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