1. Intro to Physics Units

Introduction to Units

# Rewriting in Scientific Notation

Patrick Ford

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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.

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