Scientific NotationScientific notation is simply a method for

expressing, and working with, very large or very small numbers. 

Short hand method

5.2 x 108

Scientific NotationThis is the scientific notation for the standard

number, 567 000.  Now look at the number again, with the three

parts labeled.

5.67 x 10 5         coefficient                   base   exponent

  

Scientific NotationIn order for a number to be in correct

scientific notation, the following conditions must be true:1. The coefficient must be greater than or equal to 1 and less than 10.2. The base must be 10.3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to scientific notation.  A negative exponent means that the decimal is moved to the right when changing from standard notation to scientific notation.

Scientific NotationEx.1  Change 56 760 000 000 to scientific

notationRemember, the decimal is at the end of the

final zero.The decimal must be moved behind the five

to ensure that the coefficient is less than 10, but greater than or equal to one.

The coefficient will then read 5.676The decimal will move 10 places to the left,

making the exponent equal to 10.Answer equals 5.676 x 1010

Scientific NotationEx.2  Change 0.000000902 to scientific

notationThe decimal must be moved behind the 9

to ensure a proper coefficient.The coefficient will be 9.02The decimal moves seven spaces to the

right, making the exponent -7Answer equals 9.02 x 10-7 

PracticeChange the following numbers to scientific

notation1. 345 678 0002. .000 000 5673. 3424. .000 749

PracticeChange the following numbers back to

standard numbers1. 8.5 x 106

2. 3.9 x 10 -7

3. 6.75 x 109

4. 3.34 x 10-4