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Unformatted text preview: I Introductory Material A. Mathematical Concepts Scientific Notation and Significant Figures • Scientific Notation – A method devised to express very small and very large numbers. – Based on powers of 10 e.g 123 billion is 123,000,000,000 expressed in scientific notation = 1.23 x 10 11 – 1.23 is called the coefficient • It must be greater than 1 and less than 10 – 10 11 is called the base. It is a power of 10. In this example the power of 10 is the 11 • Significant Figures – Tells how well known a measurement is. – Using Significant Figures is a way to express the error in a measurement. – The more significant figures the more accurate the measurement. – The last number listed is the value that is uncertain • e.g. – 2.3 value known to units, estimated to tenths – 2.34 value known to tenths, estimated to hundredths • Determining the number of Significant Figures – All non  zero numbers are significant – Zeros within a number are significant • Both 40.05 and 3201 have 4 significant figures – Zeros used to set the decimal point are NOT significant. • 0.00235 – 3 significant figures • 47,000 – 2 significant figures » If you want it to have more, use scientific notation: 4.7000 x 10 4 denotes 5 significant figures » Other possibility: 47,000. is sometimes used to denote 5 significant figures. • Types of Numbers – Exact • Numbers from counting • Conversions in the same system of measurement • Defined conversions between different systems of measurement • Have an infinite number of significant figures – Inexact • Numbers from measurements • Conversions between different systems of measurement • Have a finite number of significant figures • Working with Significant Figures – When doing calculations, you can not gain or lose precision. The answer can only be as good as the least precise number – Multiplication and Division • The number of significant figures in the answer depends on the number with the least number of significant digits....
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 Fall '08
 Kramer
 Chemistry, Scientific Notation

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