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September 27, 2016 Chapter 3 - Scientific Measurement 3.1 Using and Expressing Measurements Scientific Notation Measurement - a quantity that has both a number and a unit Scientific notation - a given number written as the product of two numbers: a coefficient and 10 raised to a power - The coefficient is always a number greater than or equal to one and less than 10 - 2.4 x 106 = _____________ - 6.5 x 10-3 = ____________ - 0.000 000 008 =___________ - 25 000 000 = ______________ - If the exponent is negative the number MUST BE SMALL - If the exponent is positive the number MUST BE LARGE - Multiplication and Division: X multiply the coefficients and add the exponents ÷ divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator - (3 x 104) x (2 x 102) = - (6 x 105) ÷(2 x 102) = - Addition and Subtraction the exponents must be the same, then add or subtract - 5.4 x 103 + 8.0 x 102 = -Using your calculator Find your exponent key...this replaces the (x 10) September 27, 2016 Accuracy, Precision, and Error Accuracy - is a measure of how close a measurement comes to the actual or true value of whatever is measured - must compare measurement to the correct value Precision - is a measure of how close a series of measurements are to one another, irrespective of actual value - must compare the values of two or more repeated measurements Accepted value (TV) - the correct value for the measurement based on reliable references Experimental value (EV) - value measured in the lab Error - the difference between the accepted and experimental values Percent error - relative error Error = EV - TV EV - TV x 100 Percent error = ________ TV September 27, 2016 Significant Figures Sig figs - include all of the digits that are known, plus a last digit that is estimated - Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculations. Rules: 1 Nonzero digits are significant 582 2 Zeros between nonzero digits are significant (sandwich zeros) 101 3 Placeholder zeros in front of nonzero digits are not significant 0.00025 4 Zeros at the end of a number and to the right of a decimal point are significant 2.560 000 5 Zeros at the rightmost end of a number that lie to the left of an understood decimal point are not significant if they serve as placeholders 1 000 6 Unlimited sig figs when: Counted 7 students Conversion factors 60 min = 1 hour September 27, 2016 Calculations using Sig Figs x or ÷ Keep the fewest # of sig figs + or - Keep the fewest # of decimal places Round just like you would normally round 26.45 x 1.5 = 23.562 + 1.23 = September 27, 2016 Homework P 63 # 1,2 P 65 # 3 P 68 # 4-7 P 70 # 8 - 11 P 72 # 15 - 17
