1. Chemistry Using and Expressing Measurements Section 3.1

2. 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%

3. 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

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

5. 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

6. 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

7. This number has 6 significant figures Sample How many significant figures are in this measurement? The Leftmost nonzero digit The Rightmost nonzero digit 0.0810300 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

8. Try These How many significant figures in the following measurements? 1.1.035 2.0.209 3.0.060 4.10.00 5.100 4 4 3 2 1

9. 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

10. Sample Addition/Subtraction 37.6 + 0.13 37.73 Calculator Answer 37.7 Correct sig. figs. 10.8 + 0.061 10.861Calculator Answer 10.9 Correct sig. figs. 110 + 0.9 110.9 Calculator Answer 110 Correct sig. figs.

11. Try These 1.216.73 + 2.1 = 2.0.13 + 23.6 = 3.303 + 0.04 = 4.184.7 + 15 = 5.200 – 5 = 6.100 – 51 = 218.8 23.7 303 200. 200 0

12. Sample Multiplication/Division 16.8 x 0.63 10.584 Calculator Answer 11 Correct sig. figs. 2.671 x 1.6 4.2736 Calculator Answer 4.3 Correct sig. figs. 100.3  6 16.71666 Calculator Answer 20 Correct sig. figs.

13. Try These 1.117.6 x 0.5 = 2.637.8  1.5 = 3.11 x 1 = 60 430 10