Question

How do you write `38000` in scientific notation?

Answer 1

`38000` written in scientific notation would be `3.8 times 10^4`

Explanation:

Steps:
A. The number must be between 1 and 10.
In this case, `38000` is not between 1 and 10, so we are going to have to make it a number between 1 and 10 by adding a decimal

One important thing to remember is that at the end of every number there is an understood decimal. For example, in `38000`, there is an understood decimal at the end: `38000.`. All we have to do is move the decimal and account for the spaces we have moved it.

So, we need to determine what number we could come up with that would be between 1 and 10. Right now, the only number I can see that is between 1 and 10 using the number `38000` is `3.8`

B. Determine the Exponent (or the number of spaces that need to be accounted for).
Now that we have decided that `3.8` is the only number between 1 and 10 that we can use, we must decide what the exponent must be in order to display it in scientific notation. The easiest way to do this is to do the following:

1. write down the original number:
   `38000`
2. place the decimal point where we put it in `3.8`:
   `3.8000`
3. count the number of places after the decimal point (or count the number of numbers after the decimal point):
   3./8/0/0/0 `larr` there are 4 numbers after the decimal point.

So the exponent is four.

Now to the writing part...

C. Write it in Scientific Notation.
So this is kind of the easiest step because you just put together all you did. So get your number from Step A (`3.8`) and also take your exponent (`4`).

1. First, put down 3.8:
   `3.8`
2. Then, write out a multiplication symbol right next to it:
   `3.8 times`
3. Next, write out a ten next to the multiplication symbol. The ten symbolizes each space that we need to account for. (However, the exponent determines the number of spaces):
   `3.8 times 10`
4. Now, add your exponent raised by the ten:
   `3.8 times 10^4`

And that's how you get your answer! :)

Hope this helps!