Pre-Algebra 4.7 Scientific Notation

1. What is scientific notation? Why use scientific notation? A shorthand way of writing numbers using the powers of 10 Uses the form c 10n where 1  c 10 and n is an integer To represent large or very small numbers without writing out all the zeros Pre-Algebra 4.7 Scientific Notation

2. Using Scientific Notation Ex. 1: Write the following numbers in scientific notation 120,000,000 0.00012 • 120,000,000 move the decimal point 8 places to the left 1.2  100,000,000 1.2  108 • 0.00012 move the decimal point 4 places to the right 1.2  0.0001 1.2  10-4

3. Ex. 2: Write the following numbers in standard form 3.2  107 8.69  10-5 3.2  107 3.2  10,000,000 move the decimal point 7 places to the right 32,000,000 2. 8.69  10-5 8.69  0.00001 move the decimal point 5 places to the left 0.0000869

4. How do you compare written in scientific notation? 3 Steps: Write each number in scientific notation Compare the numbers with different powers of 10 Compare the numbers with the same power of 10

5. Ex. 3: Order 3.9  106, 3,800,000, and 4.2  105from least to greatest. 1. 3,800,000 = 3.8 106 2. 105 < 106, so 4.2  105 < 3.9  106 and 4.2  105 < 3.8 106 3. 3.8 < 3.9, so 3.8 106 < 3.9  106 4.2105 < 3.8106 < 3.9106

6. How do you multiply numbers in scientific notation? Ex. 4: Multiply 1.5  10-4 by 5  103 Use the associative property of multiplication (a  b)  c = a  (b  c) 2. Then, use the product rule of exponents xa  xb = xa+b (1.5  10-4)(5  103) (1.5 5)(10-4 103) 7.5(10-4 103) 7.5 10-4+3 7.5 10-1 0.75