II Introductory Material A(2)

II Introductory Material A(2) - A. SignificantFigures...

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I Introductory Material A. Mathematical Concepts Scientific Notation and Significant Figures
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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
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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
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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.
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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
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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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