Scientific Notation Multiplying and Dividing
Pre-Algebra
Looking at multiplying and dividing with scientific notation
This afternoon, we're going to look at multiplying and dividing with scientific notation. Yesterday we looked at adding and subtracting. So here are the other two operations. Go back along, long time ago. All the way to last week. Last week we learned that when we multiply two numbers with the same base, like X squared times X squared. Then we add their exponents. X to the fourth. And when we divide two numbers with the same base, like X to the fourth, over X squared, we subtract their exponents, like X squared, example, V to the 7 times B squared equals B to the 9th.
We add their exponents. Or when we're dividing, B to the 7th over B squared, we subtract their exponents. I know, review. When we multiply in scientific notation, we're using that same process. We multiply our two coefficients three times four equals 12. Then we multiply the tens. Ten to the third. Times ten to the second. We know that when we multiply two numbers with the same base, we add their exponents, so we get ten to the 5th. 12 times ten to the 5th. I can't leave my answer this way because this is not a number between one and ten. This is an important step to remember. I have to move my decimal place over one to make a number between one and ten.
When I move it to the left one, Lars tells me to add one. So I add one to my exponent. And I get 1.2 times ten to the 6th. Well, that was easy. We're going to do the same process here. We're going to multiply our coefficients 3.2 times two, and I get negative 6.4, and then I multiply my tens, ten to the fourth, times ten to the negative first. When I multiply two numbers at the same base, I add their exponents four plus negative one. Is ten to the third. And that's my answer. Put them back together. Negative 6.4. Times ten to the third. Again, that was easy. Dividing is very similar. We still divide our coefficients, so 6 divided by three equals two, and we divide our tens.
Ten to the fourth divided by ten to the second, when I divide two numbers with the same base, I subtract their exponents and get ten to the second. My answer, I just put them back together to times ten to the second. Easy. Some problems to try on your own. You can use a calculator here to multiply. But remember, that if your answer is not a number between one and ten, then it is not in scientific notation. You need to do that step of moving the decimal over to make it a number between one and ten. If you move it over, then you have to add or subtract to your exponent.