The earth’s circumference is approximately 40.1 Mm (megameters). What is this circumference in kilometers?

Rewrite 299,800,000 m/s in scientific notation.

Metric Prefixes

Hey, guys. So now that we've seen s I units in the S I units system, a lot of times you're gonna see letters or symbols attached to your base units. Your base units are just meters, grams and seconds. They're kind of like the most simplistic basic units of metric units. So we're gonna see letters like K or M or even Greek letters like mu. These were called metric or S I unit prefixes. And the basic idea is that each one of these letters is just a shorthand for a prefix like K for kilo M family arm you for micro. And each one of these prefixes or letters just stands for a specific power of 10 that you're gonna multiplied by a base unit. So, for instance, kilo is 10 to the third Micro is 10 to the minus six. They're kind of just like easy ways to represent big and small numbers. So you don't have to write a bunch of zeros out. For example, five kilometers or five k m is gonna be. If we wanted to represent that in terms of meters, we would just look up k inside of our table. We know K stands for Kilo and the prefix kilo stands for 10 to the third or 1000 means the same thing. So five kilometers just means five times 1000 m. So five kilometers is just the same thing as 5000 m. Here's another example 4.6 m s. So here we're gonna look up this prefix M which, by the way, is not the same thing as our base unit of meters, same letter, but different meaning. So we look at this M in M stands for Millie. And this Milly prefix stands for a specific power of 10 10 to minus third or 1/1000 10.1 All those things mean the same thing. So 4.6 milliseconds just means 4.6 times 0.1 just multiplying by a specific power of 10. And so this number here just ends up being 0.46 seconds. So these prefixes just help us write these numbers in just, um, or compact way. So we're gonna use this table a lot, actually, because you're gonna have to convert between the metric prefix is. So I'm gonna give you a really simple process for doing this. Let's just do a bunch of examples and see how this works. So we're gonna express the following measurements and we're gonna basically rewrite them in the desired prefix. So let's just get to the first one. We're gonna convert 6.5 h m to M. So here's the first thing you're always going to do when you're rewriting these using metric prefix is you're gonna identify where you're starting and target prefixes are so here. I'm starting at H, so h stands for Hecht. Oh, and then I'm actually going to know base unit. So I'm actually going to know prefix. So that's actually I'm sorry. No prefix. So that's the base unit. So I'm really just going from here. Thio here. So what I have to dio is the next step is I have to move from the start to the target, and I'm just gonna count up the number of exponents that I moved. For example, I'm going from Hecht oh, to base unit. So I'm going from 10 to the to 10 to 0. So if I move from here to here, then I've jumped two exponents. So I've really gone to to the right here. And it's important that you figure out the direction because that leads us to the third step, which is we're going to shift the decimal place in the same direction that we moved in Step two. So, for example, now 6.5 h m. We shifted to to the right. So in terms of meters, now you just take the decimal place and you shifted to the right twice and you fill in a zero as needed. So 6.5 Hecht 0 m is the same thing as 650 m. That's really all there is to it. Just follow these steps and will always get the right answer. Let's just do a few more so we get comfortable with this So 3.89 millimeters to meters. So here we have this prefix, uh m eso This is Millie and we're gonna go to the base unit which is in meters, so we're gonna do the exact same procedure here. I'm starting off at Millie and I wanna go towards the base unit, so I'm just gonna go from start to finish or start to target, and I count up the number of exponents that I moved. So I'm going from here to here, and I'm going from 10 to the third of minus third 20 Just look at the number. Don't worry about the sign. We actually jumped three to the left. So from here to here, we jumped three to the left. So that means that 3.89 millimeters If I want to write this in terms of meters, I'm gonna write the number 3.89. But I have to shift it to the left three times, right? So I have to shift to the left because that's the same direction I moved in Step two. So 12 and three. And so I'm gonna fill in zeros along the way. And then I'm gonna put another zero point so that the decimal point is like, right here. So that 0.3 89 m and that's our answer. Now for this last one here, we're gonna converts, or we're going to rewrites 7.62 kg, Two micrograms. So here we just identify the prefixes I'm going from kill Oh, and then eventually I'm gonna end up at Micro. So here's what I'm gonna dio I'm gonna shift from start to the target. So from 10 to the third, I'm gonna have to cross through the zero exponents. So when I move in this direction, I'm actually going three exponents and then from zero over to Micro, which is 10 to the minus six. Then I'm jumping, actually, six exponents, So in total of actually moved nine to the rights. And so therefore, I'm just going to shift the exponents with right nine times. So 7.62 kg becomes I'm just gonna shift it. 12 and then 1234567 So it's 123456789 I'm gonna fill in seven zeros along the way. And so that is how you would convert how you would rewrite 7.62 kg, two micrograms so we can see here. What kind of a pattern? And so when you re writing these numbers with with metric prefix is there's a pretty easy rule to follow to kind of check. You know, if you're if you're doing the right thing, if you're shifting from a bigger to a smaller unit basically going to the right, Then your number is going to become larger. So if you're units are becoming smaller, there should be more of them. That's the way to think about that. And if you're going from a smaller to a bigger unit, then your number is going to become smaller. Alright, guys, that's it for this one. Let me know if you have any questions.

Physical Quantities and Units (Crash Course) | Measurement | Physics | GCE O-Level

Rewriting in Scientific Notation 

Hey, guys, We're gonna take this number here and we're gonna express this in scientific notation Now, you might be a little confused at first because you might be like, Well, this is already looks like it's in scientific notation. But the problem is, remember that our scientific notation numbers are format is a number eight point B C, in which this numbers between one and 10 times 10 to the d. So the problem is that this number here isn't really in the right format. So we're gonna take this number. I'm gonna express it in the correct format. So here's how we can do this. We can take this number that's in this weird kind of like kind of scientific notation. We could just write it out as a normal number, and then we can re compress it back into scientific notation. So here's how we do that we take this number is 0.0 That's four zeros, 5 to 9 times 10 to the minus six and we want to compress there. We're gonna actually could expand this out into a normal number again. So we're gonna follow the rules for converting numbers into standard form. We look at the the exponents that tells us how many decimal places to move and the negative means We're gonna end up with a number that is much less than one. So that tells us which way to move the decimal point. So we're gonna move to the left six times. 12 3456 We're gonna fill in the zeros so a decimal point actually ends up over here. So that means that we have this number here. And if you count this up, I think this ends up being 10 zeroes. That's before. So now that we wanna dio is this is our actual number here in terms off the standard form. Right? So this is basically this number in standard form. Now we want to take this number and re compress it back in the sight of scientific notation. So we're gonna follow the steps. The first we have to do is end up with or we wanna move the decimal so that we get a number between one and 10. So if you count this up 10 11. So we actually gonna move 11 decimal places now and with this ends up being is 5.29 And then what happens is we have times 10 And now the exponents is gonna be 11. As somebody destined places removed. And because we're starting off with the number that is much less than one, this ends up being a negative exponents. So this is our answer in scientific notation. Now it's in the correct form where this is a number between one and 10. So that's it. You guys can just move on to the next video. But if you want to stick around, I'll show you just a really quick sort of a shortcut way to do this. So one thing we can do is we actually go from the original number that's over here, and we can figure out how to get to this number really quickly. So what we do that is, we go from the decimal place, which is over here, and we're gonna go until we get a number that's between one and 10. So 5.29 And if you do that, you're gonna go 12345 So you have five decimal places that you're gonna move over here in order to get to this number. Now what happens is because we're going from a number that is much less than one. This five here actually means a negative five in the exponents. So if you take this negative five and this negative six and you kind of, like, add them together, then you're actually gonna get this negative 11. So that's kind of a shortcut way to do this. Alright, guys, that's over the speed.

Dimensions and Units

Units of Measure: Scientific Measurements & SI System

Astronomers often detect radio waves with wavelengths of 3,000,000,000 nm. What is this wavelength expressed in decameters (dam)?

 Which of the following quantities is an acceleration? 

Intro to Physics

Introduction to Units & the SI System

Hey, guys, welcome to physics. My name is Patrick. I want to be your instructor for this first video. We're just gonna talk about briefly units and the S I system of units. Let's check it out. So, guys, what's physics all really about? Well, physics is the study of natural phenomena. That's the definition. You'll senior textbook. But really, it's just a bunch of measurements and a lot of equations. I like to think about physics as a math class with rules or math with storyline. For example, if you take a ball and you drop it towards the ground, it falls to the ground because of gravity. That's a rule. There's also a math equation to describe how fast and how far it falls. And so before we get to the equations, which will see plenty of in the in the future, I want to talk about measurements and units because in nature we measure physical quantities. So things like mass length and time, all the stuff that I have in this table down here that we'll get to in just a second, and the thing about these measurements or physical quantities is that when you measure something you have to have a number and a unit in order for it to make sense. For example, let's say you measure the mass of a box, need a number and a unit to describe it. If you just said that that Mass was 10 10 by itself doesn't actually mean anything. It could be 10 kg or £10 or 10 ounces. So if you have just 10 that doesn't mean anything. But if you measure it to be 10 kg now, that's a number and a unit. And that measurement does make sense now. So kilograms ah, lot of these units will have their shorthand notations. We're going to see a bunch of those things later on in the future. So we're going to see a lot of units in physics. And so, in order for your equations toe work, but you have to remember, is that all the units inside of that equation must be compatible with each other. So the way I like to think about that is they have to speak the same language. And so groups of compatible units that speak the same language or work together form what's called a system of equations and in physics, the big one is gonna be the S I system which stands for in French, the System international. So it's just backwards. So this is the S I system. We've already been supposed to kilograms, which is K G and meters M seconds is s and Newton is n There are other systems that will see the imperial system is an example where we're using pound, feet, inches, seconds things like that. But the main way that we use in physics is the S I system. So physics equations In order for them toe work, they all the units must be compatible with each other. Here's a quick example. One of the most powerful equations you'll see in physics is gonna be force equals mass times acceleration or F equals m A. So if we replaced all these variables with their units, we can see that a newton is equal to a kilogram times acceleration. I'm just gonna give this to you. Acceleration is in units of meters per second squared. So notice how all of these units here Newton's kilograms, meters and seconds all belong to the S I unit system. Whereas if I said a Newton equals a pound times a meter per second squared. This is actually incompatible, whereas this first equation is compatible. So this is actually incorrect. And you're gonna get a wrong answer if you start mixing and matching things from different systems. So make sure that all your equations and all the units speak the same language and are compatible. Alright, guys, that's really all there is to it for this one. Let's move on to the next video.

Rewrite 0.00016 kg in scientific notation.

Rewrite 3.41 × 10−4 in standard form:

 Metric Prefixes and Conversions

Rewrite 9.98 × 107 &nbsp;in standard form.

Scientific Notation

Hey, guys. So a lot of times in physics, we're gonna work with really long numbers, whether the really big or really small. For example, the mass of the earth is this crazy long number here. Imagine we had to write this out every single time we used it. Well, fortunately, we can use a type of notation called scientific notation, and we use scientific notation to compress really long, inconvenient numbers into much shorter ones. For example, we could take this long number here with a bunch of zeros and we could rewrite the mass of the Earth as 5.97 times 10 to the 24th kilograms. So this is a much shorter way of representing that number. So the general format first scientific notation is going to be a number a point B C times 10 to the d. So a point B c is just gonna be a number that's greater than or equal to one, but less than 10. So, for example, 5 97. So then that's the number, and you're gonna multiply it by 10. Raised to a power, this d is just a exponents. So how do we actually get all these numbers, I'm gonna show you really simple process for how we convert or how we rewrite standard form into scientific notation. Standard form is just normal numbers and then into scientific notation. Let's just do a bunch of examples. So we get the hang of this. So we're gonna take this number and rewrite it in scientific notation. The first thing gonna dio is you're gonna move the decimal place until you get to a number that's between greater than or equal to one, but less than 10. So here the decimal places over here and we have to move it to the left. 1234 and then five. So we're gonna move it five decimal places to the left in orderto land at this number 3.4 the next we wanna dio is we want around this number two the second decimal place. If it's a really long number with a lot of non zero numbers like this one is so we're gonna take this, I'm gonna round it to the second decimal place. So we're gonna have to look at the next digit over here and it's greater than five. So we're gonna have to round it up. So I'm gonna round this up to 3.5 and I'm multiplied by 10. And now I have to figure out what the exponents is. Well, that's the third step. The third step is the number of decimal places that you moved in. The first step is gonna be equal to your exponents. And if you came from a new original number, that's greater than 10. That exponents is positive. So, for example, we moved from a number that original number greater than 10. We move five spaces to the left, so our exponents is positive five. And that's how you rewrite this number. That's really all there is to it. Let's do a couple more examples. We get the hang of this. So now we're gonna do the same thing over here. We now have to move the decimal place until we get a number that's between one and 10. So we actually have to shift it forward to 34 So there was actually four spaces to the right that we moved here. So we end up with is a number that's 1.2 We don't have to round it or anything. Times 10. And now we have to figure out the exponents what we came for. An original number that was less than once, or exponents is negative. So it's 10 to the minus four. The four meetings did number of decimal places that we moved. And now you might also see some weird ones you might also see. Like you might have to. You know, your professor might ask you to represent seven in terms of scientific notation. So we're gonna follow the same exact steps, move the decimal place until we get to a number that's between one and 10. But if you think about it, the decimal places right here. And this number is already between one and 10. So the way you would, right? This is seven. You don't have to move it. Times 10. And the number of decimal places is equal to your exponents. But you didn't actually move any decimal places. So this is just times 10 to the zero. So just in case you see some weird stuff like this, this is actually how you would represent this in scientific notation. Um all right, that's really all there is to it. And the next thing you might see, the other kinds of questions you might see is you might actually have to go backwards. And what I mean by that is you might have to go from scientific notation out back into standard form, so you might have to rewrite scientific notation numbers as normal numbers. So let's get a few examples. Let me show you really simple process for doing that too. So imagine we wanted to take this number here, and we want to write it as a normal number. Well, really, all you're gonna do here is the exponents is just gonna be the number of decimal places that you moved just as it was up above. And if the exponents is positive, your number becomes larger. If it's negative, it becomes smaller. So, for example, 5.45 times 10 to the eighth. This eight here means move the decimal place. In order for the number of to become larger, you're gonna have to move it to the right. So 5.45 what you do is take this number and you're gonna shifted to the right eight times. 12345678 And you're gonna fill in six zeroes over here. So this is how this number would be in standard form. And for this last 19.62 times 10 to the minus five. So we're gonna do is 9. 62 and the exponents is the number of decimal places they're gonna move. And if the expo is negative, your number becomes smaller. So you're gonna have to shift to the left. You're gonna go 12345 and then fill in your zeros. 123 and four. Your decimal place ends up over here. You're gonna put another zero there. So that means that this here is how you would expand the scientific notation back out to a normal number. Our guys, that's all there is to it.

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