Measurement Significant Figures Sig figs Significant Figures The

Measurement & Significant Figures (Sig figs)

Significant Figures The numbers in a measurement (all certain numbers plus the first uncertain number) are called…. . Significant figures! The number of significant figures is determined by the uncertainty associated with a particular measuring device. Rules for counting sig figs in a measurement: 1) Nonzero numbers are always significant Ex. 1457 (4 sig figs) 2) Zeros. Three possibilities: a) Leading zeros – precede all nonzero digits and are never significant (they only indicate position of decimal point) Ex. 0. 00234 (3 sig figs) b) Captive zeros – fall between nonzero digits and are always significant Ex. 45003 (5 sig figs) c) Trailing zeros – fall to the right of nonzero digits and are only significant when a decimal point is present Ex. 23000. (5 sig figs) vs 23000 (2 sig figs) 3) Exact numbers – numbers not obtained using a measuring device. They come from counting or are based on a definition. We can assume exact numbers have unlimited significant figures.

Calculation with Significant Figures

General rule: The accuracy of answer is limited by the least accurate measurement involved in the calculation. Rounding : 50/50 If 1 st digit to be dropped is: • < 5 Round number to be rounded DOWN • > 5 Round number to be rounded UP • = 5 Round number to be rounded so it will be EVEN Addition And Subtraction Round answer to least number of decimal places (least accurate measurement). 101. + 23. 643 124. 643 125 (accurate to ones place) Multiplication And Division Round answer to least number of significant digits found in measurements. 3. 0 g / 12. 60 m. L = 0. 238095238 g/m. L 0. 24 g/m. L

Mixed Operations • Follow PEMDAS • Apply Sig Fig rule once operation has been performed. (2. 8 x 4. 467) + 12. 854 = ?