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Donate Login Sign up Search for courses, skills, and videos. Math 8th grade Numbers and operations Scientific notation intro.

Scientific notation example: 0. Scientific notation examples. Practice: Scientific notation. Scientific notation review. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript There are two whole Khan Academy videos on what scientific notation is, why we even worry about it. And it also goes through a few examples. And what I want to do in this video is just use a ck So let's take some things that are written in scientific notation. Just as a reminder, scientific notation is useful because it allows us to write really large, or really small numbers, in ways that are easy for our brains to, one, write down, and two, understand.

So let's write down some numbers. So let's say I have 3. And I want to write it as just a numerical value. It's in scientific notation already. It's written as a product with a power of So how do I write this?

It's just a numeral. Well, there's a slow way and the fast way. The slow way is to say, well, this is the same thing as 3. And then we have 1, 2, 3 numbers behind the decimal point, and that'd be the right answer. This is equal to Now, a faster way to do this is just to say, well, look, right now I have only the 3 in front of the decimal point.

When I take something times 10 to the second power, I'm essentially shifting the decimal point 2 to the right. So this might be a faster way of doing it.

Every time you multiply it by 10, you shift the decimal to the right by 1. Let's do another example. Let's say I had 7. Well, let's just do this the fast way.

Let's shift the decimal 4 to the right. Times 10 to the 1, you're going to get Then times 10 to the second, you're going to get We're going to have to add a 0 there, because we have to shift the decimal again. And then 10 to the fourth, you're going to have 74, Notice, I just took this decimal and went 1, 2, 3, 4 spaces. So this is equal to 74, And when I had 74, and I had to shift the decimal 1 more to the right, I had to throw in a 0 here.

I'm multiplying it by Another way to think about it is, I need 10 spaces between the leading digit and the decimal. So right here, I only have 1 space. I'll need 4 spaces, So, 1, 2, 3, 4. Let's do a few more examples, because I think the more examples, the more you'll get what's going on.

So I have 1. This is in scientific notation, and I want to just write the numerical value of this. So when you take something to the negative times 10 to the negative power, you shift the decimal to the left. So this is 1. So if you do it times 10 to the negative 1 power, you'll go 1 to the left. But if you do times 10 to the negative 2 power, you'll go 2 to the left.

And you'd have to put a 0 here. And if you do times 10 to the negative 3, you'd go 3 to the left, and you would have to add another 0.

So you take this decimal and go 1, 2, 3 to the left. So our answer would be 0. And another way to check that you got the right answer is if you have a 1 right here, if you count the 1, 1 including the 0's to the right of the decimal should be the same as the negative exponent here. So you have 1, 2, 3 numbers behind the decimal. That's the same thing as to the negative 3 power. You're doing 1,th, so this is 1,th right there.

Actually let's mix it up. Let's start with something that's written as a numeral and then write it in scientific notation.

So let's say I have , So that's just its numerical value, and I want to write it in scientific notation. So this I can write as-- I take the leading digit-- 1. And if you want to internalize why that makes sense, 10 to the fifth is 10, So it's 1. You have five 0's. That's 10 to the fifth.