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Mathematical Fundamentals

Mathematical Fundamentals. SI System. Standard International System of measurement – metrics Has seven base units and many other units derived from these seven. Quantity. Unit. Abbreviation. length. meter. m. mass. gram. g.

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Mathematical Fundamentals

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  1. Mathematical Fundamentals

  2. SI System • Standard International System of measurement – metrics • Has seven base units and many other units derived from these seven

  3. Quantity Unit Abbreviation length meter m mass gram g time second s temperature kelvin K amount mole mol current ampere amp intensity candela cd Seven Base Units

  4. Derived Units • Many other units are used in the metric system, but they are combinations of the base units • Volume - volume = length x width x height (m) x (m) x (m) = m3 - .001 m3 = 1 liter (L) - 1 cm3 = 1ml

  5. Prefixes • Metric system utilizes prefixes which indicate multiples of 10 of the unit • kilo- k 1000 • hecto- h 100 • deka- da 10 • deci- d .1 • centi- c .01 • milli- m .001

  6. Converting Between Metric Units 3.65 dam = __________cm 2587 mm = __________hm .0087 hl = __________cl

  7. More Prefixes Tera- T 1012 Giga- G 109 Mega- M 106 Micro- u 10-6 Nano - n 10-9 Pico- p 10-12

  8. Use the appropriate prefixes 3 x 106 L 15 x 10-9 g 8 x 108 m 3.5 x 10-6 A 1.46 x 1010 J

  9. Temperature • Metric unit – Kelvin – not used for measurement • Measured in C (celsius) • K = C + 273.15 • Old system is F (farenheit) • C = 5/9 (F -32) • What is 69 F in C and K?

  10. Temperature is an intensive property- does not depend on the amount • Extensive properties do depend on the amount • In the statement “a yellow sample is solid at 25 C. It weighs 6.0g and has a density of 2.3g/cm3” what are the intensive and extensive properties?

  11. Uncertainty • We do not know infinite digits of a measurement • Exact numbers are known for sure • Inexact – have some question (estimates)

  12. Precision and Accuracy Accuracyrefers to the agreement of a particular value with the truevalue. Precisionrefers to the degree of agreement among several measurements made in the same manner. Precise but not accurate Precise AND accurate Neither accurate nor precise

  13. Reporting Numbers • In recorded measurements, all the digits are considered exact up until the last digit which may be off by one 2.2405 ± .0001 • All digits including the uncertain one are called significant figures • We are fairly confident of these digits • Further uncertainty can be eliminated by repeating the experiment

  14. Which Digits Are Significant? • Any non-zero number is significant • Any number to the left of a decimal is significant • Zeros to the right of a decimal and behind other numbers are significant • Zeros to the right of a decimal but in front of other numbers are not significant

  15. How many Significant Figures in each below? • 28.6 9) 3440. • 910 10) 0.04604 • 0.0076000 11) 804.05 • 0.0144030 12) 1002 • 400 13) 400. • 700.0 14) 0.000625000 • 0.4004 15) 6000 • 1.30 16) 0.00067

  16. Round each to 3 Significant Figures • 31.068 6) 149.51 • 2.613 7) 6.561 • 81.436 8) 13.1252 • 0.001567 9) 143.81 • 1.1353 10) 0.000355

  17. Multiplying and Dividing • Multiply or divide the number out as normal but round the answer to the least number of significant figures in the problem

  18. Solve each with correct Sig Figs • 2.4 x 15.82 = • 94.20  3.16722 = • (5.682 x 105) x (2.87 x 104) = • (2.145 x 10-5)  (6.75 x 104) =

  19. Addition and Subtraction • Add or subtract as normal but round the answer with the same number of decimal places as the quantity in the calculation having the least

  20. Solve each with correct Sig Figs • 5.44 – 2.6103 • 2.099 + 0.05681 • 87.3 – 1.655 • 8.2 – 7.11

  21. Conversions • Often the units must be changed in order to do a problem • Conversion factor method Is utilized • A26

  22. Examples • How many inches in 3.5 km? • A chemical reaction produces 3.5 x 1025 atoms of product every hour. How many will be produced in 2.5 hours? • How many square cm in a square inch?

  23. Density • Identification tag for a substance • Every substance has a unique density

  24. The density of silver is 10.5 g/cm3. If 5.25g of silver pellets are added to a graduated cylinder containing 11.2 ml of water, to what volume will the water rise?

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