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Uncertainty and Significant Digits

Uncertainty and Significant Digits. 2.4-2.5. How long is the nail?. Uncertainty. Every measurement has some degree of uncertainty. When making analog (non-digital) measurements, you record all certain digits and the first uncertain digit. Significant Digits.

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Uncertainty and Significant Digits

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  1. Uncertainty and Significant Digits 2.4-2.5

  2. How long is the nail?

  3. Uncertainty • Every measurement has some degree of uncertainty. • When making analog (non-digital) measurements, you record all certain digits and the first uncertain digit.

  4. Significant Digits • The numbers recorded in a measurement are significant digits. • More sigfigs = more precise (exact)

  5. Determining Sigfigs • Any nonzero digit IS significant • Leading zeros NEVER significant • Captive zeros ALWAYS significant • Trailing zeros ARE significant IF there is a decimal • EXACT numbers have UNLIMITED sigfigs • Defined numbers or counting numbers

  6. 0.00220500 Trailing zero-zero after the last nonzero digit Leading zeros-zeros before the first nonzero digit Captive zero-zero between two nonzero digits

  7. How many sigfigs are there in 0.000304 g? • 3 • 0.0

  8. How many sigfigs in 1.270 x 102 • 4 • 0.0

  9. 10900. • 5 • 0

  10. 1000 • 1 • 0.0

  11. 0.09020 • 4 • 0.0

  12. Sigfigs in Calculations • Rounding off • Don’t round off until after the final calculation. • Multiplication or division: # of sigfigs in answer = least number of sigfigs of measurements • Addition or subtraction: # of decimal places = least number of decimal places of measurements

  13. Examples

  14. 3.3 x 5820 • 17000 • 0.0

  15. (3.60 x 10-3) x (8.123) / 4.3 • 0.0068 • 0.0

  16. 1.842 + 45.2 + 87.55 • 134.6 • 0.0

  17. 714.3-18.56 • 695.7 • 0.0

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