# Scientific Notation

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###### Explanation

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.

###### Transcript

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 thatÃ¢Â€Â™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, thatÃ¢Â€Â™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 thatÃ¢Â€Â™s much more manageable. Okay and thatÃ¢Â€Â™s how we do Scientific notation.

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scientific notation exponents