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Significant Figures in Chemistry: Rules and Examples

Understand the concept of significant figures in chemistry, including rules for determining the number of significant digits, scientific notation, rounding, and handling calculations. Learn the differences between physical and chemical changes in matter. Practice examples provided.

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Significant Figures in Chemistry: Rules and Examples

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  1. Chapter 1 Understanding the Math in Chemistry

  2. I. What are significant figures/digits? • Significant figures (digits) are a combination of certain as well as uncertain numbers. B. Example: 48.3 Estimated Certain value 48.3101 (rounded down) 48.2896 (rounded up)

  3. This is the way I learned the sig. fig. rules 1. Any digit that is not zero is significant. 1234.56 6 significant figures 1234.56 6 significant figures 2. Zeros between non-zero digits are significant. 1002.5 5 significant figures 3. Zeros to the left of the first non-zero digit are not significant. 000456 3 significant figures 0.0056 2 significant figures 4. If the number is greater than one (1), then all zeros to the right of the decimal point are significant. 457.12 5 significant figures 400.00 5 significant figures 5. If the number is less than one, then only zeros that are at the end of the number and between non-zero digits are significant. 0.01020 4 significant figures 6. For numbers that do not contain decimal points, the trailing zeros may or may not be significant. In this course assume the digits are significant unless told otherwise. 1000 1, 2, 3, or 4 significant figures. UNCLEAR assume 4 in calculation 0.0010 2 significant figures 1.000 4 significant figures 7. Assume defined and counted quantities have an unlimited number of significant figures.

  4. This will not be the way I teach it to you!! Here are two simple rules!! Know them! C. Significant Figures RULES Rule #1: If a decimal point is present count from Left to Right (L R) DO NOT START WITH 0 Rule #2: If a decimal point is absent count from Right to Left (L R) DO NOT START WITH 0

  5. D. Predict the amount of sig. figs in the following: 4 sig. figs. 9. 1000. 4 sig. figs. 1. 138.7 2. 100 1 sig. fig. 10. 10500 3 sig. figs. 3. 0.00320 3 sig. figs. 4. 0.0050 2 sig. figs. 5. 89.0 3 sig. figs. 6. 890 2 sig. figs. 7. 0.0030 2 sig. figs. 8. 1000 1 sig. fig.

  6. II. Scientific Notation A. General Equation: M X 10n n= the number of decimal places moved to get to an acceptable M value +n= greater than 1 -n = less than 1 Examples: 1. 138.7 1≤ M <10 Is this an acceptable M? . Answer: 1.387 X 10 2 How many places do you have to move the decimal to get to an acceptable M? 2. 100 # of sig. figs in value must match the # of sig figs in scientific notaion Answer: 1 X 10 2 3. 0.000320 Answer: 3.20 X 10 -4

  7. B. On your own: Answer: 5.0 X 10 -3 4. 0.0050 Answer: 8.90 X 101 5. 89.0 Answer: 8.9 X 10 2 6. 890 Answer: 3. 0 X 10 -3 7. 0.0030 Answer: 1 X 10 3 8. 1000 Answer: 1.000 X 103 9. 1000. 10. 10500 Answer: 1.05 X 104

  8. C. Going backwards 1.50 X 10 2 Move decimal point to make it larger than 1 150. Move decimal point to make it smaller than 1 3.5 X 10 -4 .00035

  9. Warm up Are these equal? If they are, write yes, if not, correct the “regular” value. • 2.5 X 10-4 = .000025 • 9.91 X 102= 991 • 4.500 X 103= 4500 • 5.700 X 10 -3= .057 Incorrect: .00025 Correct Incorrect: 4500. Incorrect: .005700

  10. Rounding Rules

  11. III. Adding and Subtracting Rounding Rules The answer must contain as many decimal places as the least accurate value (the one with the least # of decimal places) 3. 86.232 - 5.00_____ • 122.5 • 52.68 • + 2.11 L.a 2. 101 6.8 + 3.17 4. 122.4 0.05 + 1.000 81.232 123.45 177.29 110.97 177.3 81.23 111 123.4 123.5

  12. If you stand on the scale and it says: 122.5lbs? Would it be fair to say 123??? Why do you always round up?? I don’t think so!!

  13. IV. ODD/EVEN Rule is used when only a 5 is next to the digit you are interested in rounding…… ODD Digit Round up Even Digit Leave it alone (EVEN…LEAVIN!!)

  14. Let’s practice rounding to 3 sigs figs. 1. 107.5= 108 112 2. 112.5= 1.16 3. 1.155 9.85 4. 9.8451= 855 5. 854.54= .0254 6. .02545=

  15. V. Multiplication and Division Rules The answer must contain as many significant figures as the value with the least number of significant figures

  16. Examples: 3 4 .210748 .211 1. 35.72 (0.00590)= 5 2 2. 6810.2/2.4 = 2837.58333 2800 3 3 How many sig figs? 890. 890 3. 4450/ 5.00= 4 3 14.85724 14.9 4. .3287 (45.2)=

  17. VI. Forms of Matter Video clip a. Element: Smallest, indivisible part of a substance When a metal and nonmetal combine by giving and taking electrons! Ex: Table salt b. Compound: When two or more nonmetals combine by sharing electrons!! Ex: Water (H2O) c. Molecule:

  18. d. Mixture Heterogeneous Mixture: Homogeneous Mixture: Visible components are all similar Has visible distinction between parts

  19. VII. Changes in Matter can be physical or chemical A. Physical change: Identity of substance is NOT altered. B. Chemical change: New substance has different set of properties. Changes in Matter Video clip

  20. According to your understanding….What’s more dense? Casanova Kim Ba Active English A Rock or A Sponge

  21. Ice Cubes or Liquid Water Ice (H2O(s)) Water expands 11% when it freezes Liquid water (H2O(l))

  22. Adding water based food coloring Oil  Water

  23. Which one is more dense?? WWF Wrestler Sumu Wrestler

  24. Coke v. Diet Coke

  25. So what’s the difference between accuracy and precision? Accuracy refers to how closely a measured value agrees with the correct value. Precision refers to how closely individual measurements agree with each other. The repeatability of the results. accurate(the average is accurate)not precise precisenot accurate accurateandprecise

  26. Definition for Density Equation for Density • The amount of matter in a certain amount of space (volume) D=Mass (g) Volume (ml) or (cm3)

  27. Practice Quiz • A rock is submerged in a graduated cylinder. The water level rises from 13.0ml to 14.5 ml. If the rock weighs 6.00g, what is the density of the rock? • If a piece of metal has a density of 50.78g/cm3 and a mass of 20mg, what is its volume? • Explain why cm3 is equal to a ml.

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