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8.4 Scientific Notation We will compare scientific notation vs. standard notation and will identify how numbers can be written and represented in scientific notation 1. Simplify using only positive exponents: x2y-3 ANSWER x2/y3 2. Simplify using only positive exponents: (6x-2y3)-3 ANSWER x6 / (216y9) 3. Simplify using positive exponents 2 8x-2y-6 ANSWER x2y6 4 The Form A number is written in scientific notation when it is in the form n c x 10 where c is a value ³ 1and <10 and n is an integer. c × 10n The Form where c is a value 1and < 10 and n is an integer. Not Scientific Notation Scientific Notation 31.2 10 3.12 10 .65 10 6.5 10 3 7 8042 10 6 4 6 8.042 10 3 Large and small values One purpose of scientific notation is to allow you to write very large numbers and very small numbers easily, without lots of 0’s. Large numbers have positive exponents. 84,912 8.4912 × 10 4 Small numbers have negative exponents. .000265 2.65 × 10 -4 Scientific Notation Decimal Move decimal point right for positive exponent. Move decimal point left for negative exponent. 1. 3.128 × 10 2. 6.4 × 10 3. 3.9 × 10-1 .39 4. 6.12 × 10-5 .0000612 3 4 3128 64,000 Decimal Scientific Notation Move decimal point right or left to arrange one digit to the left of decimal point. 1. 52,314 Move left 4 places 2. 3.2 No need to move 3. 4. .0000428 5.2314 × 10 Move right 5 places 602,000,000 Move left 8 places 4 3.2 × 10 0 4.28 × 10-5 6.02 × 10 8 Exercises Rewrite in decimal form. 1. 2.834 × 10 2. 1.23 × 10 2 -6 283.4 .00000123 Rewrite in scientific notation. 3. 34,690 3.469 × 10 4. .039 3.9 × 10 -2 4 Computing with Scientific Notation Another purpose of scientific notation is to allow you to compute with large and small values easily using the rules of exponents. Numbers can be multiplied. (8 × 10 ) (3 × 10 ) 4 2 = (8 × 3) (10 × 10 ) 4 = 24 × 10 4+2 2 = 24 × 10 = 2.4× 10 6 7 Computing with Scientific Notation Numbers can be divided. 4.8 × 10 4.8 10 = × 2 2 2.4 × 10 2.4 10 6 = 2 × 10 6-2 6 = 2 × 10 4 Exercise Evaluate. Write answer in scientific notation. (1.4 × 10 ) (7.6 × 10 ) 4 3 = (1.4 × 7.6) (10 × 10 ) 4 3 10.64 × 10 7 1.064 × 10 8 Associative property Simplify Rewrite in SN Exercise Evaluate. Write answer in scientific notation. (8 × 10 ) -5 (5 × 10 ) -3 8 10 = -5 5 10 -3 1.6 × 10 -3-(-5) 1.6 × 10 2 Associative property Subtract exponents Simplify to SN Homework w/s