CH100 F10 C3 - Chapter 3 Measurement and Chemical...

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Chapter 3 Measurement and Chemical Calculations Problems 1-15, 27, 33-51, 63-77 3.2 Scientific Notation A method of expressing numbers precisely. Useful for large or small numbers. coefficient exponential a.bc x 10 n The coefficient, a.bc , is a decimal (between 1 and 10). The ‘n’ is an integer. The exponential is 10 or 0.1 (1/10) to the n th power: 10 3 = 10x10x10 = 1,000 10 -3 = = 10 0 = = -9.972 x 10 3 = 3.56 x 10 -3 = 7.33 x 10 0 = *A negative exponent has no relation to the sign of the coefficient*
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3.5 Significant Figures (SF) Measurements always have an uncertainty. That is, the last digit of a measurement is uncertain. For example, a length measurement of 9.654 m implies 9.654 m + 0.001 m. Or 9.654 m has 3 accurate digits and 1 uncertain digit. When making measurements, one measures one decimal place past the accuracy of the measuring device. For example, given a meter stick (with no gradations), your reported measurement should be to the 0.1 meter.
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3.5 Significant Figures - 2 The number of significant figures is the number of accurate digits plus the one uncertain digit. How many significant figures are in a measurement? Decimals: Sum the digits from the first non-zero digit to the last digit. Trailing zeros are significant (in a decimal). How may S.F.? 1) 9.654 m ? SF 2) 75.290 m ? SF 3) 0.0075290 m ? SF 4) 0.75290 m ? SF 5) 65,000,000 years ? SF For 5), 8 SF implies we know the number very accurately, i.e., the dinosaurs died out 65,345,242 years ago. If there is no decimal point, trailing zeros may or may not be significant. Scientific Notation: # SF = # digits in coefficient (do not include leading zeros) 1) 6.5 x 10 7 ? SF 2) 6.500 x 10 7 ? SF 3) 6.5345242 x 10 7 ? SF
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3.5 Significant Figures-3 Rounding: Reducing the number of SF: If digit dropped is less than 5, leave preceding digit If digit dropped is 5 or greater, increase preceding digit by 1.
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