1. Significant Figures How to determine and use the proper sig. figs.

2. What is a significant figure? There are 2 kinds of numbers: 1) Exact numbers 2) Measured numbers

3. What is a significant figure? 1) Exact: don’t come in fractions or decimals!!! Ex: humans Ex: bacterial colonies on a petri dish

4. What is a significant figure? On the other hand…not everything is so easy…sometimes you have to … Approximate: A close guess that is in the ball park.

5. When to use Significant figures 2) Measured numbers Using a tool/ device to measure…you must ask yourself what are the limits of the tool/ device. Ex:

6. When to use Significant figures You could measure Arrow “A” as 3.9cm. But to some mathematicians 3.9cm, or 3.90cm is the same. A

7. Key difference But, to a scientist 3.9cm and 3.90cm is NOT the same

8. Uncertainty The limit of the device! Uncertainty is defined as ½ of the smallest certain unit *You should report the uncertain digit If a Centimeter Ruler was used… ArrowLength ± 0.5cm* Arrow “A”3.9 Arrow “B”3.4 If a Millimeter Ruler was used… ArrowLength ± 0.5mm* Arrow “A”39.1 Arrow “B”33.8 A B

9. Uncertainty The limit of the device! Uncertainty is defined as ½ of the smallest certain unit Digital Balances: The last digit is uncertain. For example: The mass of the powder is 5.00g ± 0.05 * some electronic devices have published uncertainty, If you have access to the manual, refer to it. What about electronic devices?*

10. Uncertainty Random Uncertainty: a deviation from the normalized value (as likely to be “too high” or “too low” How can you reduce this uncertainty? More trials!!!!  average Will still need to evaluate the range of the data or the standard deviation of the data…if graph  “Error Bars!” Systematic Uncertainty Results shifted one direction consistently ex: balance weighing 0.8g too little ! Fix: calibrate the equipment Ex: dispense an extra 3 microliters when using micropipette! Fix: use tool properly, don’t use “hard stop”!!!

11. How do I know how many Sig Figs? Basic Decim al Rules If no Decimal, then start counting at the first NON zero, and stop counting at the last NON zero! 30  1 sig fig 303  3 sig figs 3030  3 sig figs

12. How do I know how many Sig Figs? Basic Decim al Rules If Decimal, then start counting at the first NON zero, and count until the end! 3.1  2 sig fig 3.03  3 sig figs 3.030  4 sig figs 0.303  3 sig figs

13. How many sig figs? 7 40 0.5 0.00003 7 x 10 5 7,000,000 1 1 1 1 1 1

14. How many sig figs here? 1.2 2100 56.76 4.00 0.0792 7,083,000,000 2 2 4 3 3 4

15. Identify the uncertain digit in each number? 1.2 2100 56.76 4.00 0.0792 7,083,000,000 1.2 2100 56.76 4.00 0.0792 7,083,000,000

16. How many sig figs here? 3401 2100 2100.0 5.00 0.00412 8,000,050,000 4 2 5 3 3 6

17. How would you indicate uncertainty? 3401 2100 2100.0 5.00 0.00412 8,000,050,000 3401 ±5 2100 ±500 2100.0 ±0.5 5.00 ±0.05 0.00412 ±0.00005 8,000,050,000 ±50,000

18. What about calculations with sig figs? Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

19. Add/Subtract examples 2.45cm + 1.2cm = 3.65cm, Round off to = 3.7cm which digit is uncertain? 3.7

20. Add/Subtract examples 7.432cm + 2cm = 9.432 round to  9cm which digit is uncertain? 9 cm

21. Multiplication and Division Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

22. A couple of examples 56.78 cm x 2.45cm = 139.111 cm 2 Round to  139cm 2 which digit is uncertain? 139 cm 2

23. A couple of examples 75.8cm x 9.6cm = ? Do the math and round to… Which digit is uncertain? How would you record uncertainty?

24. Sig fig Math!!!