1. Significant Figures (Sig figs)
Measurement &
Significant Figures (Sig figs)

2. 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.   (3 sig figs)
Captive zeros – fall between nonzero digits and are always significant
Ex (5 sig figs)
Trailing zeros – fall to the right of nonzero digits and are only significant when a decimal point is present
Ex  (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.

3. Calculation with Significant Figures

4. 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.
(accurate to ones place)
Multiplication And Division
Round answer to least number of significant digits found in measurements.
3.0 g / mL  =  g/mL
0.24 g/mL

5. (2.8 x 4.467) + 12.854 = ? Mixed Operations Follow PEMDAS
Apply Sig Fig rule once operation has been performed.
(2.8 x ) = ?