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Understanding Measurements: Units, Accuracy, and Calculations

Learn about the International System of Units (SI Units), scientific notation, density, precision vs. accuracy, sig figs, and more in measurements and calculations.

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Understanding Measurements: Units, Accuracy, and Calculations

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  1. STEM I Measurements and Calculations

  2. Units of Measurement “How do scientists measure things? The use standard units of measure called the International System of Units, SI Units.

  3. Units of Measurement • There are seven base units… • Length – meter, m • Mass – kilogram, kg • Time – second, s • Temperature – kelvin, K • Electric current – ampere, A • Amount of substance – mole, mol • Luminous intensity – candela, cd Derived Units: combinations of base units. - speed (meters per second, m/s) - density (kg per cubic meter, kg/cm3) P. 34 – 35

  4. Scientific Notation • Answer has to have 1 digit before the decimal. • Use exponents to show the number of digits after the decimal. • 1.54 x 10-2 • 2.002 x 103 • 4.1 x 10-4 • 7.023 x 101

  5. What’s the difference between…? Mass is the measure of how much matter is present. It does not depend on gravity. Weight is the measure of the gravitational pull on matter. “The weight of an object is different on the moon than on the earth…but the mass does not change.” Volume is the amount of space occupied by an object. Density is the ratio of mass to volume.

  6. Density: a measurement of how much matter is contained in a certain volume. Calculate Density D = Mass Volume What is Density? M V D ***Test: Density of Water: 1.00 g/cm3

  7. Precision vs. Accuracy • Accuracy: how close a measurement is to the correct answer. • Precision: how close each measurement is to one another.

  8. Precision vs. Accuracy

  9. Percentage Error % Error = | EXP – ACT | x 100 ACT Used to evaluate how accurate your measurements were.

  10. Estimations and Errors in Measuring • What is the smallest interval? • Go one more digit past the smallest interval.

  11. Estimations and Errors in Measuring • What is the smallest interval? 0.0 cm • Go one more digit past the smallest interval. 0.00 cm

  12. Estimations and Errors in Measuring What is the volume of the liquid? • What is the smallest interval? 0.0 mL • Go one more digit past the smallest interval. 0.00 mL

  13. Estimations and Errors in Measuring What is the volume of the liquid? 6.62 ± 0.01 mL

  14. Rounding

  15. Try these: Round to 3 decimal places. 1. 4.2225  2. 17.1111  3. 20.0075  4. 0.0127  • 3.14527  • 7.9999  • 7. 14.5055 

  16. Try these: Round to 3 decimal places. 1. 4.2225  4.222 2. 17.1111  17.111 3. 20.0075  20.008 4. 0.0127  0.013 • 3.14527  3.145 • 7.9999  8.000 • 7. 14.5055  14.506

  17. Significant Figures (Sig Figs) Conversion factors do not affect significant digits b/c conversion factors are EXACT.

  18. Significant Figures (Sig Figs) How many sig figs? • 804.05 • 0.014403 • 1002 • 400 • 30000. • 0.000625000

  19. Significant Figures (Sig Figs) How many sig figs? • 804.05 • 0.0144030 • 1002 • 400 • 30000. • 0.000625000

  20. Significant Figures (Sig Figs) How many sig figs? • 804.05 • 0.0144030 • 1002 • 400 • 30000. • 0.000625000

  21. Adding and Subtracting Sig Figs When adding or subtracting decimals, the answer must have: - the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. - In other words: Round to the fewest number of decimal places. Express each answer to the correct number of significant figures. * 5.44 m - 2.6103 m = * 1.22 mL + 15.8 mL =

  22. Adding and Subtracting Sig Figs When adding or subtracting decimals, the answer must have: - the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. - In other words: Round to the fewest number of decimal places. Express each answer to the correct number of significant figures. * 5.44 m - 2.6103 m = 8.0503  8.05 mL * 1.22 mL + 15.8 mL = 17.02  17.0 mL

  23. Multiplying and Dividing Sig Figs For multiplication or division, the answer: • can have no more significant figures than are in the measurement with the fewest number of significant figures. • In other words: Round to the fewest number of significant digits. Express each answer to the correct number of significant figures. * 4.22 m x 1.05976 m = * 2.4 g/mL  15.82 mL =

  24. Multiplying and Dividing Sig Figs For multiplication or division, the answer: • can have no more significant figures than are in the measurement with the fewest number of significant figures. • In other words: Round to the fewest number of significant digits. Express each answer to the correct number of significant figures. * 4.22 m x 1.05976 m = 4.4721872  4.47 m (3 SF’s) * 2.4 g/mL  15.82 mL = 37.968  38 mL (2 SF’s)

  25. Direct Proportion As one variable increases, the other variable also increases.

  26. Inverse Proportion As one variable increases, the other variable decreases.

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