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Significant Figures and Rounding

Significant Figures and Rounding. So you can stop asking “How many decimal places should I write?”. 4 4.233 x 10 3 2 2.2 x 10 2 1 4 x 10 -3. How many sig. figs are there?. # of sig figs Sci. notation.

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Significant Figures and Rounding

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  1. Significant Figuresand Rounding So you can stop asking “How many decimal places should I write?”

  2. 4 4.233 x 103 2 2.2 x 102 1 4 x 10-3 How many sig. figs are there? # of sig figsSci. notation 4 1.005 x 100 2 1.0 x 10-2 3 3.30 x 102 4 2.201 x 100 Value 4,233 220 0.004 1.005 0.010 330. 2.201

  3. Rules to Rounding • Do we really need to cover this? • 0 – 4: Round down • 6 – 9: Round up • 5 and some other non-zero digit(s): Round up • 5 and no other digit: Round the previous digit to be EVEN (not odd)

  4. Write each of these to have three (3) sig figs. Round if you must. Value • 4,233 • 5,220 • 15.104 • 2.005 • 0.010 • 330.5 • 2.225 • 0.05422 Answers • 4,230 • 5,220 • 15.1 • 2.00 • 0.0100 • 330. • 2.22 • 0.0542 Answers • 4,230 • 5,220 • 15.1 • 2.00 Why not? • 4,200 • 5,220. • 15.10 Why not? • 4,200 • 5,220. • 15.10 • 2.01 • 0.01 • 330 • 2.23 • 0.054

  5. Multiplication • Remember • (factor1) x (factor2) x (factorn) = product • Answer (product) should have the same number of sig figs as the least of the factors. • Example: 17.04 x 2.2 = 37.488 (from calculator) (4 sig fig) x (2 sig fig)  answer with 2 sig figs 37.448  37

  6. Multiplication (cont’d) • Answer (product) should have the same number of sig figs as the least of the factors. • Example: 17.04 x 2.20 = 37.488 (from calculator) (4 sig fig) x (3 sig fig)  answer with 3 sig figs 37.488  37.5 Only do your rounding in the FINAL STEP or you could create rounding errors.

  7. Division • Remember • (dividend) ÷ (divisor) = quotient • Answer (quotient) should have the same number of sig figs as the lesser of the dividend or divisor. • Example: 170 ÷ 2.25 = 75.5555 (from calculator) (2 sig fig) ÷ (3 sig fig)  answer with 2 sig figs 75.5555  76

  8. Division (cont’d) • Answer (quotient) should have the same number of sig figs as the lesser of the dividend or divisor. • Example: 170. ÷ 2.25 = 75.5555 (from calculator) (3 sig fig) ÷ (3 sig fig)  answer with 3 sig figs 75.5555  75.6 Only do your rounding in the FINAL STEP or you could create rounding errors.

  9. How many sig figs does the answer have? Computations 1 1 2 • 10 x 2.55 • 100 x 25 • 100. x 25 • 24.00 / 12.0 • 480 / 4 • 22.44 / 14.2 • (16 / 2) x 9 25.5  30 2500  2000 2500  2500 3 1 3 1 2  2.00 120  100 1.580 28  1.58 72  70

  10. Put these numbers in standard notation Computations • 102.55 + 101.9 • 100.0 + 91.22 • 90 + 25.6 • 102.55 + 101.9 • 14,400 + 490 • 22.74 – 14.2 • (16 / 2.0) + 9.0 204.45  204.4 191.22  191.2 115.6  120 or 116 (Why?) 204.45  204.4 14,890 14,900 18.54 18.5 8.0 + 9.0 17.0

  11. Quiz TimeDepending on the class’s behavior, it may be open-note or closed-note. So now you can stop asking “How many decimal places should I write?”

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