at this and say well, this looks shorter.

I mean, how important is it to get this right? As you use it more, you will understand its advantages. What if I have one hundred fifty-one and I wanted to convert it to scientific notation? It would be a point five one times ten to the power of two. Where this comes in handy a lot of times is what if you were measuring distance? so you know the Sun or something, what if it came out two three seven four nine three eight seven two one and that's a number of kilometers, so that's a lot of digits, obviously each digit is important, but it's probably mainly what Are you interested?

This is the kind of general order of magnitude that you know, the last digits here, yes, they are important to be exact, but in reality, when you talk about the distance to Mars, you may not care until the last digit, so than the shape. to really handle that, you could write this as two point three seven four nine let's say you want to take it up to here but then you would multiply by 10 to the one two three four five six seven eight nine times ten to the power of nine because in scientific notation the decimal is here but when I multiply by 10 to nine only the decimal moves let me ask you something what happens when you multiply something by 10 let's say you have four and you multiply by 10 what happens well that's 40 true everything you've done and you see that there is a decimal point here, You can't see it because it's four point zero, but the decimals here, if I multiply them by ten, I move the decimal to the other side of that little invisible zero here, making 40, what happens?

If I multiply by 4 by 100, well, I will get 400, what happens if I multiply 4 by 1000, will I get 4000? You see, every time I multiply by a larger multiple of 10, that's who I am. I just move the decimal point one point to the right, that's all I'm doing, so if the decimal is here, I move it one point. I get 40 decimal places here, I move it two points. I get 400 decimal places here. I move it three points. get 4,000 so this is 10 this is 10 squared this is 10 cubed to the right so this is 10 to the ninth power it just means moving the decimal nine points in that direction that's all it means so all you have to do is do when you look at the scientific notation of something is look at this exponent on the right there are a lot of points now yes, this answer that you get is not going to be exactly the same because I've truncated, I've left out some of the digits, but when you're talking about really long distances , that is enough for most cases.

Now let's look at a different example. What if we have something small zero dot zero zero two three? How would you write that in scientific notation zero zero two three? Well, if I use positive numbers. to make me move the decimal point to the right and then when I mean, I'm not going to end up using negative exponents to move the decimal point in the other direction, so the way you do that is by looking at your first few numbers here. If you have the first non-zero number, it's two and three, so we have two point three, always put the decimal after the first digit multiplied by 10.

Imagine you have a decimal point here, you will move the decimal one two to the left . three point 10 to the power of negative three and this is really where it shines too because you know this is kind of ugly zero point zero zero two three what if you have five zero zero point you know zero zero zero two three well this is going to end. Being shorter is also true and it is something that you will have to learn and you will see many of your problems that will express the number of grams in terms of scientific notation, so you have to understand what happens if we have three point one two. multiplied by ten to the power of negative five, how do we convert that back to a normal number?

Well, we have a negative decimal here, so my advice to you is to write your numbers three one two, stick your finger right here, where the decimal is. and then you're going to have to shift it to the left one two three four and put a decimal point here and just check it, put your decimal point here and shift it to the left five one two four five and you could put a zero here if you wanted zero dot zero zero zero zero three one two and I can't tell you how many, I actually wrote down a number and stuck my finger in there and counted the decimals and you'll have to do it. do it like this, but if it is a the most important thing to take away here is that if your scientific notation has a positive exponent, you are moving the decimal point to the right, you are forming a large number if it is a negative exponent, you are moving the decimal to the left, which means you're doing a very small number, one.

The last example is how you would write that as a normal number. Well, I just write five four, stick my finger in there and start writing. zeros 1 2 3 4 5 I check myself. I paste a decimal here and move it six ends to the right. 1 2 3 4 5 6 and that's what occurred to me so often you could put a minus zero or whatever, see for yourself. and then you have to add a zero to be sure, but this is what it means 5 point 4 times 10 to the power of 6 is the same as 5,400,000 and that's a good introduction to scientific notation and again I'll say it one more time.

If you need more practice with scientific notation, if you're not sure if this is enough, check out the unit conversion tutorial. It has a whole section on scientific notation with many different problems. I think again that this is enough to achieve it. Especially if you've seen it before and we're going to be working with it so much that you'll probably get very comfortable with it here quickly, but if you need additional help, unit conversions there for hours of concentrated coverage. Of that, we've covered another section, we've talked about the really important topic of units, unit conversions, and chemistry, we've talked about the SI system, we've talked about metric prefixes, we've talked about what they mean.

I have talked about converting units and showing you. I don't really want to call it a trick. It's not my trick. Many people use it, but unfortunately many books don't show you how to do unit conversions this way. I'm telling you this will save you a lot of time when you get to more complicated units, you know your mind will just think about how easy it is, after that you might occasionally run into one of your friends who's never seen this before and you'll save them, ya You know, from pulling out their hair, you know, when they're doing their homework.

We've also talked about scientific notation, measurement or should I say writing legal numbers and also very small numbers, a lot of your problems. I hope you see the number of grams or the number that you know or the distance of something or the amount of something in terms of scientific notation, so you just need to know that it's a different way of writing a big number and a small number. number and you can enter scientific notation right into your scientific calculator or your graphing calculator, so just write it down as you see it and you can use it there.

My name is Jason. I hope you enjoyed this section. I learned something here, stay with me. I'll take you step by step in the next sections. We will start talking about real chemistry, putting elements together to create compounds and then we will look at chemical reactions, but you need to do things step by step, the most important thing you can do for yourself is to go observe everything and absorb everything. If you try to skip too much, you'll get confused for no good reason. I'm Jason, practice your problems, practice your unit conversions. I promise it will save you a lot of time on your assignments and exams.