# Write each number in scientific notation

So I have 1.

### Scientific notation definition

Everything else goes behind the decimal. The slow way is to say, well, this is the same thing as 3. So this might be a faster way of doing it. So when you take something to the negative times 10 to the negative power, you shift the decimal to the left. So hopefully that's sinking in. I'll need 4 spaces, So, 1, 2, 3, 4. Decimal Exponent Symbol is part of the Unicode Standard ,  e. And how did I know 4 0's? Times 10 to the 1, you're going to get You have five 0's. When I take something times 10 to the second power, I'm essentially shifting the decimal point 2 to the right. And to get the decimal to move over the right by 5 spots-- let's just say with 0, 0, 0, 0, 2, 9. Because I'm counting,, this is 1, 2, 3, 4, 5 spaces behind the decimal, including the leading numeral.

Every time you multiply it by 10, you shift the decimal to the right by 1. If a number is greater than 1, the exponent of base 10 is positive.

None of these alter the actual number, only how it's expressed. Fractional values can be used, so if within 0. If you keep moving the decimal point to the left in 2,, you will get 2. When the decimal is moved towards the right, the count for the exponent of base 10 should be negative.

## 78 million in scientific notation

This is a little bit more than 1. So let's say I have 3. We're going to have to add a 0 there, because we have to shift the decimal again. Now let's do another one, where we start with the scientific notation value and we want to go to the numeric value. So this is 1. 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. Notice, I just took this decimal and went 1, 2, 3, 4 spaces. Every time you multiply it by 10, you shift the decimal to the right by 1.

Begin by locating the initial decimal point, and where it is going. Or it might be a small number, like 0.

### Scientific notation rules

You had to move it 6 places to the right to change 0. In this usage the character e is not related to the mathematical constant e or the exponential function ex a confusion that is unlikely if scientific notation is represented by a capital E. It's written as a product with a power of And just to verify, do the other technique. If you keep moving the decimal point to the right in 0. Let's do one more like that. Let's do a few more examples, because I think the more examples, the more you'll get what's going on. Scientific notation also avoids misunderstandings due to regional differences in certain quantifiers, such as billion , which might indicate either or And then you're going to have your decimal. And then 10 to the fourth, you're going to have 74, And you'd have to put a 0 here. Times 10 to the 1, you're going to get So how do I write this? None of these alter the actual number, only how it's expressed.

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. And so it'll be 2.

## Scientific notation problems

Scientific notation also avoids misunderstandings due to regional differences in certain quantifiers, such as billion , which might indicate either or Well, I'll just make up something. Our final scientific notation answer should be Example 5: Rewrite the given decimal number 0. You're doing 1,th, so this is 1,th right there. So I have 1, 2, 3, 4, 5 digits. Decimal Exponent Symbol is part of the Unicode Standard ,  e. Just to mix things up. If you keep moving the decimal point to the right in 0. We're going to have to add a 0 there, because we have to shift the decimal again. So our answer would be 0. And you have 1, 2, 3, 4, 5, 6 digits. If I take the decimal and I move it 3 spaces to the right, this part right here is going to be equal to 2. You can show that you moved it 6 places to the right by noting that the number should be multiplied by

So one way you could think about it is, you can multiply.

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