Chemistry Lecture L.S. 3

1. Chemistry Lecture L.S. 3 Significant Figures and Scientific Notation

2. Significant Figures • We use significant figures to demonstrate the uncertainty involved in a measurement. • There are rules for determining the number of significant figures a measurement has.

3. Significant Figures • Non-zero integers always count as significant figures. • Rules for zeros are as follows: • Leading zeros are zeros that precede all the non-zero digits. These are not significant. • Captive zeros are those between non-zero digits. These are significant. • Trailing zeros are those at the right end of the number. They are significant only if the digit contains a decimal.

4. Significant Figures • Exact numbers are those that are not obtained by using measuring devices. They are considered to have an infinite number of significant digits. • An example of an exact number would be a known constant used for calculations such as a conversion factor.

5. Significant Figures • Let’s try some counting! • 1100 • 2 significant figures (trailing zeros w/ no decimal are not significant) • 0.001 • 1 significant figure (leading zeros aren’t significant) • 1.001 • 4 significant figures (captive zeros are always significant) • 1.100 • 4 significant figures (trailing zeros w/ decimal are significant)

6. Significant Figures Questions?

7. Significant Figures • When doing calculations involving measurements, the answer must be presented with the correct number of significant figures. • There are rules which dictate how many significant figures an answer should have based on the measurements used to calculate and the operations done.

8. Significant Figures • For multiplication and division, the number of significant figures in the result is the same as the number in the least precise measurement used in the calculation. • 4.56 x 1.4 = 6.38 • Since 1.4 is the least precise measurement, the result should have 2 significant figures • 4.56 x 1.4 = 6.4

9. Significant Figures • For addition and subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation. • 12.11 + 18.0 + 1.013 = 31.123 • since 18.0 is the least precise measurement, the result should only go out the tenths place. • 12.11 + 18.0 + 1.013 = 31.1

10. Significant Figures • A Note on Rounding: • If you are performing a series of calculations, carry the extra digits through to the final result, then round. • If the digit to be removed • is less than 5, the preceding digit stays the same. • is greater than or equal to 5, the preceding digit is increased by 1. • Only look to the digit immediately following the last significant digit for rounding purposes.

11. Significant Figures • Let’s try some! • 97.382 + 4.2502 + 0.99195 • 102.614 (97.382 is least precise, so result should only go to thousandths) • 0.14 * 6.022 • 0.84 (0.14 is least precise, so result should only have 2 significant figures) • 21.901 – 13.21 – 4.0215 • 4.67 (13.21 is least precise, so result should only go to hundredths) • 4.184 * 100.62 * (25.27 – 24.16) • 467.3 (all but 100.62 have 4 significant figures, so result should as well)

12. Significant Figures Questions?

13. Scientific Notation • Scientific notation is used to make a very large or very small number easier to write. • Scientific notation is also useful when trying to determine the number of significant figures as all non-significant digits are removed. • Scientific notation expresses a number as a product of a number between 1 and 10 and the appropriate power of 10.

14. Scientific Notation • The distance from the Earth to the sun is approximately 93 million miles. • 93,000,000 miles • This number can be converted to scientific notation for ease of use. • 93,000,000 = 9.3 * 10 * 10 * 10 * 10 * 10 * 10 * 10 • 93,000,000 = 9.3 * 107

15. Scientific Notation • The easiest way to determine the appropriate power of 10 for scientific notation is to count how many places the decimal will have to move in order to have a number between 1 and 10. • When the decimal moves to the left the exponent is positive. • When the decimal moves to the right the exponent is negative.

16. Scientific Notation

17. Scientific Notation • Let’s try some! • 21,000 • 2.1 * 104 • 0.000256 • 2.56 * 10-4 • 10,010,000 • 1.001 * 107 • 0.000000080042 • 8.0042 * 10-8

18. Scientific Notation • When multiplying, only multiply the first part of each number. • Then add the exponents together. • If necessary, move the decimal to maintain scientific notation adjusting the exponent accordingly.

19. Scientific Notation • When dividing, only divide the first part of each number. • The subtract the exponent belonging to the divisor from that of the divided. • If necessary, move the decimal to maintain scientific notation adjusting the exponent accordingly.

20. Scientific Notation • To add or subtract in scientific notation, you must first make sure that the exponents are all the same. • If the exponents are the same, then the first part of each number can be added or subtracted. • If the exponents are not the same, then the numbers must be either taken out of scientific notation or manipulated so that the exponents do match.

21. Scientific Notation • Let’s try some! • (4.32 * 104)(2.76 * 10-2) • (4.32 * 2.76) * 104 + (-2) • 11.9 * 102 • 1.19 * 103 • (6.02 * 1023)/(2.2 * 103) • (6.02/2.2) * 1023 – 3 • 2.7 * 1020 • (3.25 * 105) + (4.2 * 104) • (32.5 * 104) + (4.2 * 104) • 36.7 * 104 • 3.67 * 105

22. Scientific Notation Questions?

23. Assignment: WS_SignificantFigures