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# Lecture4 scientific notation

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### Lecture4 scientific notation

1. 1. 15,000,000,000 jellybeans are produced each year for the Easter holiday. One individual gold atom is 0.000000006 inches in diameter Is there an alternative way to write these numbers! Scientific Notation - Product of a coefficient and 10 raised to a power. (coefficient usually between 1 and 10) Example : 2000 can be written as the product of 2 x 1000 However 1000 = 10 x 10 x 10 = 10 3 Therefore 2000 = 2 x (10 x 10 x 10) = 2 x 10 3
2. 2. 0.002 can be written as the product of 2 x 1/1000 However
3. 3. Method for Representing Any Number in Standard Scientific Notation <ul><li>Count the number of decimal places the decimal point would be moved in order to obtain a number between 1 and 10. </li></ul><ul><li>Take the number between 1 and 10 and multiply it by 10 to the power of the number of decimal places determined. </li></ul><ul><li>If the decimal places moved the left, the power of 10 is positive, if the decimal places moved to the right, the power of ten is negative. </li></ul>
4. 4. 1 5 0 0 0 0 0 0 0 0 0 10 decimal places to the left 1.5 x 10 10 jellybeans 0.0 0 0 0 0 0 0 0 6 9 decimal places to the right 6.0 x 10 -9 inches
5. 5. Convert the following numbers to Scientific Notation 0.00137 15237 59000005 123.025 0.00005025 1.37 x 10 -3 1.5237 x 10 4 5.9000005 x 10 7 1.23025 x 10 2 5.025 x 10 -5
6. 6. Multiplication and Division of With Scientific Notation <ul><li>Multiplication – Multiply Coefficients and add Exponents of 10 </li></ul><ul><li>(2.0 x 10 4 ) x (4.0 x 10 2 ) = (2.0 x 4.0) x 10 4+2 = 8 x 10 6 </li></ul><ul><li>Division– Divide Coefficients and subtract Exponents of 10 </li></ul>
7. 7. Addition and Subtraction with Scientific Notation <ul><li>Make sure that both numbers have the same power of ten </li></ul><ul><li>Add or subtract the coefficients multiply by the common power of 10 </li></ul><ul><li>Example: </li></ul><ul><li>Adding 2.75 x 10 3 and 7.5 x 10 2 </li></ul>
8. 8. General Rule <ul><li>When the coefficient gets smaller, the exponent gets bigger. (c  e  ) </li></ul><ul><li>When the coefficient gets bigger, the exponent gets smaller. (c  e  ) </li></ul>
9. 9. Homework <ul><li>Scientific Notation Handout </li></ul>