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Significant Figures

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.

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Significant Figures

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  1. Significant Figures

  2. Uncertainty • We do not know infinite digits of a measurement • Exact numbers are known for sure • Inexact – have some question (estimates)

  3. Precision and Accuracy Accuracyrefers to the agreement of a particular value with the truevalue. Precisionrefers to the degree of agreement among several measurements made in the same manner. Precise but not accurate Precise AND accurate Neither accurate nor precise

  4. 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

  5. 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

  6. How many Significant Figures in each below? • 28.6 9) 3440. • 910 10) 0.04604 • 0.0076000 11) 804.05 • 0.0144030 12) 1002 • 400 13) 400. • 700.0 14) 0.000625000 • 0.4004 15) 6000 • 1.30 16) 0.00067

  7. Round each to 3 Significant Figures • 31.068 6) 149.51 • 2.613 7) 6.561 • 81.436 8) 13.1252 • 0.001567 9) 143.81 • 1.1353 10) 0.000355

  8. 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

  9. Solve each with correct Sig Figs • 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) =

  10. 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

  11. Solve each with correct Sig Figs • 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

  12. Conversions • Often the units must be changed in order to do a problem • Conversion factor method Is utilized

  13. 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?

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