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Mastering Scientific Measurements and Notation

Learn how to calculate significant figures, use scientific notation, and accurately measure volume. Understand precision, accuracy, and dimensional analysis in this comprehensive guide.

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Mastering Scientific Measurements and Notation

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  1. Using Scientific Measurements 2.3

  2. Objective/Warm-Up • SWBAT identify and calculate significant figures and use scientific notation. • What is the correct measurement for this buret? 4.85 mL

  3. Notes-Accuracy How close the measurement is to the real, true, or correct value accuracy

  4. Notes-Precision precision How close measurements are to each other

  5. Add your own • What would a picture look like that is neither precise nor accurate?

  6. Objective/Warm-Up • SWBAT review dimensional analysis, density, and metric conversions. • Record the measurement for each cylinder.

  7. Significant Figures • Sig figs – all the digits known with certainty plus one final digit, which is somewhat estimated or uncertain • Graduated cylinder example • 42.5 mL - the 5 is the estimated number

  8. Rules for Determining Sig. Figs. • All non zero digits are significant • Zeros at the end only count if there is a decimal point • Decimal = go to 1st non zero and count everything to the right • Exact numbers have infinite significant figures (1m = 1000mm) • Calculators exaggerate precision

  9. Sig. Fig Examples • How many sig figs are in… • 203000 • 1000.00 • 0.00052 • 0.06400 • 79.810

  10. Significant Digits 4 4 4 3 4 3 4 2 3 4 3 2 2 5 1

  11. Objective/Warm-Up • SWBAT review conversions and SI units. • What is the measurement shown in the graduated cylinder? • How many significant figures in these numbers? • 5.0070 • 3.4000 • 3500 • 0.00120 • 0.07070

  12. Objective/Warm-Up • SWBAT accurately and precisely measure volume and calculate using scientific notation. How many sig figs are in… • 203000 • 1000.00 • 0.00052 • 0.06400 • 79.810

  13. Significant Figures • Multiplication and division sig. figs = answer has no more figs. than the msmt. with the least # of sig. figs. 12.257 5 #’s x 1.162 4 #’s 14.2426340 4 #’s = 14.24

  14. Multiply/Divide with Sig Figs • Your answer must have the same number of sig figs as the measurement with the fewest number of sig figs. Calculate the volume if L = 3.65 cm, W = 3.20 cm, and H = 2.05 cm V = 23.944 cm3, after rounding to the correct number of sig figs, V=23.9 cm3

  15. Significant Figures • Addition and subtraction = answer has no more numbers to the right of the decimal pt. than the number with the least numbers to the right of the decimal. 3.9 5 2.8 79 + 213.6 220.4 29 = 220.4

  16. Addition/Subtraction with Sig Figs • Your answer must have the same number of decimal places as the value with the fewest decimal places 28.0 + 23.538 + 25.68 = 77.218 Round so that the answer is 77.2

  17. Check-Up • How can we judge accuracy? • How can we judge precision? • How do accuracy and precision relate to measurement?

  18. Objective/Warm-Up • Students will be able to use significant digits and scientific notation in calculations. • Warm-Up: Section Review Worksheet

  19. Scientific Notation • 29640000000000000000000 copper atoms in 1 penny • 2.964 x 1022 atoms • 2 Parts to scientific notation • # between 1 and 10 • Power of 10

  20. Scientific Notation • We use the idea of exponents to make it easier to work with large and small numbers. • 10,000 = 1 X 104 • 250,000 = 2.5 X 105 • Count places to the left until there is one number to the left of the decimal point. • 230,000 = ? • 35,000 = ?

  21. Scientific Notation Continued • 0.00006 = 6 X 10-5 • 0.00045 = 4.5 X 10-4 • Count places to the right until there is one number to the left of the decimal point • 0.003 = ? • 0.0000025 = ?

  22. Scientific Notation Examples Change from scientific notation • the distance from Pluto to the Sun is 5.9×10 12 meters • the Milky Way disk radius is 3.9×1020 meters. • The speed of light is 3 x 10 8 meters/second. • the sun is 1.5x 1011 meters from earth • Mass of proton : 1.6726 x 10-27 kg • Mass of neutron: 1.6749 x 10-27 kg • Mass of electron: 9.10939 × 10-31 kg Change into scientific notation • 0.000 000 000 753 kg is the mass of a dust particle • A proton has a diameter of approximately 0.000000000001 mm

  23. Positive Exponents • 101 = 10 • 102 = 10X10= 100 • 103 = 10X10X10 = 1000 • 104 = 10X10X10X10 = 10,000

  24. Negative Exponents • 10-1 = 1/10 = 0.1 • 10-2 = 1/100 = 0.01 • 10-3 = 1/1000 = 0.001 • 10-4 = 1/10000 = 0.0001

  25. Quick Review • When multiplying: • Add the exponents • When dividing: • Subtract the exponents

  26. Multiplying with Scientific Notation • Add the Exponents • 102 X 103 = 105 • 100 X 1000 = 100,000

  27. Multiplying with Scientific Notation (2.3 X 102)(3.3 X 103) • 230 X 3300 • Multiply the Coefficients • 2.3 X 3.3 = 7.59 • Add the Exponents • 102 X 103 = 105 • 7.59 X 105, round to 7.6 x 105

  28. Multiplying with Scientific Notation • (4.6 X 104) X (5.5 X 103) = ? • (3.1 X 103) X (4.2 X 105) = ?

  29. Dividing with Scientific Notation • Subtract the Exponents • 104/103 = 101 • 10000/ 1000 = 10

  30. Dividing with Scientific Notation • (3.3 X 104)/ (2.3 X 102) • 33000 / 230 = 143.4783 • Divide the Coefficients • 3.3/ 2.3 = 1.434783 • Subtract the Exponents • 104 / 102 = 102 • 1.4347823 X 102, round to 1.4 x 102

  31. Dividing with Scientific Notation • (4.6 X 104) / (5.5 X 103) = ? • (3.1 X 103) / (4.2 X 105) = ?

  32. Wrap-Up • Summarize the rules for multiplying and dividing in scientific notation. • Why do we use scientific notation?

  33. Scientific Notation • 0.000000000000003332 kg • 3.332 x 10-15 kg • 1970000000 L • 1.97 x 109 • What is ….. In scientific notation? • 4.58 x 105 • 9.05 x 10-3

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