Now we're going to take a look at how exactly we change standard notation into scientific notation. The key is to look at the coefficient. We're going to say to convert a number into a scientific notation value, make sure the coefficient is equal to or greater than 1 but less than 10. So what we learned in the very beginning of scientific notation is the key to changing standard notation into scientific notation. So if we take a look here, we're going to say increasing the coefficient makes the exponent value decrease. Alright. So here we have a number of 0.000 145. We need to make sure that that coefficient, which we're going to make, has to fall between 1 and 10. Here is our decimal place. We're going to have to move it 1, 2, 3, 4, 5 spaces, so that we can get 1.45, which is a value between 1 and 10. Now we made the coefficient larger. Since we made the coefficient larger, that means the exponent has to become smaller. So the coefficient increased by 5, so the exponent has to decrease by 5 because they're opposites of one another.
Now, decreasing the coefficient value makes the exponent value increase. So here in this one, there is we could think of there being a decimal point there and we're going to move it over enough spaces in order to make this coefficient a number between 1 and 10. So we're going to move 1, 2, 3, 4, 5, 6, 7, 8 spaces. So that becomes 1.0132500 times 10. Now we moved over 8 spaces in order to make this smaller. So if the coefficient is decreasing by 8 spaces, that means our exponent has to be increasing by 8 spaces. So it'll be a positive 8 here. So that would be the scientific notation value for this number here. Later on, we'll talk about things such as significant figures, which will help us to even simplify this scientific notation even more because there's an awful lot of zeros here at the end. But for now, this would be the entire value that we place to show that we moved the decimal place 8 spaces over to make the coefficient smaller and thereby increasing the exponent by 8.
Now that we've seen these examples, move on to the practice question left at the bottom of the page.
