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Significant Figures

Significant Figures. Chem 140. Why significant figures?. Weight of penny: 3 g ± 1 g Not very accurate Weight of truck: 41 057 214 g Also ± 1 g Much more accurate. Cardinal Scale Mfg. Co. Cardinal Scale Mfg. Co. Cardinal Scale Mfg. Co. Why significant figures?. Measure of accuracy 3 g

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Significant Figures

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  1. Significant Figures Chem 140

  2. Why significant figures? • Weight of penny: 3 g • ± 1 g • Not very accurate • Weight of truck: 41 057 214 g • Also ± 1 g • Much more accurate Cardinal Scale Mfg. Co. Cardinal Scale Mfg. Co. Cardinal Scale Mfg. Co.

  3. Why significant figures? • Measure of accuracy • 3 g • Error: 33 % • One significant figure

  4. Why significant figures? • Measure of accuracy • 3 g • Error: 33 % • One significant figure • 41 057 214 g • Error: 0.0000024 % • Eight significant figures

  5. Rules for significant figures • Nonzero numbers: Always significant • Captive zeroes: Always significant • Leading zeroes: Never significant • Trailing zeroes: Significant when the decimal point is written

  6. Examples 13060

  7. Examples four s.f. 13060

  8. Examples four s.f. 13060 13060.

  9. Examples four s.f. 13060 five s.f. 13060.

  10. Examples four s.f. 13060 five s.f. 13060. 0.001040

  11. Examples four s.f. 13060 five s.f. 13060. four s.f. 0.001040

  12. Examples four s.f. 13060 five s.f. 13060. four s.f. 0.001040 6.022 × 1023

  13. Examples four s.f. 13060 five s.f. 13060. four s.f. 0.001040 6.022 × 1023 four s.f.

  14. Multiplying and dividing • The number with the fewest s.f. determines how many are in the result.

  15. Multiplying and dividing • The number with the fewest s.f. determines how many are in the result. • 0.043 × (6.022 × 1023) = 2.58946 × 1022

  16. Multiplying and dividing • The number with the fewest s.f. determines how many are in the result. • 0.043 × (6.022 × 1023) = 2.58946 × 1022 • = 2.6 × 1022

  17. Adding and subtracting • Don’t count significant figures, count decimal places.

  18. Adding and subtracting • Don’t count significant figures, count decimal places. • 3.54 + 0.0152 = 3.5552

  19. Adding and subtracting • Don’t count significant figures, count decimal places. • 3.54 + 0.0152 = 3.5552

  20. Adding and subtracting • Don’t count significant figures, count decimal places. • 3.54 + 0.0152 = 3.5552 • 3.56

  21. Exact numbers • Some numbers have infinite s.f. • 60 seconds in a minute • 2.54 cm in an inch • 2 measurements being averaged

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