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Powers of 10 and Scientific Notation

Learn about the concept of powers of 10 and scientific notation with examples and practice exercises. Understand how to convert numbers from standard notation to scientific notation and vice versa.

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Powers of 10 and Scientific Notation

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  1. Watch “Powers of 10” http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

  2. Scientific Notation - LARGE Numbers - POSITIVE Exponents Your pencil has 602,200,000,000,000,000,000,000carbon atoms. Write this number in scientific notation. Remember, every whole number has a imaginary decimal point at the end. 602,200,000,000,000,000,000,000 • +23 6022 x 10 • 1. Find the first non-zero number ... ... and the last non-zero number. BASE NUMBER x POWER OF TEN 2. Write that number underneath. • Put a decimal after the first digit (6). • * This is the BASE NUMBER Your pencil has 6.022 x 1023 atoms. 4. Multiply the base number by the POWER OF TEN . • Count the number of decimal places from your OLD decimal point. NEW decimal point to your 6. Write that number as an exponent of 10.

  3. Scientific Notation - SMALL Numbers - NEGATIVE Exponents The radius of an atom is about 0.0000000005 m. Express in scientific notation. 0.0000000005 • –10 x 10 5 It’s negative because the number is really small. 1. Find the first non-zero number ... Since it’s just a whole number, get rid of the decimal. ... and the last non-zero number. 2. Write that number underneath. • Put a decimal after the first digit (5). • * This is the BASE NUMBER 4. Multiply the base number by the POWER OF TEN The radius of an atom is 5 x 10-10 m. • Count the number of decimal places from your OLD decimal point. NEW decimal point to your 6. Write that number as an exponent of 10.

  4. Changing Scientific Notation --> Standard Form EXAMPLE 2 Writing Numbers in Standard Form Convert each value from scientific to standard notation • The exponentwill tell you how • many spaces to move the decimal. 7 x 103 0 0 0 Remember, every number has an imaginary decimal point after it. 7000 4.398 x 108 –4 • Since the exponent is +3 ,move • the decimal 3 spaces to the right. –7 +8 439,800,000 7 8 left 4 6.001 x 10–4 .0006001 3. Fill the empty place values with zeros. 3 x 10–7 .0000003

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