Significant Figures The valid measurements or digits are called SIGNIFICANT!
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
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
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!
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)
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.