Compute with scientific notation
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1) Scientific notation is a way of writing numbers in the form c × 10n, where c is between 1 and 10 and n is an integer. 2) Scientific notation allows very large and very small numbers to be written easily without lots of zeros by moving the decimal point and changing the exponent. 3) Operations like multiplication and division with scientific notation follow the normal rules of exponents - the exponents are added or subtracted.
Compute with scientific notation
- 2. The Form A number is written in scientific notation when it is in the form n c × 10 where c is a value ≥ 1and < 10 and n is an integer.
- 3. c × 10n The Form where c is a value ≥ 1and < 10 and n is an integer. Not Scientific Notation 31.2 × 10 .65 × 10 3 7 8042 × 10 −6 Scientific Notation 3.12 × 10 6.5 × 10 4 6 8.042 × 10 −3
- 4. 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
- 5. 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
- 6. 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 5.2314 × 10 No need to move 3. 4. .0000428 Move right 5 places 602,000,000 Move left 8 places 4 3.2 × 10 0 4.28 × 10-5 6.02 × 10 8
- 7. Exercises Rewrite in decimal form. 1. 2.834 × 10 2. 1.23 × 10 2 -6 283.4 .00000123 Rewrite in scientific notation. 3. 4. 34,690 3.469 × 10 .039 3.9 × 10 -2 4
- 8. 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
- 9. 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
- 10. 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
- 11. 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
- 12. Homework pg. 63 #’s 1, 2, 4, 6, 8, 9, 10, 11