1. SIGNIFICANT FIGURES

2. Significant Figures Instruments are only so precise. The number of digits reported are considered significant figures. There are rules for determining the number of significant figures.

3. Rules for Significant Figures 1. Non-zero numbers are always significant. Ex. 72.3  has 3 significant figures. 2. Zeros between non-zero numbers are always significant. Ex. 60.5  has 3 significant figures. 3.Zeros before (to the left of) non-zero numbers are not significant. Ex. 0.0253  has 3 significant figures

4. 4. All Zeros after (to the right of) non-zero numbers are significant IF there is a decimal point in the number. Ex. 123.00  5 significant figures (decimal) Ex. 12,000  2 significant figures (no decimal) Ex. 120.0  4 significant figures (decimal) Ex. 12,000.  5 significant figures (decimal)

5. RULE #1 SIG FIG2 SIG FIGS3 SIG FIGS4 SIG FIGS5 SIG FIG 161718334.2512,375 2101500103500112,305 35050.125,00012.0012.000 40.0000010.0068502502.0502,340,000

6. Let’s try some together…. How many significant digits are in these numbers? 1.35 g 2.3.57 m 3.3.507 km 4.0.0035 kg 5.2406 L 6..0004 m 7.240.00 g 8.20.04080 g

7. How did you do? 1.35g2 2.3.57m3 3.3.507km4 4.0.0035kg2 5.2406 L4 6..0004m1 7.240.00 g5 8.20.04080 g7

8. Rounding Numbers Often times your calculator will give you more digits than necessary. In these cases you will round. Let try a few. 1. Round 3.515014 to 5 significant figures. = 3.5150 2. Round 3.5150 to 3 significant figures = 3.52 3. Round 3.52 to 1 significant figure = 4 4. Round 3430 to 2 significant figures = 3400

9. Round all of the numbers to four significant figures a. 84791 kg b. 38.5432 g c. 256.75 cm d. 4.9356 m e. 0.00054818 g f. 136,758 kg g. 308,659,000 mm h. 2.0142 ml

10. Round all of the numbers to four significant figures a.84791 kg = 84790 kg b.38.5432 g = 38.54 g c.256.75 cm = 256.8 cm d.4.9356 m = 4.936 m e.0.00054818 g = 0.00005482 g or 5.482 x 10 -5 g f.136,758 kg = 136,800 kg or 1.368 x 10 5 kg g.308,659,000 mm = 308,700,000mm or 3.087 x 10 8 mm h.2.0142 ml = 2.014 ml

11. Calculations with significant figures 1. For addition and subtraction, the answers should be rounded off to the same number of decimal points as the measurement with the fewest decimal places. Ex. 2.56 + 2.1 = 4.66  4.7 Ex. 34.232 + 22.4 = 56.632  56.6 2. For multiplication and division, the answers should be rounded off to the same number of significant figures in the measurement with the fewest significant figures Ex. 3.01 x 2.0 = 6.02  6.0 Ex. 45 / 9.00 = 5.00  5.0

12. Practice: 1)4.5 + 2.34 = _____________________ 2.) 4.5 – 5 = ________________________ 3) 6.00 + 3.411 = _____________________ 4) 3.4 x 2.32 = _______________________ 5) 7.77 / 2.3 = ______________________ 6) 3.890 / 121 = ______________________ 6.8 9.41 7.9 3.4

13. 7) 1200 x 23.4 = ______________________ 8) 120 x 0.0002 = _____________________ 9) 78.5 + 0.0021 + 0.0099 = ___________ 10) (3.4 x 8.90) x (2.3 + 9.002) = _________ 11) (2.31 x 10 3 ) / (3.1 x 10 2 ) = ___________ 12) 0.0023 + 65 = __________________

14. Scientific Notation Learn to express large and small numbers in scientific notation.

15. An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about 0.00000003 centimeters across. The length of these numbers in standard notation makes them awkward to work with. Scientific notation is a shorthand way of writing such numbers.

16. The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Helpful Hint In scientific notation the number of atoms in a penny is 2.0  10 22, and the size of each atom is 3.0  10 –8 centimeters across.

17. 135,000 1.35  100,000 Think: Move the decimal right 5 places. A. 1.35  10 5 1.35  10 5 10 = 100,000 5 Write the number in standard notation.

18. 0.0027 Think: Move the decimal left 3 places. B. 2.7  10 –3 Write the number in standard notation.

19. C. –2.01  10 4 –20,100 Think: Move the decimal right 4 places. Write the number in standard notation.

20. 2,870,000,000 Think: Move the decimal right 9 places. D. 2.87  10 9 Write the number in standard notation.

21. 0.000019 Think: Move the decimal left 5 places. E. 1.9  10 –5 Write the number in standard notation.

22. Translating Standard Notation to Scientific Notation Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative. 0.00709 Move the decimal to get a number between 1 and 10. 7.09 7.09  10 Set up scientific notation. Think: The decimal needs to move 3 places. 7.09  10 –3 = 0.00709 Write 0.00709 in scientific notation.

23. Think: The decimal needs to move left to change 8.11 to 0.000811, so the exponent will be negative. 0.000811 Move the decimal to get a number between 1 and 10. 8.11 8.11  10 Set up scientific notation. Think: The decimal needs to move 4 places. Check 8.11  10 = 0.000811 –4 Write 0.000811 in scientific notation. So 0.000811 written in scientific notation is 8.11  10 –4.

24. Lesson Quiz Write in standard notation. 1. 1.72  10 4 2. 6.9  10 –3 4. 57,000,000 17,200 0.0069 3. 0.0053 5.3  10 –3 5.7  10 7 Write in scientific notation. 5. A human body contains about 5.6 x 10 6 micro-liters of blood. Write this number in standard notation. 5,600,000