Significant Figures

1
Significant Figures

• The valid measurements or digits are called
  SIGNIFICANT!

2
Uncertainties of Measurements

• Precision or Accuracy is the degree of
  exactness to which the measurement quantity can
  be reproduced.
• Parallax is the apparent shift in the position of
  the object when it is viewed from different angles

3
Significant Digits

• Nonzero digits are always significant
• All final zeros after the decimal point are
  significant
• Zeros between two other significant digits are
  always significant
• Zeros used solely for spacing the decimal point
  are not significant

4
Accuracy

• Is the extent to which a measured value agrees
  with the standard value of the quantity.
• The instrument determines the amount of precision
  of the data.
• CALCULATORS DO NOT INCREASE THE ACCURACY!

5
Examples of Significant Digits

• Add 24.686 m 2.343 m 3.21 m ?
• 30.239 m . 30.24 m (significant digits)
• Multiply 3.22 cm by 2.1 cm
• 6.762 cm2 6.8 cm2 (significant digits)
• Divide .005673 by 2.1
• 0.0027014285714285714285714285714286
• .0027 (significant digits)

6
Summary

• All measurements are subject to uncertainty
• The number of significant digits is limited by
  the precision of the instrument
• The result of any mathematical or electronic
  operation can never be more precise than the
  least precise instrument display.