# Entry 2 writing answers in scientific notation

So what's the largest 10 that goes into this?

Hopefully that last video explained it. Let me throw some commas here just to make this a little easier to look at. Convert from scientific to standard notation. But let's put it into scientific notation.

### Scientific notation calculator

Count the number of places n that you moved the decimal point. And more than just being able to calculate this, which is a good skill by itself, I want you to understand why this is the case. The next number in that sequence must result from another division by So if we multiply these two things, this is equivalent to 6 -- let me do it in a different color -- 6. Hopefully that last video explained it. Then we had 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 0's. So the way we can do that, let's multiply it by 10 on this side. But it's 5 times and then how many numbers to the right, or behind to the right of the decimal will do we have? The next number I'll do -- I'm having a lot of 7's here. So it would be equivalent to a 1 followed by 12 0's. Apply scientific notation in an application. Similarly, when expressing small numbers in scientific notation, a negative power of ten denotes the number of places that the decimal point moves to the left. You can think of it that way and so this would be equal to 10 to the 17th power. So that's 10 to the fifth power, right? That's the same thing as 10 to the 17th times 10 to the minus 1, right?

Just like that. Or another way to think about it is if you have 1 -- you have the same bases, 10 in this case, and you're dividing them, you just take the 1 the numerator and you subtract the exponent in the denominator.

Let's do 0. That's 10 to the minus 1. It's equal to 10 to the 11th times 10 to the minus 6 to the minus 1.

Then we had 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 0's. Let me just write down a bunch of numbers. You can think of it that way and so this would be equal to 10 to the 17th power. One place to the left gives 0.

### How to convert numbers to scientific notation

So what's the largest 10 that goes into this? Let's say I stop there. If you multiply these two things, you'll get that right there. You divide by 10 and multiply it by My second number is Be careful not to include the leading 0 in your count. And this is a valid answer. Just as a positive power often denotes how many times a number is multiplied by 10, so a negative power of ten denotes how many times a number is divided by Or this is equal to 10 to the 11th times 10 to the sixth.

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