Chapter 2.2 Scientific Notation

Expresses numbers in two parts: A number between 1 and 10 Ten raised to a power Examples: 2.32 x x

Interpreting Scientific Notation When the power of ten is positive, than the number is larger than 1 Move the decimal to the right Examples: 4.56 x 10 3 = 4, x 10 5 = 120, x 10 2 = 680 When the power of ten is positive, than the number is larger than 1 Move the decimal to the right Examples: 4.56 x 10 3 = 4, x 10 5 = 120, x 10 2 = 680

Interpreting Scientific Notation When the power of ten is negative, than the number is smaller than 1 Move the decimal to the left Examples: 5.23 x = x = x =

Converting Data into Scientific Notation Move the decimal to produce a factor between 1 and 10 Count the number of places the decimal moved and in what direction If it moved to the left, express the exponent as a positive number If it moved to the right, express the exponent as a negative number

Example 2,345,000 Expressed as a factor between 1 and 10: Decimal moved 6 places to the left: x 10 6

Example Expressed as a factor between 1 and 10: 1.78 Decimal moved 3 places to the right: 1.78 x 10 -3

Adding and Subtracting Only add and subtract numbers with the same exponent Convert numbers to the same power of ten before adding or subtracting 6 x x 10 3 = 6 x x 10 2 = 36 x 10 2 = 3.6 x 10 3

Multiplying and Dividing The numbers do not have to have the same exponent For multiplying: Multiply the first factors, then add the exponents For dividing: Divide the first factors, than subtract the exponent of the divisor from the exponent of the dividend

Multiplication Example (4 x 10 3 ) x (2 x 10 4 ) Multiply the first factors 4 x 2= 8 Add the exponents = 7 Combine the factors 8 x 10 7

Division Example (15 x 10 3 ) ÷ (3 x ) Divide the first factors 15 ÷ 3 = 5 Subtract the exponents 3 – (-4) = 7 Combine the factors 5 x 10 7

Homework Practice problems on pages 32-35