Significant Figures & Calculations

1. Significant Figures & Calculations Chapter 2 Section 3 p. 36-42

2. 1. Nonzero digits are always significant 37.6 has three sig figs 4567 has four sig figs How many sig figs do the following have? a. 42 g b. 38.78 m c. 5 L d. 176.4 ml Significant Figures Rules

3. Significant Figures Rules 2. Zeros between nonzero digits are significant 30.6 has three sig figs 24007 has five sig figs How many sig figs do the following have? a. 404 g b. 30.8 m c. 5601 L d. 170.4 ml

4. Significant Figures Rules 3. Zeros in front of nonzero digits are not significant 0.72 has two sig figs 0.005 has one sig fig How many sig figs do the following have? a. 0.395 g b. 0.000008 m c. 0.602 L d. 0.0507 ml

5. Significant Figures Rules 4. Zeros at the end of a number that contains a decimal point are significant (this includes all the zeros at the end to the left and right of decimal point) 4700.0 has five sig figs 0.7200 has four sig figs How many sig figs do the following have? a. 349.0 g b. 5.730 m c. 0.60 L d. 500. ml

6. Significant Figures Rules 5. Zeros at the end of a number that does not contain a decimal point are not significant 4700 has two sig figs 720 has two sig figs How many sig figs do the following have? a. 3490 g b. 5000 m c. 700 L d. 800. ml

7. Go through rules step by step Zeros between nonzero digits are significant 0 . 0 0 0 8 9 0 0 0 7 0 0 Zeros in front on nonzero digits are not significant Nonzero digits are always significant Zeros at the end of a number that contains a decimal point are significant 3 + 3 + 2 = 8 sig figs

8. Sig Fig Calculations

9. Calculations Involving Sig Figs • Addition and subtraction - The result can be no more certain than the least certain digit in the calculation Ex. ++3.10 g ++1.376 g +12.4 g +16.876 g ---------> round off to 16.9 g

10. Addition and subtraction Ex’s ++2.105 ml ++1.3146 ml +16.26 ml +19.6796 ml ---------> round off to 19.68 ml

11. Addition and subtraction Ex’s +22.987 m ++7.34 m - 2.0 m +13.647 m ---------> round off to 13.6 m

12. Calculations Involving Sig Figs 2. Multiplication and division - The result cannot have more sig figs than there are in the measurement with the smallest number of sig figs Ex. ++10.13 g X 12.4 g + 24.312 g <--------- 4 sig figs <--------- 2 sig figs ---------> round off to 24 g

13. Multiplication and Division Ex’s Ex. ++1000 g X 24 g + 24000 g <--------- 1 sig fig <--------- 2 sig figs ---------> round off to 20000 g

14. Calculations Involving Sig Figs 3. If a calculation has both addition or subtraction and multiplication (or division), round after each operation.

15. Calculations Involving Sig Figs Ex. 12.7 ml + 8 ml x 2.51 = (remember always do multiplication and division first unless there are parentheses) ++2.51 X 8 ml + 20.08 ml <--------- 3 sig figs <--------- 1 sig fig 20 ml ---------> round off to

16. Calculations Involving Sig Figs Ex. 12.7 ml + 8 ml x 2.51 = Now becomes: 12.7 ml + 20 ml = So: + 12.7 ml + 20 ml + 32.7 ml The final answer ---------> round off to 33 ml

17. Exact Values 1. Measurements have uncertainty. 2. Things that you count do not have uncertainty and therefore we consider them to have an unlimited number of sig figs in calculations (ex. I have two thumbs) 3. Conversion factors also have an unlimited number of sig figs (ex. 1 g = 1000 mg)

18. Homework • Read pgs 38-42 • Do problem #'s 31- 39, 43, and 44