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Scientific Notation

Teacher/Instructor Matt Jones
Matt Jones

M.Ed., George Washington University
Dept. chair at a high school

Matt is currently the department chair at a high school in San Francisco. In his spare time, Matt enjoys spending time outdoors with his wife and two kids.

Scientific notation is used to make extremely large or small numbers more manageable. Numbers written in scientific notation are the products of a digit term and an exponential term and are written in the general form a x 10^n. For example, 0.0000234 is written 2.34 x 10^n and 456,000 is written as 4.56 x 10^5.

So we're going to talk about Scientific notation. Scientific notation is basically a way to take very big numbers or very small numbers and simplify them in a way that's easier to write and keep track of. So let's look at how we do that trying to determine proper Scientific notation we need to write a number a times 10 to the b. Now a is going to be a number between 1 and 10, to get that number between 1 and 10, we're going to usually have to move our decimal point to the right or to the left. If we move the decimal point to the right, that's going to be a negative exponent. If we move it to the left it's going to be a positive exponent.

Okay let's look at how we do that with some problems. Over here I've got a number 1,100 not a terribly big number not a lot of zeros but to put it in proper Scientific notation we need to move the decimal point, the decimal point is right here, we need to move 1, 2, 3 spots now we have 1.1 times 10 to the third. Sorry 1.1 times 10 to the third okay that was pretty straight forward. Now we've got a very small number with a lot of zeros to the right of the decimal point. So we need to make this number larger by multiplying it by a negative exponent. So if we start with a decimal point we go 1, 2, 3, 4 units to get 5.4 times 10 in this case to the negative 4 since we're moving to the right of a decimal point.

Okay now let's look at a really big number with a lot of zeros and again who wants to write all those zeros? I don't want to write them so let's simplify that okay, we're going to go 1, 2, 3, 4, 5, 6, 7, 8, 9 units to the left of the decimal point. And so we're going to take 7.12 times 10 to the ninth. And we've simplified this very big number with a lot of zeros into a number that's much more manageable. Okay and that's how we do Scientific notation.