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Scientific Notation

Scientific Notation. Why use scientific notation?. For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. Numbers expressed in scientific notation can be used in a computation with far greater ease.

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Scientific Notation

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  1. Scientific Notation

  2. Why use scientific notation? • For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. • Numbers expressed in scientific notation can be used in a computation with far greater ease.

  3. Scientific notation consists of two parts: • A number between 1 and 10 • A power of 10 N x 10x

  4. What is scientific Notation? A method to write very large or very small numbers Coefficient – any number from 1-9 Exponent – shows the number of times 10’s are multiplied together (102 = 10 x 10 = 100)

  5. Changing standard form to scientific notation.

  6. Changing Standard Numbers to Scientific Notation • Numbers greater than 10 • Move decimal until only ONE number is to the left of the decimal. • The exponent is the number of places the decimal has moved and it is POSITIVE. Ex. 125 = 15,000,000,000 = 1.25  102 1.5  1010

  7. Changing Standard Numbers to Scientific Notation, cont. • Numbers less than 1 • Move decimal until only one number is to the left of the decimal. • The exponent is the number of places the decimal has moved and it is NEGATIVE. Ex. 0.000189 = 0.5476 = 1.89  10-4 5.476  10-1

  8. Example 1 • Given: 289,800,000 • Use: 2.898 (moved 8 places) • Answer: 2.898 x 108

  9. Example 2 • Given: 0.000567 • Use: 5.67 (moved 4 places) • Answer: 5.67 x 10-4

  10. Changing Standard Numbers to Scientific Notation, cont. • To change a number written in incorrect scientific notation: • Move the decimal until only one number is to the left of the decimal. • Correct the exponent. (remember: take away, add back) Ex. 504.2  106 = 0.0089  10-2 = 5.042  108 8.9  10-5

  11. Changing scientific notation to standard form.

  12. To change scientific notation to standard form… • Simply move the decimal point to the right for positive exponent 10. • Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

  13. Changing Numbers in Scientific Notation to Standard Notation • If the exponent is (+) move the decimal to the right the same number of places as the exponent. • 1.65  101 = • 1.65  103 = • If the exponent is (-) move the decimal to the left the same number of places as the exponent. • 4.6  10-2 = • 1.23  10-3 = 16.5 1650 0.046 0.00123

  14. Example 3 • Given: 5.093 x 106 • Answer: 5,093,000 (moved 6 places to the right)

  15. Example 4 • Given: 1.976 x 10-4 • Answer: 0.0001976 (moved 4 places to the left)

  16. Even More Practice • Below is a list of links to games and activities all having to do with scientific notation. • http://www.aaamath.com/dec71i-dec2sci.html • http://janus.astro.umd.edu/cgi-bin/astro/scinote.pl • http://www.sciencejoywagon.com/physicszone/lesson/00genral/dectosci.htm

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