Scientific Notation

by Michael Martinez

Definition 

Scientific notation is a way to write a number as the product of a number between 1 and 10 and a multiple of 10.

About Scientific Notation

Scientific notation is also known as standard form.

The use of scientific notation was to display large numbers by using powers of 10 because in science they use very large numbers and it is very tiring to have to write nineteen billion over and over again. So they thought of a way to easily write such large numbers. That way was called Scientific Notation.

The Rules

 The rules are simple.

The number being multiplied by a power of 10 must be nine or below, and equal to or greater than one. So the equation 2.516414511561465436 x 10 to the 19th power would be acceptable.

How it looks

Scientific notation looks something like this.

Parts

There are two parts of scientific notation. They are the coefficients and the exponents.

Converting numbers to scientific notation:

To convert a large number to scientific notation, divide the number by 10 as many times as is needed to get a digit value less than 10 and greater than 1. Multiply this digit value by an exponential term where the exponent is the number of times that you have divided by 10.

Examples

How to write .000001 in standard form:

.000001 = 1 × 10^-6

The quotient is 10^-6 because it is the

Multiplying

Yes, you can multiply and divide when using sientific notation. 

I'll use (1.15 x 10⁹)(8.5 x 10⁴) for multiplication. 

Thanks to the Associative Property of Multiplication, you could combine 10⁹ and 10⁴ together

and leave 1.15 and 8.5 to be multiplied by eachother.  

It should look something like this: (1.15 x 8.5)(10⁹ x 10⁴) 

Next you multiply them, and in the end look like this: 9.775 x 10¹³

 Dividing

You can also divide using Scientific notation.

Let's use the phrase:

 3.1 x 10⁴

 1.1 x 10²

 The first step in dividing is simplifying the equation. You seperate the coefficients an the exponents. It should look something like this.

 3.1 x 10⁴

1.1 x 10²

 The final step is dividing. You just need to subtract the exponents.

 It should come out to 3.1 x 10²

Addition

Addition is the easiest part of scientific notation. All you have to do is add the exponents and then the coefficients.

Subtraction 

Subtracting is pretty much the same as adding. The only thing you do differently is subtract the exponents and coefficients

Sources: www.coolmath.com

http://www.mathsrevision.net/gcse/pages.php?page=43

www.mathwords.com