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Significant Figures Uncertainty We do not know infinite digits of a measurement Exact numbers are known for sure Inexact – have some question (estimates) Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements made in the same manner. Neither accurate nor precise Precise but not accurate Precise AND accurate Reporting Numbers In recorded numbers, all the digits are considered exact up until the last digit which may be off by one 2.2405 ± .0001 All digits including the uncertain one are called significant figures We are fairly confident of these digits Further uncertainty can be eliminated by repeating the experiment Which Digits Are Significant? Any non-zero number is significant Any number to the left of a decimal is significant Zeros to the right of a decimal and behind other numbers are significant Zeros to the right of a decimal but in front of other numbers are not significant How many Significant Figures in each below? 1) 2) 3) 4) 5) 6) 7) 8) 28.6 910 0.0076000 0.0144030 400 700.0 0.4004 1.30 3440. 10) 0.04604 11) 804.05 12) 1002 13) 400. 14) 0.000625000 15) 6000 16) 0.00067 9) Round each to 3 Significant Figures 1) 2) 3) 4) 5) 31.068 2.613 81.436 0.001567 1.1353 149.51 7) 6.561 8) 13.1252 9) 143.81 10) 0.000355 6) Multiplying and Dividing Multiply or divide the number out as normal but round the answer to the least number of significant figures in the problem Solve each with correct Sig Figs 1) 2) 3) 4) 5) 6) 2.4 x 15.82 = 94.20 3.16722 = 0.8102 x 3.44 = 25.75 0.00045 = (5.682 x 105) x (2.87 x 104) = (2.145 x 10-5) (6.75 x 104) = Addition and Subtraction Add or subtract as normal but round the answer with the same number of decimal places as the quantity in the calculation having the least Solve each with correct Sig Figs 1) 2) 3) 4) 5) 6) 7) 5.44 – 2.6103 2.099 + 0.05681 87.3 – 1.655 6.078 + 0.3329 8.2 – 7.11 4.6521 + 183.2 + 240 0.004375 – 0.0036 Conversions Often the units must be changed in order to do a problem Conversion factor method Is utilized Examples How many inches in 3.5 km? A chemical reaction produces 3.5 x 1025 atoms of product every second. How many will be produced in 2.5 hours? How many square cm in a square inch?