# Standard Form to Scientific Notation

In order to change a number from standard form to scientific notation, you must first rewrite the number so it is between 1 and 10 by moving the decimal either to the left or right. For example, 32,581 would be changed to 3.2581. Then multiply the number by 10 raise to the power of how many places you moved the decimal. In the previous example, we moved the decimal over four spaces, which means 3.2581 should be multiplied by 10^{4}. Written out, it looks like this:

32,581 = 3.2581x10^{4}.

## Changing a Number from Standard Form to Scientific Notation

To change a number from standard form to scientific notation you need to first rewrite the number so that it is between 1 and 10 by moving the decimal to the left or the right. Let’s look at 32,581. To write this in scientific notation, the first thing we have to do is take our decimal and move it to the left or to the right so that this number is between 1 and 10. Where’s my decimal? It’s at the end of my number. I’m going to have to move it to right between my 3 and my 2 so that my number is now 3 and 2,581 ten thousandths.

Now we’re going to multiply this times 10 raised to -and this power is found by determining how many places we had to move our decimal- we had to move it 1, 2, 3, 4 places which means we would need to multiply this number times 10 to the fourth power to achieve our original number. 32,581 is 3 and 2,581 ten thousandths times 10 to the fourth power in scientific notation. The same pattern applies when expressing very small numbers in scientific notation. Let’s consider the value 65 thousandths. **We’re going to start again by moving our decimal so that our number is between 1 and 10.**

I’m going to have to move it to between my 6 and my 5. That gives us 6 and 5 tenths. Right now, these numbers aren’t equal, not until we add our times 10 raised to the -now we have to figure out the power. We moved it 1,2 places to the right. We’d have to multiply 6 and 5 tenths times 10 to the negative 2 power to achieve our original number. 65 thousandths is equal to 6 and 5 tenths times 10 to the negative 2.