1. Scientific Notation

2. Scientific notation
is a way of writing numbers that are too large or too small to be conveniently written in standard decimal notation.
In scientific notation all numbers are written in the form of
a is the number between 1 and 10 , b the exponent is a positive or negative integer .

3. Example
An electron's mass is about kg. In scientific notation, this is written ×10−31 kg.
The Earth's mass is about kg. In scientific notation, this is written ×1024 kg.
The Earth's circumference is approximately m. In scientific notation, this is 4×107 m
Explanation:
count the number of the places that the decimal point must be moved to give the number a . If the decimal point has to be moved to the left then b is positive integer ; if it has to be moved to the right, b is negative integer.
= x 10 2
= 7.72 X 10-6

4. Standard decimal notation Normalized scientific notation
300
3×102
4,000
4×103
-53,000
−5.3×104
6,720,000,000
6.72×109
7.51×10−9

5. Addition and Subtraction
1- write each quantity – a1 and a2 with the same exponent b.
2- combine a1 and a2 ; the exponents remain the same
( 4.31 X 104 ) + ( 3.9 X 103 ) = ( 4.31 X 104 ) + ( 0.39 X 104) = 4.70 X 104
( 2.22 X 10-2 ) - ( 4.1 X 10-3 ) = ( 2.22 X 10-2 ) - ( 0.41 X 10-2) = 1.81 X 10-2

6. Multiplication and Division
1- multiply a1 and a2 , but add the exponents together.
2- divide a1 and a2 , and subtract the exponents .
( 8.0 X 104 ) X ( 5.0 X 102 ) = ( 8.0 X 5.0 ) (104+2) = 40 X 106 = 4.0 X 107
( 4.0 X 10-5 ) X ( 7.0 X 103 ) = ( 4.0 X 7.0 ) (10-5+3) = 28 X = 2.8 X 10-1
( 6.9 X 107 ) / ( 3.0X 10-5 ) = ( 6.9 / 3.0 ) 107-(-5) = 2.3 X 1012