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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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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.
Scientific notation consists of two parts: • A number between 1 and 10 • A power of 10 N x 10x
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)
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
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
Example 1 • Given: 289,800,000 • Use: 2.898 (moved 8 places) • Answer: 2.898 x 108
Example 2 • Given: 0.000567 • Use: 5.67 (moved 4 places) • Answer: 5.67 x 10-4
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
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.)
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
Example 3 • Given: 5.093 x 106 • Answer: 5,093,000 (moved 6 places to the right)
Example 4 • Given: 1.976 x 10-4 • Answer: 0.0001976 (moved 4 places to the left)
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