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Significant Figures

Significant Figures. There are two kinds of numbers in the world: Exact There are exactly 12 eggs in a dozen Most people have exactly 10 fingers and 10 toes Inexact Any measurement. If I quickly measure the width of a piece of notebook paper, I might get 220 mm 2 significant figures

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Significant Figures

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  1. Significant Figures • There are two kinds of numbers in the world: • Exact • There are exactly 12 eggs in a dozen • Most people have exactly 10 fingers and 10 toes • Inexact • Any measurement

  2. If I quickly measure the width of a piece of notebook paper, I might get • 220 mm 2 significant figures • If I am more precise • 216 mm 3 significant figures • Even more precise • 215.6 mm 4 significant figures

  3. Precision vs. Accuracy • Accuracy • Refers to how closely a measured value agrees with the correct value • Precision • Refers to how closely individual measurements agree with each other. Accurate and precise Accurate but not precise Precise not accurate

  4. Significant Figures • Significant figures are critical in any measurement. • The number of sig. figs. is the number of digits believed to be correct by the person doing the measuring. • The measurement always includes one estimated digit.

  5. Significant Figures • When we measure something, we can (and do) always estimate between the smallest marks 4.5 cm estimate

  6. Sig Figs • The better the measuring device the better we can estimate • Remember the last number measured is an estimate 4.55 cm estimate

  7. Sig Fig Rules • Needed a set of rules to decide which zeros count. • All other numbers do count as significant figs • Which zeros count:

  8. Sig Figs • Which zeros count • Leading zeros are never significant 0.00682 3 significant figures • Imbedded zeros are always significant 1.072 4 sig figs • Trailing zeros are significant only if the decimal point is specified. 300 1 sig fig 3 x 102 300. 3 sig figs 3.00 x 102 300.0 4 sig figs 3.000 x 102

  9. Calculating with Sig Figs • Adding and Subtracting • The last sig fig in a measurement is an estimate. • Your answer can not be better than your worst estimate. • Last digit retained is set by the first doubtful digit.

  10. Rounding Rules • Look at the number to the right, or after the one you are rounding. • If it is 0 to 4 don’t change it • If it is 5 to 9 make the one you are rounding one bigger • Round 45.462 to four sig figs • To three sig figs • To two sig figs • To one sig fig

  11. Multiplication and Division • Rule is simpler • Same number of sig figs in the answer as the least in the question • 3.6 x 653 • 2350.8 • 3.6 has 2 sig figs and 653 has 3 sig figs • Answer can only have 2 sig figs • 2400

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