Significant Figures (Sig figs)

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Presentation transcript:

Significant Figures (Sig figs) 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: Nonzero numbers are always significant Ex. 1457 (4 sig figs) Zeros. Three possibilities: Leading zeros – precede all nonzero digits and are never significant (they only indicate position of decimal point) Ex. 0.00234 (3 sig figs) Captive zeros – fall between nonzero digits and are always significant Ex. 45003 (5 sig figs) 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) 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

101. + 23.643 124.643 125 (accurate to ones place) 0.24 g/mL General rule: The accuracy of answer is limited by the least accurate measurement involved in the calculation. Rounding : 50/50 If 1st 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 mL = 0.238095238 g/mL 0.24 g/mL

(2.8 x 4.467) + 12.854 = ? Mixed Operations Follow PEMDAS Apply Sig Fig rule once operation has been performed. (2.8 x 4.467) + 12.854 = ?