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Measurement and Calculation

Measurement and Calculation. Unit 2. The Fundamental SI Units (le Système International, SI). Physical Quantity Name Abbreviation. Mass. kilogram. kg. Length. meter. m. s. Time. second. Temperature. Kelvin. K. Electric Current. Ampere. A. Amount of Substance. mole. mol.

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Measurement and Calculation

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  1. Measurement and Calculation Unit 2

  2. The Fundamental SI Units(le Système International, SI) Physical QuantityNameAbbreviation Mass kilogram kg Length meter m s Time second Temperature Kelvin K Electric Current Ampere A Amount of Substance mole mol Luminous Intensity candela cd

  3. SI Units

  4. SI PrefixesCommon to Chemistry Kilo (k) 1,000 103 Deci (d) 1/10 10-1 Milli (m) 1/1000 10-3 Giga (G) 109 Nano (n) 10-9 Micro (μ) 1/1000000 10-6 Mega (M) 1,000,000 106 Pico (p) 10-12 Centi (c) 1/100 10-2 Base unit 1 100

  5. Dimensional Analysis • A simple mathematical approach to converting between units. • Involves conversion factors (fractions). • Follows simple math functions (x/÷) • We can use conversion factors for metric conversions as well as other conversions. • Dim. analysis can be used to convert from 1 unit to another. • One step or several steps. • Each conversion factor represents a math function – treat it as such.

  6. Unit conversions • View this video: • https://www.khanacademy.org/math/arithmetic/rates-and-ratios/metric-system-tutorial/v/unit-conversion

  7. Unit conversions • Examples: 1. What is the volume of a 250-mL beaker in L? 2. What is the mass of a 9.5 g sugar cube in mg? 3. A car travels 74,000 meters. How many km is this trip?

  8. Accuracy vs. Precision • Accuracy refers to how close a measurement is to the true or actual value. • Precision refers to how close a series of measurements are to one another.

  9. Accuracy vs. Precision Are the following pictures illustrating accuracy, precision, neither, or both?

  10. Accuracy vs. Precision A class of chemistry students determined the mass of a quarter to be 5.200 g. To confirm this, several students reported their “massing” 4 times. The following data was collected. Classify these students results as precise, accurate, neither, or both. STUDENT MASS (g) A 5.240 5.242 5.239 5.240 B 5.200 5.205 5.199 5.200 C 5.251 5.100 5.105 5.244 D 5.201 5.100 5.300 5.205

  11. Reporting Measurements • To indicate the uncertainty of a single measurement scientists use a system called significant figures • Our data can only be as precise as the least precise measuring tool/instrument • The last digit on any measurement is estimated by the reporter

  12. How HOT are you?? • Heat (energy) cannot be measured directly. • We can measure heat transfer by change in temperature. • We define temperature as the average kinetic energy of a system. • movement within a substance • Measure temperature with a thermometer.

  13. Temperature Scales • Fahrenheit Scale, °F • Relative scale • Celsius Scale, °C • Relative scale • Water’s freezing point = 0°C, boiling point = 100°C • Kelvin Scale, K • Absolute scale • Water’s freezing point = 273 K, boiling point = 373 K • oC = K - 273 K = oC + 273

  14. Temperature Conversion Practice • Convert the following from oC to K: 1. 55oC 2. 173oC 3. -28oC 4. -215oC 5. 88oC • Convert the following from K to oC: 1. 15 K 2. 295 K 3. 415 K 4. 63 K 5. 186 K

  15. Graphing • Determine the variables. • Independent  x-axes • Dependent  y-axes • Determine the range of values. • Utilize all of 1 side of the graph paper. • usually start at ‘0’ but NOT ALWAYS 4. Makes scales easy & keep consistent

  16. Graphing 5. Label both axes (include unit). - draw axes with a straight edge • Give your graph an appropriate title. - dependent vs. independent 7. Titles, axes, & labels must be in INK! 8. Plot data with ‘x’ not ‘•’ (may be in pencil) 9. Draw “best-fit” line through your data

  17. Graphing 10. You may be asked to use your graph to draw conclusions & make predictions. • Two examples would include: • Interpolation – within the limits of the data • Extrapolation – beyond the limits of the data

  18. “Best-Fit” Line Distance vs. Time for Freefall

  19. Scientific Notation • A shorthand method of expressing large and small numbers using exponents. • Expresses values to the precision of the instrument. M x 10n M = any number between 1 & 10 n = any integer (including 0) • Example: 2.34 x 104 6.001 x 10-4

  20. Scientific Notation • Identify the correct scientific notations: • 3 x 102 • 4.5 • 6.7 x 10-3 • 0.573 x 105 • 12 x 10-2

  21. Scientific Notation • Express the following in scientific notation: 1. 2,300,000 2. 0.00401 3. 5.0500 • Express the following in long-hand form: 1. 6.1 x 102 2. 6.01 x 103 3. 6.6 x 101 4. 6.01 x 10-4

  22. Scientific notation • View these videos: • https://www.khanacademy.org/math/arithmetic/exponents-radicals/computing-scientific-notation/v/multiplying-in-scientific-notation • https://www.khanacademy.org/math/arithmetic/exponents-radicals/computing-scientific-notation/v/scientific-notation-3

  23. Scientific Notation • Perform the following calculations, expressing your answer in scientific notation. 1. (6.0 x 104) (2.0 x 105) 2. (4.0 x 104) (2.0 x 10-6) 3. (8.0 x 103) / (2.0 x 106) 4. (2.0 x 10-3) / (4.0 x 10-8)

  24. Rules for Counting Significant Figures 1. Nonzero integers are always significant Ex. 46.3 m  3 sig. figs. 6.295 g  4 sig. figs 2. ‘0’ between nonzero digits are significant. Ex. 40.7 L  3 sig. figs. 87009 km  5 sig. figs.

  25. Significant Figures 3. ‘0’ in front of nonzero digits are not significant. Ex. 0.009587 m  4 sig. figs. 0.0009 kg  1 sig. fig. *The zeros in these cases are ‘placeholders’; they are used for spacing.

  26. Significant Figures 4. Zeros are the end of a number and to the right of a decimal are significant. Ex. 85.00  4 sig. figs. 9.070000000  10 sig. figs. 5. A decimal point placed after zeros indicates that the zeros are significant. Ex. 2000.  4 sig. figs 2000  1 sig. fig.

  27. Significant Figures • Do NOT count sig. figs. in the following numbers: 1. Counting numbers 2. Constants 3. Conversion factors

  28. Practice: Give the SigFigs • 54.9 • 0.0023 • 1000.5 • 2.4 x 105 • 0.0970 x 10-3 • 8500. • 8500

  29. Adding/Subtracting Numbers with Significant Figures • When adding/subtracting, look for the LEAST DECIMAL measurement to determine the correct number of sig. figs. (the least precise) • Round answer to the same decimal place Ex. 54 g + 108.6 g + .0004 g = 55.24 mL – 2.1 mL =

  30. Multiplication/Division with Significant Figures • Result has the same number of significant figures as the measurement with the smallest number of significant figures • Count the number of significant figures in each measurement • Round the result so it has the same number of significant figures as the measurement with the smallest number of significant figures 4.5 cm x 0.200 cm = 0.90 cm2 2 sig figs 3 sig figs 2 sig figs

  31. Practice: give the SigFigs • 87.9 + 156.098 + 40 • 63.7 – 56.987 • 62.4 x 3.1 • 587 / 6.247 • 3.567 x π

  32. Density • Density is a property of matter representing the mass per unit volume • For equal volumes, denser object has larger mass • For equal masses, denser object has small volume • Solids = g/cm3 • 1 cm3 = 1 mL • Liquids = g/mL • 1 mL of H2O = 1 g at 4oC • Gases = g/L • Volume of a solid can be determined by water displacement

  33. Using Density in Calculations

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