Chemistry Using and Expressing Measurements Section 3.1

Accuracy How close a measurement is made to the actual value or accepted value Percent Error is a way to show the accuracy of a measurement % Error = │Actual – Experimental│ Actual X 100%

Precision How consistently the measurement is made How “exact” a measurement is It is impossible to make an “exact” measurement With every measurement there comes uncertainty

Measuring The nail is obviously between 6.3 and 6.4 cm. Imagine 10 divisions within the smallest increment. The uncertainty is ±0.01cm

Measuring If no range of uncertainty is specified, it is assumed the last digit is uncertain ±1 If the uncertainty is not ±1, then it needs to be included in your measurement Measurements should include all the certain figures plus one that is uncertain

Significant Figures Maintain the precision when doing calculations with measurements Rules 1.Determine Leftmost and Rightmost Non-zero digits 2.All non-zero digits are significant 3.All zeros between Leftmost and Rightmost Non- zero digits are significant 4.All zeros left of Leftmost Non-zero digit are NOT significant 5.All zeros right of the Rightmost Non-zero digit are significant ONLY if there is a decimal point

This number has 6 significant figures Sample How many significant figures are in this measurement? The Leftmost nonzero digit The Rightmost nonzero digit All Nonzero digits are significant Zeros between Leftmost and Rightmost Non-zero digits are significant All zeros left of Leftmost Non-zero digit are NOT significant All zeros right of the Rightmost Non- zero digit are significant ONLY if there is a decimal point O

Try These How many significant figures in the following measurements?

Calculating with Sig. Figs. For addition/subtraction align the decimal points and use the fewest DECIMAL places for the result For multiplication/division use the fewest number of digits for the result

Sample Addition/Subtraction Calculator Answer 37.7 Correct sig. figs Calculator Answer 10.9 Correct sig. figs Calculator Answer 110 Correct sig. figs.

Try These = = = = – 5 = – 51 =

Sample Multiplication/Division 16.8 x Calculator Answer 11 Correct sig. figs x Calculator Answer 4.3 Correct sig. figs  Calculator Answer 20 Correct sig. figs.

Try These x 0.5 =  1.5 = 3.11 x 1 =