Download Scientific Notation

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 .
Example
• An electron's mass is about
0.00000000000000000000000000000091093822 kg. In
scientific notation, this is written 9.1093822×10−31 kg.
• The Earth's mass is about
5973600000000000000000000 kg. In scientific
notation, this is written 5.9736×1024 kg.
• The Earth's circumference is approximately 40000000
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.
568.762 = 5.68762 x 10 2
0.00000772 = 7.72 X 10-6
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
0.000 000 007 51
7.51×10−9
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
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 10-2 = 2.8 X 10-1
( 6.9 X 107 ) / ( 3.0X 10-5 ) = ( 6.9 / 3.0 ) 107-(-5) = 2.3 X 1012