 Hello everyone, welcome to another Tutor-Terrific video. This is our physics course chapter 1 lesson 3 We are going over the basics of physics including measurements units estimating and problem solving in today's lesson We're gonna look at prefixes and unit conversions Now this might seem like a game to some of you a cruel game or some sort of crazy maze you have to go through But it is absolutely essential to understanding physics And how numbers are used and manipulated in physics. So let's get started So let's first talk about prefixes, so physically speaking prefixes are these symbols that are added to the front of any word but in Physics especially or chemistry. They're added to the front of units to modify their value by specifically powers of 10 So some examples would be things like kilo Millie and nano now I know all of you have experience with this because of your background in chemistry So I can add kilo to the front of meter and it becomes a kilo meter or in other words as we say In more conversational English kilometer The second I can add the Millie prefix in front of second and get Millie second and Gram I can add nano in front of gram and I could get nanogram now these prefixes have different meanings depending on which one we use and This metric prefix scale is perfect for understanding what each one means. So here are those prefixes Now a power of 10 is associated with each and every prefix that you see It's used to show how much larger About it by a certain factor of power of 10 the value is then the single unit when the prefix is Proceeding the unit. So for example, we saw kilo meters back there kilo 10 to the 3 10 to the 3 meters so a kilo stands for 1,000 or 10 to the 3 times whatever unit it proceeds For example, let's set something up. Let's pick a unit the meter Let's pick a prefix the kilo when you place them together you get the kilo meter This is how you read the chart 1 kilo meter stands for 10 to the 3 regular meters, okay? I've gone all the way out to Tara those of you who work at computers, you know these prefixes kilo mega giga and Tara stand for a thousand million Billion and trillion respectively, so that's how these work and that's how they're used We're gonna look at micro nano and pico throughout physics and we're gonna use senti quite a lot when we're talking about meters So let's practice using this scale to convert now I'm gonna use the factor label method to do these prefix conversions that I'm asking you I'm asking you to go from one prefixed unit back to the standard unit at first. So look here. We have 100 mm Well, milli is the abbreviation for M is the abbreviation for milli meters, so we have millimetres here, okay? And you can see up at the top of our prefix scale here the abbreviation for each of these Prefixed units, okay? So 100 millimeters convert that back to standard units, which would be standard meters So here's how that's done with this factor label method here We write out the starting unit first, which would be 100 millimeters We put the desired units on top of those same starting units But we equate a certain quantity in the desired units to that quantity in the starting units And then the starting units will of course cancel and we'll get our desired units. This is called the factor label method Let's see how it works for converting a hundred millimeters to meters So if you look here, we have a hundred mean millimeters Then we place meters the desired units on top millimeters the starting units on bottom And we set equivalent quantities of them using the chart the chart says that one millimeter is equal to 10 to the minus three meters And so what I end up doing is taking a hundred and multiplying it by ten to the three You can see that you can cancel the starting units because they're on top and bottom So a hundred times ten to the three over here needs to be converted to proper scientific notation as we saw in the last video we would move the decimal over two places to the left and add two by doing that to the Exponent so we get one times ten to the minus one Meters and that is correct a hundred millimeters is one times ten to the minus one or point one meters What about two point five mg? M Capital M stands for mega. So this is mega grams We don't usually use that very much But it's possible you could use it if you wanted to two point five mega grams convert that to regular grams Here we have our M standing for mega which stands for ten to the six So we'll put our starting units first two point five mega grams Put our desired units next on top divide it by our starting units And it will cancel those if we want but the main thing is the numbers we put in according to this chart One mega gram is equal to ten to the six grams. So again, we're gonna multiply now This is when we multiply these in perfect scientific notation right out the box 2.5 times ten to the six grams or 2.5 million grams 775 nanoseconds Nanos way down here a billionth or ten to the minus nine So we're talking about 775 really small units of time Place that first by itself then create this Equivalent numerator and denominator Converting from nanoseconds to seconds one nanosecond is equal to ten to the minus nine seconds We multiply those together and you can see that we have to move the decibel two places to the left to get it in proper scientific notation Add two to the exponent. We'll get seven point seven five times ten to the minus seven seconds, okay, so now we practice going from prefixed units to Regular standard units using the factor label method and now we are going to try the opposite way I'm gonna have some large or really small numbers written with standard units And I want you to see how using prefix units can really help you instead of scientific notation All these numbers aren't scientific notation, but they might be easier to understand using a prefix 7.33 times ten to the seven seconds Maybe using a prefix could help you see it better. So we're gonna convert to a prefix It's done really similarly to the above factor label method except we're starting with an unprefixed unit 7.33 times 10 to the 7th seconds. I'm gonna multiply that by this fraction. I'm gonna go to the nearest power of ten Which prefix has the nearest power of ten to ten to the seven? Mega Ten to the six. It's only one away. So I'm gonna multiply My 7.33 times ten to the seven seconds by one mega second over The equivalent ten to the six seconds Now in order to show how this works I'm going to say that I'm actually multiplying this number by ten to the minus six, which is equivalent to one over Ten to the six Now it's just simply subtracting these exponents or rather adding them because they're We consider adding when they're on both on top 7 plus negative 6 makes positive 1 so I really have a correct scientific notation 7.33 times 10 to the 1 Mega seconds or 73 ish millions of seconds. All right next one 1.0 times 10 to the minus 4 meters That's a pretty small length. Maybe a prefix Close by as power of ten is concerned would be better suited to see this number So as you can see ten to the minus four is closest to ten to the minus three. So we're gonna use milli So let's go ahead and set this up. What point note times ten to the minus four meters? Multiply that by my equivalent fraction here by getting to Millimeters one millimeter is ten to the minus three meters So if you cancel these if you want you end up with millimeters and we see we're dividing by a ten to the negative three Which is the same as multiplying by ten to the positive three So one point out times ten to the minus four times ten to the positive three Let's add those exponents. We'd get minus one. So we have one point. Oh times ten to the minus one Millimeters improper scientific notation. So about a tenth of a millimeter All right, and last one my goodness seven times ten to the thirteen days Yeah, let's look at the nearest prefix for ten to the thirteen. That would be Tara Ten to the twelve. So I'm gonna convert regular days to Tara days Seven times ten to the thirteen days. You multiply that by one Tara day over Ten to the twelve regular days ten to the twelve by the way stands for trillion Tara is trillion and so we would cancel the days We'd end up with seven times ten of the thirteen times ten to the negative twelve. So thirteen minus twelve. That's one So this would revert to seven times ten to the one Tara days or Seventy Tara days tens of trillions of days. That's a lot of days But this is a example of using our conversions for prefixes Now we could go beyond prefixes we can convert between different units all together not just a prefixed version of a unit and the standard version of the same unit It's a very similar method Okay, but we are going to need something more than just this prefix conversion chart We're gonna need what I call conversion factors These are equations that relate a quantity in one unit to that exact same quantity in another Unit another unit. So I call this a conversion factor here are some examples that we Probably know pretty well one mile five thousand two hundred eighty feet One inch that's two point five four centimeters one hour. That's equivalent to thirty six hundred seconds That's a very common one that is very useful in lots of these chapters in physics Then we've got the mole which you know from chemistry that stands for six point oh two times ten to the twenty three particles and One pound kilograms on earth Each quantity on the left is equivalent to that same quantity on the right in a different unit How do you get from one unit to the other with a conversion factor? You use the factor label method again You start with the units you have and the quantity of them and you multiply that by this fraction Which is an equivalent fraction where the top the units you want is Equated to the denominator in a different quantity the units you have Using that conversion factor the units you have will of course cancel and you end up with the units you want So let's let's try a simple conversion 195 pounds To kilograms on earth and you'll learn more about why I say on earth and have to quantify it that way later 195 pounds well according to a Conversion factor that I didn't show you but it does exist one pound is equal to four point five Excuse me point four five four Kilograms and so we can put one of those on top of the other since they're equivalent and so this fraction would equal one But since we're converting units the numbers are going to change So I'll put pounds on bottom so that they'll cancel it was the unit I had to start with the unit I want is now on top So I'm going to have a hundred ninety five times point four five four Kilograms and when I do the calculation, that's going to equal eighty eight point five three kilograms However, I can't write that as my answer based on Significant figures rules which we are sticklers for in science, especially physics and chemistry What you need to do now is you need to round to the proper number of significant figures Which would be three for this problem because the initial starting spot had a hundred ninety five Pounds as its measurement. That's three sick figs. You never use a conversion factor You always assume that each thing in here has infinite sick fix It's an exact number so you go by the initial measurement three sick figs It had and so I have to round to the tenths place here to have three sick figs in my final answer Okay, some conversions take more than one step to do there isn't a conversion factor to go right from the You start with to the unit you want So you'd have to use what this diagram calls linking units or just multiple factor label method Fraction steps to get from one place to the last place your desire Okay, everything is going to cancel when you write it first on top in one spot And then on bottom in the next section of your calculation Here's an example a hundred yards to meters now There may be a nice conversion factor out there, but I don't know it So I'm going to use multiple conversions to go from yards all the way to meters If I have a hundred yards, I could convert that to feet the following way There's three feet in every yard. So that's a conversion factor the yards will cancel And I'm multiplied a hundred by three now. I'm in feet now. I need to get to meters. So I'll go through inches Okay, so inches there's 12 inches in one foot So now I've canceled the feet units and I multiplied my result by 12 Then I could go from inches to centimeters because one inch equals 2.54 centimeters. So I canceled the inches Now I multiply by 2.54 now. I'm in centimeters I want meters a high snuck in a prefix conversion for you if you look at the chart One meter is equal to a hundred centimeters or ten to the two You could have also written one centimeter equals ten to the minus two meters Which is the way I did it on my images and when you multiply these all out you get ninety one point four four meters Notice that prefix conversion there Okay, the last thing you would need to do is use proper sig figs here My original measurement really technically had one or you could put a decimal at the end of that zero and have three To get if you had three ninety one point four meters if you had one you'd have to round down to ninety meters All right one more practice This is gonna also involve both prefix conversions and unit conversions 1.7 mega seconds into hours. I Want to start with the prefix conversion. You don't have to but it'd be nice to look at seconds instead of mega seconds That's one step according to the prefix conversion chart 1.7 mega seconds. Well, that's ten to the six seconds one mega second ten to the six seconds So I can cancel those mega seconds and now I'm in seconds now. We need to convert between units to get to hours We're gonna complete those necessary unit conversions now It takes a couple steps if you do not know the direct Conversion between hours and seconds you could go through minutes. So right now. I'm in seconds So I'm gonna divide by 60 seconds to get to minutes one minute equals 60 seconds Then I'm gonna get to hours by dividing by 60 again because there's 60 minutes in each hour Now with all my units canceled being on top and bottom Successive sections of this conversion. I have hours as my final unit now The raw answer in the calculator is 472.22222 forever. That's what I put this bar up here for to repeating hours I cannot write that as my final answer. Why why why? Go back to your original measurement. You were given 1.7 mega seconds. How many sig figs does that have? It has two so I have to round this to two significant figures Okay, you'd have to round to the tens place So the two after it would round down so you'd have 470 for some people this is a little odd because you're past the decimal on the left side So some people would immediately write this in scientific notation so that it's clear that zero is not Significant as I showed you in the last video now. I only have this two significant digits 4.7 times 10 to the two hours All right guys, thanks so much for watching that's it for this lesson. I'll see you next time. This is Falconator signing out