Scientific Notation

Scientists often work with very small and very large numbers. They usually write such numbers in a way that doesn't require writing all the zeroes. This different way of writing numbers is called... Scientific Notation.

Scientific notation is a more convenient way to write very big or very small numbers so you don't have to write so many zeroes.

It can be used to rewrite any number, but it's particularly convenient for very big and very small numbers.

A number written in scientific notation has two parts:
1) a coefficient, multiplied by
2) 10 to a power

The coefficient is always greater than or equal to 1 and less than but not equal to 10.
(1 <= Coefficient < 10)

The power is any whole number (negative, zero, or positive).

Examples: Numbers Written in Scientific Notation:

Here are some examples of numbers written in a form similar to scientific notation but not technically scientific notation.

Examples: Not Scientific Notation
34 x 107
 The coefficient is not between 1 and 10.
0.27 x 1023
7.3 x 10-6.5

 The power of 10 is not a whole number.
3.53 / 104
 This is division instead of multiplication
..................................................................

 Note:The coefficient must be greater than or equal to 1 & less than but not equal to 10. Mathematically, this is written: 1 <= Coefficient < 10
 This one is ok. The coefficient can equal 1 exactly.
 This one is not ok. The coefficient is not allowed to be 10 exactly.

1 x 108 10 x 105
People who saw this lesson also found the following lessons useful:
 Turn Regular Numbers into Scientific Notation Writing Scientific Notation To Convert to Scientific Notation From a Normal Number To Convert From Scientific Notation to a Normal Number When The Coefficient is Not Between 1 and 10

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