Scientific Notation THE LOGICAL APPROACH

Warm Up Write each number in standard notation. 2.54 x 102 6.7 x 102 1.14 x 103 Write each number in scientific notation. 75,000,000 208 907,100

Positive Exponents 101 = 10 102 = 10X10= 100 103 = 10X10X10 = 1000

Negative Exponents 10-1 = 1/10 = 0.1 10-2 = 1/100 = 0.01 10-3 = 1/1000 = 0.001 10-4 = 1/10000 = 0.0001

Scientific Notation We use the idea of exponents to make it easier to work with large and small numbers. 10,000 = 1 X 104 250,000 = 2.5 X 105 Count places to the left until there is one number to the left of the decimal point. 230,000 = ? 35,000 = ?

Scientific Notation Continued 0.00006 = 6 X 10-5 0.00045 = 4.5 X 10-4 Count places to the right until there is one number to the left of the decimal point 0.003 = ? 0.0000025 = ?

Multiplying with Scientific Notation Add the Exponents 102 X 103 = 105 100 X 1000 = 100,000

Multiplying with Scientific Notation (2.3 X 102)(3.3 X 103) 230 X 3300 Multiply the Coefficients 2.3 X 3.3 = 7.59 Add the Exponents 102 X 103 = 105 7.59 X 105 759,000

Multiplying with Scientific Notation (4.6 X 104) X (5.5 X 103) = ? (3.1 X 103) X (4.2 X 105) = ?

Dividing with Scientific Notation Subtract the Exponents 104/103 = 101 10000X 1000 = 10

Dividing with Scientific Notation (3.3 X 104)/ (2.3 X 102) 33000 / 230 = 143.4783 Divide the Coefficients 3.3/ 2.3 = 1.434783 Subtract the Exponents 104 / 102 = 102 1.4347823 X 102 143.4783

Dividing with Scientific Notation (4.6 X 104) / (5.5 X 103) = ? (3.1 X 103) / (4.2 X 105) = ?