1. Mastery of Significant Figures, Scientific Notation and Calculations Goal: Students will demonstrate success in identifying the number of significant figures within a number, converting decimal form to scientific notation and calculating and rounding an answer properly. 9-14-09 Chemistry

2. SIGNIFICANT FIGURES All non-zero digits are significant. 825 has three sig. fig. Zeros located between non-zero digits are significant. 2007 has four sig. fig. When a decimal or mixed decimal ends in zero, the zero is significant. 43.270 has five sig. fig. When a whole number ends in zero (with no decimal point), the zero is not significant. 400 has one sig. fig. When a whole number ends in zero (with a decimal point), the zero is significant 450. has three sig. fig.

3. Identifying Significant Figures 5.8000 95,000 200.0 1010 0.001010 0.0010 0.12540 0.000400 0.01 52,000,000,000.000 000 000 000

4. More Converting 5.8000 95,000 200.0 1010 0.001010 0.0010 0.12540 0.000400 0.01 52,000,000,000.000 000 000 000

5. More Converting 5.8000 = 5.8000 x 10 0 95,000 = 9.5 x 10 4 200.0 = 2.000 x 10 2 1010 = 1.01 x 10 3 0.001010 = 1.010 x 10 -3 0.0010 = 1.0 x 10 -3 0.12540 = 1.2540 x 10 -1 0.000400 = 4.00 x 10 -4 0.01 = 1 x 10 -2 52,000,000,000.000 000 000 000 = 5.20… x 10 10

6. More Identifying 0.000 000 000 200 602,000,000,000,000,000,000,000 3.00x10 8 200. 2500 5 99949 1,010,101,000 52,000.0 10.00

7. Converting Scientific Notation 0.000 000 000 200 602,000,000,000,000,000,000,000 3.00x10 8 200. 2500 5 99949 1,010,101,000 52,000.0 10.00

8. Converting Scientific Notation 0.000 000 000 200 = 2.00 x 10 -10 602,000,000,000,000,000,000,000 = 6.02 x 10 23 3.00x10 8 = 3.00 x 10 8 200. = 2.00 x 10 2 2500 = 2.5 x 10 3 5 = 5 x 10 0 99949 = 9.9949 x 10 4 1,010,101,000 = 1.010101 x 10 9 52,000.0 = 5.20000 x 10 4 10.00 = 1.000 x 10 1

9. Converting from Sci. Not. To Decimal 6.8700 x 10 4 2.50 x 10 2 4.000 x 10 3 1.01 x 10 6 1.010 x 10 -4 1.0 x 10 -3 1.540 x 10 -5 4.00 x 10 -2 6.050 x 10 -6

10. Converting from Sci. Not. To Decimal 6.8700 x 10 4 68,700. 2.50 x 10 2 250. 4.000 x 10 3 4000. 1.01 x 10 6 1,010,000 1.010 x 10 -4 0.0001010 1.0 x 10 -3 0.0010 1.540 x 10 -5 0.00001540 4.00 x 10 -2 0.0400 6.050 x 10 -6 0.000006050

11. Addition Subtraction Rules for Sig. Figs. Adding and Subtracting: Add or Subtract using your calculator, and round the answer to the least accurate decimal place. 1.23 + 0.1 + 16.529 = 17.859 => 17.9 the tenths place in 0.1 is the least accurate decimal place.

12. +/- with Sig Figs 1.58.02 + 4.001 + 0.1 = 2.0.0025 + 500. + 1.00 = 3.862.1 + 5.640 – 0.346 = 4.100.50 + 24,000. - 60.99 = 5.85.6435 + 978.50 – 79.5 =

13. +/- with Sig Figs 1.58.02 + 4.001 + 0.1 = 62.121  62.1 2.0.0025 + 500. + 1.00 = 501.0025  501 3.862.1 + 5.640 – 0.346 = 867.394  867.4 4.100.50 + 24,000. - 60.99 = 24039.51  24040. 5.85.6435 + 978.50 – 79.5 = 984.6435  984.6

14. More +/- with sig figs 6.97.381 + 4.2502 + 0.99195 = 7.171.5 + 72.915 – 8.23 = 8.1.00914 + 0.87104 + 1.2012 = 9.21.901 – 13.21 – 4.0215 = 10. 0.99195 + 8.23 – 1.2012 =

15. More +/- with sig figs 6.97.381 + 4.2502 + 0.99195 = 102.62315  102.623 7.171.5 + 72.915 – 8.23 = 236.185  236.2 8.1.00914 + 0.87104 + 1.2012 = 3.08138  3.0814 9.21.901 – 13.21 – 4.0215 = 4.6695  4.67 10. 0.99195 + 8.23 – 1.2012 = 8.02075  8.02

16. Multiplication and Division with Sig. Figs. Round off to the least number of significant figures in any individual factor. i.e. (25.1) (3.9) (0.0016) = 0.156624 => 0.16 3 22 The answer must be rounded to 2 sig. figs.

17. Multiply/Divide with Sig. Figs 1.(0.102) (0.0821) ( 273) / (1.01) = 2.(0.14) (6.022 X 10 23 )= 3.(4.0 X 10 4 ) (0.00521) (734.933) = 4.(2.00 X 10 6 ) / (3.00 X 10 -7 ) = 5.(0.005246) (25,000) / (52.01) =

18. Multiply/Divide with Sig. Figs 1.(0.102) (0.0821) ( 273) / (1.01) = 2.263521386  2.26 2.(0.14) (6.022 X 10 23 )= 8.428 X 10 22  8.4 X 10 22 3.(4.0 X 10 4 ) (0.00521) (734.933) = 153,160.0372  150,000 4.(2.00 X 10 6 ) / (3.00 X 10 -7 ) = 6.666666666667 X 10 12  6.67 X 10 12 5.(0.005246) (25,000) / (52.01) = 2.521630456  2.5

19. More Multiply Divide 6.(2.50) (0.0015) / (10.) = 7.(200.0) (8.1) / (0.0010) = 8.(350) (5.001) / (0.00100000000000000000) = 9.(5,000,000) (10.) / (1,000,000) =

20. More Multiply Divide 6.(2.50) (0.0015) / (10.) = 0.000375  0.00038 7.(200.0) (8.1) / (0.0010) = 162,000  160,000 8.(350) (5.001) / (0.00100000000000000000) = 1,750,350  1,800,000 9.(5,000,000) (10.) / (1,000,000) = 50.0000  50

21. CFA #1 Convert the following from decimal to scientific notation 1. 0.000540 2. 1500. 3.297,000 Calculate the following and use significant figure rules to round the answer properly 4. 1.04 + 38.01 + 10.000 = 5.(100.0) (1.000) (1.0) = 6. (100.) (1.000) / (10)=

22. CFA #1 Convert the following from decimal to scientific notation 1. 0.0005405.40 x 10 -4 2. 1500. 1.500 x 10 3 3.297,000 2.97 x 10 5 Calculate the following and use significant figure rules to round the answer properly 4. 1.04 + 38.016 + 10.000 =49.06 5.(100.0) (1.000) (1.0) =1.0 x 10 2 6. (100.) (1.000) / (10)=10