To put a number into scientific notation, we multiply or divide the number by 10 over and over until we have a number between 1 and 10. But we can't just change a number so we have to account for what we did by describing how many times we multiplied or divided with exponents.
Each time we multiply by 10 the decimal moves 1 place to the right. Each time we divide by 10 the decimal moves 1 place to the left. The exponent we use will describe the number of times we moved the decimal to the right or left. The exponent will be positive or negative to describe the direction we need to move the decimal to represent our original number.
I know... that sounds confusing, but it's really easy! Let's do yours...
0.063
Now we need to move the decimal to get a number between 1 and 10. So we move the decimal 2 places to the right to get 6.3
Now we have to describe how to get to the original number with the exponents. We moved the decimal 2 places right so to get our number back we would have to move it back 2 places to the left so negative exponent 2... Here's how we represent it..
6.3 x 10^-2
So what that says is if we take 6.3 and divide it by 10 twice we will get our original number.
Let's do another...
0.000000000623
We move the decimal 10 places to the right so our scientific notation is
6.23 x 10^-10
What about very large numbers...
650,000,000,000 = 6.5 x 10^11
(In that one the exponent is positive because we have to multiply to get back to the original number)
