1. Significant Figures Mr. Kane

2. What is the point of Significant Figures (sig figs) Different measuring tools offer different precision (see measurement presentation for details ) Different measuring tools offer different precision (see measurement presentation for details ) When using measurements in mathematical calculations, you can only report the precision of the least precise calculation that goes into the measurement. When using measurements in mathematical calculations, you can only report the precision of the least precise calculation that goes into the measurement. That is what sig figs is all about – reporting the best answer possible and rounding off the answer where appropriate. That is what sig figs is all about – reporting the best answer possible and rounding off the answer where appropriate.

3. Addition example For example, let’s say you want to find the total mass of 3 fish. Their masses are 12.1g, 11.23g, and 14.111g. For example, let’s say you want to find the total mass of 3 fish. Their masses are 12.1g, 11.23g, and 14.111g. 12.1 g 12.1 g 11.23 g 11.23 g + 14.111 g 37.441 g 37.441 g Answer to report is 37.4 g *You cannot report your answer to the thousandths place because of the fact that your least precise measurement only goes to the tenths place!

4. Division example Lets say you wanted to determine the density of an object that had a mass of 2.2 kg and a volume of 3 cm 3 Lets say you wanted to determine the density of an object that had a mass of 2.2 kg and a volume of 3 cm 3 density = mass/volume density = mass/volume = 2.2 kg 3.3 cm 3 3.3 cm 3 = 0.6666666666666666666666666... kg/cm 3 = 0.67 kg/cm 3 You can’t keep writing the number six. So where do you stop??? You can’t keep writing the number six. So where do you stop??? Sig fig rules say that your reported answer should be 0.67 kg/cm 3 Sig fig rules say that your reported answer should be 0.67 kg/cm 3 Does this sound confusing? It isn’t if you know the sig fig rules! Does this sound confusing? It isn’t if you know the sig fig rules!

5. Sig fig rules for addition and subtraction If you add or subtract, the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places. If you add or subtract, the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places. 6.50 m 6.50 m 5.3 m 5.3 m +3 m +3 m 14.8 m 14.8 m 15 m is the answer you should report 15 m is the answer you should report

6. sig fig rules for multiplication and division If you multiply or divide two numbers, the answer is rounded off to the number of significant figures in the measurement with the least number of sig figs. If you multiply or divide two numbers, the answer is rounded off to the number of significant figures in the measurement with the least number of sig figs. 12.011 g/6.00 g = 2.0018333 g 12.011 g/6.00 g = 2.0018333 g 5 sig figs 3 sig figs The reported answer should be 2.00 g because it has 3 sig figs

7. so what digits are considered “significant”?????? all non-zero digits are significant 203.0, 0.404, 1000. 11.00 all non-zero digits are significant 203.0, 0.404, 1000. 11.00 zeros between other sig figs are significant 203.0, 0.404, 1000, 11.00 zeros between other sig figs are significant 203.0, 0.404, 1000, 11.00 all final zeros after the decimal point are significant 203.0, 0.404, 1000, 11.00 all final zeros after the decimal point are significant 203.0, 0.404, 1000, 11.00 zeros only used for spacing are not significant 203.0, 0.404, 1000, 11.00 zeros only used for spacing are not significant 203.0, 0.404, 1000, 11.00 203.0 0.404 1000 11.00 3 sig figs 4 sig figs 3 sig figs 4 sig figs 4 sig figs 1 sig fig

8. what about scientific notation??? The rules are the same for the number that comes before the multiplier. The rules are the same for the number that comes before the multiplier. 6.022 x 10 23 atoms 6.022 x 10 23 atoms 4 sig figs 4 sig figs You can use scientific notation to report your answer in the appropriate number of sig figs You can use scientific notation to report your answer in the appropriate number of sig figs 1500 cm x 15 cm = 22,500 cm 2 1500 cm x 15 cm = 22,500 cm 2 2 sig figs 2 sig figs 2 sig figs 2 sig figs your reported answer can only have two sig figs, therefore it could be 23,000 cm 2 or 2.3 x 10 4 cm 2 your reported answer can only have two sig figs, therefore it could be 23,000 cm 2 or 2.3 x 10 4 cm 2

9. practice problems! 1. find the total mass of 20.2 kg and 11.00 kg 2. find the area of a rectangle that has a length of 10.0 m and a width of 12.34 m (a=l x w) 3. find the change in mass of a 2.00 kg piece of dry ice that lost 0.50 kg 4. find the change in mass of a 4.00 kg piece of dry ice that lost 0.5 kg 5. find the density of a sample of water that has a mass of 0.0050 g and a volume of 0.005 cm 3 (d=m/v) 6. find the total volume of 2 objects that are 2.33 x 10 3 L and 1.0 x 10 2 L

10. more practice! 7. multiply 3.05 x 10 10 km and 2.1100 x 10 5 km 8. divide 6.00 x 10 15 m by 3.0 x 10 5 m 9. 40.20 sec/20.1000 m 10. (6.6 x 10 -6 ) (3.30 x 10 -2 ) 11. 3000 + 200 12. 4000/200

11. more practice! Put the following numbers in scientific notation with the appropriate number of sig figs! 13. 103,000 14. 105,000.0 15. 0.00004 16. 0.000000890 17. 0.0000001204 18. 198,000,000,000 19. 30 20. 0.5000