Significant Figures

1. Significant Figures • There are 2 different types of numbers • Exact • Measured • Measured number = they are measured with a measuring device so these numbers have ERROR. • An exact number is obtained when you count objects or use a defined relationship.

2. Numbers without Significant Figures Counting objects are always exact 2 soccer balls 4 pizzas Exact relationships, predefined values, not measured 1 foot = 12 inches 1 meter = 100 cm

3. Learning Check Classify each of the following as an exact or a measured number. • 1 yard = 3 feet • The diameter of a red blood cell is 6 x 10-4 cm. • There are 6 hats on the shelf. • Gold melts at 1064°C.

4. Learning Check 1 yard = 3 feet - This is a defined relationship. The diameter of a red blood cell is 6 x 10-4 cm. - A measuring tool is used to determine length. There are 6 hats on the shelf. -The number of hats is obtained by counting. Gold melts at 1064°C. - A measuring tool is required.

5. Measurement and Sig Figs • Every experimental measurement has a degree of uncertainty. • The volume, V, at right is certain in the 10’s place, 10mL<V<20mL • The 1’s digit is also certain, 17mL<V<18mL • A best guess is needed for the tenths place.

6. Measurement & Sig Figs • The mass is certain to the tenths – between 0.5 and 0.6g • Best guess is needed for hundredths place. • My guess is 0.58g – 2 significant figures

7. What is the Length? • We can see the markings between 1.6-1.7cm • We can’t see the markings between the .6-.7 • We must guess between .6 & .7 • We record 1.67 cm as our measurement • The last digit an 7 was our guess...stop there

8. Learning Check What is the length of the wooden stick? 1) 4.5 cm 2) 4.54 cm 3) 4.547 cm

9. Measured Numbers • Do you see why measured numbers have error…you have to make that guess! • All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimate. • To indicate the precision of a measurement, the value recorded should use all the digits known with certainty.

10. Significant Figures Used to report all precisely known numbers + one estimated digit

11. Rule #1 • Every nonzero digit is significant Examples: 24 = 2 3.56 = 3 7 = 1

12. Rule #2 • Zeros between non-zeros are significant Examples: 7003 = 4 40.9 = 3

13. Rule #3 • Zeros appearing in front of non-zero digits are not significant • Act as placeholders • Can’t be dropped unless written in scientific notation Examples: 0.00024 = 2 0.453 = 3

14. Rule #4 • Zeros at the end of a number and to the right of a decimal point are significant. • They show how precise the measurement was Examples: 43.00 = 4 1.010 = 4 1.50 = 3

15. Rule #5 • Zeros at the end of a number when no decimal point is present aren’t significant. • You can’t tell if the number was rounded Examples: 300 = 1 27,300 = 3

16. Rule # 6 • All numbers use in scientific notation are significant. • They show precision of measurement. Examples: 4.00 x 10 = 3 5.0977 x 10 = 5 1.5000 x 10 = 5 2 4 4

17. Practice with Zeroes • 45.8736 • .000239 • .00023900 • 48000. • 48000 • 3.982106 • 1.00040 • 6 - All digits count • 3 - Leading 0’s don’t • 5 - Trailing 0’s do • 5 - 0’s count in decimal form • 2 - 0’s don’t count w/o decimal • 4 - All digits count • 6 - 0’s between digits count as well as trailing in decimal form

18. Sig. Fig. Math Rules Multiplication / Division: • Your answer can’t have more sig. figs. than the number in the problem with the least amt. of sig. figs. • Your are only as good as your least accurate measurement Example = 60.56227892 x 35.25 Calculator says – 2134.890832 (wrong) Answer - 2135

19. Mult/Div Significant Figures

20. Sig. Fig. Math Rules • Addition / Subtraction: Answers can’t have more numbers to the right of the decimal point than the number in the problem with the least amt. of numbers to the right of the decimal point. Example = 24.1 + 3.35 + 2.23 Calculator says – 29.68 (wrong) Answer – 29.7

21. Add/Sub Significant Figures • Line up decimal just like you always do when adding or subtracting with decimals • Round your answer to have the same number of sig figs as the measurement with the least.

22. Add/Sub Examples 5600 + 997.5 6597.5 6600 Can only have 2 sig fig so you must round answer.

23. Rounding • Once you decide how many digits to retain, the rules for rounding off numbers are straightforward: • RULE 1. If the first digit you remove is 4 or less, drop it and all following digits. 2.4271 becomes 2.4 when rounded off to two significant figures because the first dropped digit (a 2) is 4 or less. • RULE 2. If the first digit removed is 5 or greater, round up by adding 1 to the last digit kept. 4.5832 is 4.6 when rounded off to 2 significant figures since the first dropped digit (an 8) is 5 or greater. • If a calculation has several steps, it is best to round off at the end.

24. Learning Check • 32.27  1.54 = 49.6958 • 3.68  .07925 = 46.4353312 • 1.750  .0342000 = 0.05985 • 3.2650106  4.858 = 1.586137  107 • 6.0221023  1.66110-24 = 1.000000 49.7 46.4 .05985 1.586 107 1.000

25. Learning Check • .56 + .153 = .713 • 82000 + 5.32 = 82005.32 • 10.0 - 9.8742 = .12580 • 11 – 9.8742 = 1.12580 .71 82000 .1 1

26. More Practice • http://www.chemistrywithmsdana.org/wp-content/uploads/2012/07/SigFig.html • http://www.chemistrywithmsdana.org/wp-content/uploads/2012/07/SigFigOperations.html • http://www.sciencegeek.net/APchemistry/APtaters/sigfigs.htm