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Math and Measurement

Math and Measurement. Unit 2. 10 mL Graduate. What is the volume of liquid in the graduate?. _ . _ _ mL. 6. 6. 2. Self Test. Examine the meniscus below and determine the volume of liquid contained in the graduated cylinder. The cylinder contains:. 7. 6. 0. _ _ . _ mL.

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Math and Measurement

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  1. Math and Measurement Unit 2

  2. 10 mL Graduate What is the volume of liquid in the graduate? _ . _ _ mL 6 6 2

  3. Self Test Examine the meniscus below and determine the volume of liquid contained in the graduated cylinder. The cylinder contains: 7 6 0 _ _ . _ mL

  4. Reading the Thermometer Determine the readings as shown below on Celsius thermometers: 8 7 4 3 5 0 _ _ . _ C _ _ . _ C

  5. Numbers…which ones are important? What is 13/7? Is it 1.8571428? Or…is it 1.86? Or 1.9? Or 2? Where do we round?

  6. Significant Digits

  7. Rules for Counting Significant Figures - Details • Exact numbershave an infinite number of significant figures. • How many beakers are on the shelf? • Exactly 5.

  8. Rules for Counting Significant Figures - Details • Nonzero integersalways count as significant figures. • 3456has • 4sig figs.

  9. Rules for Counting Significant Figures - Details • Zeros • -Leading zeros do not count as • significant figures. • 0.0486 has • 3 sig figs.

  10. Rules for Counting Significant Figures - Details • Zeros • -Captive zerosalways count as • significant figures. • 16.07has • 4 sig figs.

  11. Rules for Counting Significant Figures - Details • Zeros • Trailing zerosare significant only if the number contains a decimal point. • 9.300 has • 4 sig figs.

  12. Sig Fig Practice #1 How many significant figures in each of the following? 1.0070 m  5 sig figs 17.10 kg  4 sig figs 100,890 L  5 sig figs 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000  2 sig figs

  13. Rules for Significant Figures in Mathematical Operations • Multiplication and Division:# sig figs in the result equals the number in the least precise measurement used in the calculation. • 6.38 x 2.0 = • 12.76 13 (2 sig figs)

  14. Sig Fig Practice #2 Calculation Calculator says: Answer 22.68 m2 3.24 m x 7.0 m 23 m2 100.0 g ÷ 23.7 cm3 4.22 g/cm3 4.219409283 g/cm3 0.02 cm x 2.371 cm 0.05 cm2 0.04742 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 5870 lb·ft 1818.2 lb x 3.23 ft 5872.786 lb·ft 0.3588850174 g/mL 0.359 g/mL 1.030 g ÷ 2.87 mL

  15. Rules for Significant Figures in Mathematical Operations • Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. • 6.8 + 11.934 = • 18.734  18.7 (3 sig figs)

  16. Sig Fig Practice #3 Calculation Calculator says: Answer 10.24 m 3.24 m + 7.0 m 10.2 m 100.0 g - 23.73 g 76.3 g 76.27 g 0.02 cm + 2.371 cm 2.39 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1821.6 lb 1818.2 lb + 3.37 lb 1821.57 lb 0.160 mL 0.16 mL 2.030 mL - 1.870 mL

  17. Practice Question Questions 1-2 refer to the following sets of numbers. • 1.023 g • 0.0030 mL • 40,500 m • Is a number containing three significant figures • Is a measure of mass

  18. Scientific Notation In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we deal with some very SMALL numbers: Mass of an electron = 0.000000000000000000000000000000091 kg

  19. Imagine the difficulty of calculating the mass of 1 mole of electrons! 0.000000000000000000000000000000091 kg x 602000000000000000000000 ???????????????????????????????????

  20. Scientific Notation: A method of representing very large or very small numbers in the form: M x 10n • M is a number between 1 and 10 • n is an integer

  21. . 2 500 000 000 9 7 6 5 4 3 2 1 8 Step #1: Insert an understood decimal point Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

  22. 2.5 x 109 The exponent is the number of places we moved the decimal.

  23. 0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

  24. 5.79 x 10-5 The exponent is negative because the number we started with was less than 1. If the number is larger than 1, the exponent is positive. If the number is smaller than 1, the exponent is negative

  25. Pause for a Cause Scientific Notation #1. Write the following numbers in scientific notation: a. 0.000 673 0 b. 50 000.0 c. 0.000 003 010 #2. The following numbers are in scientific notation. Write them in ordinary notation. a. 7.050 X 103 g b. 4.000 05 X 107 mg c. 2.350 0 X 104 mL

  26. Multiplying and Dividing in Scientific Notation 1. Multiply or divide the “M” values 2. If multiplying, add the exponents 3. If dividing, subtract the exponents. 4. If necessary, adjust to put back in scientific notation. Example #1 (1.35 x 104) x (2.35 x 105) Example #2 (2.6 x 108) / (4.6 x 103)

  27. You try 1. (6.00 X 106) x (4.0 X 10-3) 2. (3.2 x 104) x (4.5 x 105) 3. ( 4.5 x 10-5) / (9 x 10-3)

  28. Nature of Measurement Measurement – quantitative observation consisting of 2 parts Part 1 – number Part 2 – unit Examples: 20grams 6.63 x 10-34Joule seconds

  29. Accurate or Precise? Accurate measurements are close to the actual or accepted value. Precise measurements are close to one another. More than one measurement must be taken to determine if the measurements are precise.

  30. Pause for a Cause Accuracy and Precision • A handbook gives the density of calcium as 1.54 g/cm3. A student runs three experiments and determines the density to be 2.25 g/cm3, 2.28 g/cm3 and 2.20 g/cm3. Discuss this student’s accuracy and precision. • A student measures the mass of a sample as 9.67 grams, 9.99 grams and 8.85 grams. The actual mass is 7.50 grams. Discuss this student’s accuracy and precision.

  31. The Fundamental SI Units(le Système International, SI)

  32. SI Prefixes Common to Chemistry

  33. Now Let’s Do Metrics the Right Way!

  34. Practice Conversion Factors Express a mass of 5.712 grams in milligrams. 5.712 g Given: Unknown: mass in mg quantity given × conversion factor = quantity sought Conversion Factor 1 g = 1,000 mg 1000 mg 5.712 g = 5712 mg 1 g

  35. Practice Conversion Factors Express a mass of 5.712 grams in kilograms. quantity given × conversion factor = quantity sought 5.712 g 1 kg = 0.005712 kg 1000 g

  36. Let’s do the following metric conversions using unit cancellation. • 2500 grams = ___ kilograms • 5600 centimeters = ____ meters • 500 liters = ____ milliliters • 75000 milligrams = ____ kilograms • 25 meters = ____ decimeters • 4.5 kilograms = ____ grams • 45 decimeters = ____ centigrams

  37. Pause for a Cause 2 Now Its your turn! 1. 1500 centigrams = ___ grams 2. 6.00 milliliters = ____ liters 3. 700 meters = ____ kilometers 4. 750 milligrams = ____ centigrams 5. 250 meters = ____ decimeters 6. 0.25 kilograms = ____ grams 7. 0.75 decimeters = ____ millimeters 8. 47 grams = ____ centigrams 9. 2.5 meters = ____ millimeters 10. 500 deciliters = ____ liters 11. 250 kilograms = ____ grams 12. 3500 centigrams = ____ kilograms

  38. Which is more dense? Select the object that you think has the highest density and write one sentence explaining your answer. Styrofoam cup Gatorade Rock

  39. Derived SI Units • Produced by multiplying or dividing standard units. For Example: 5 m Width Area = (Length)(Width) Length 2.5 m Area = (2.5 m)(5 m) = 12.5 m2

  40. What does density describe? Density describes how tightly particles are packed within a sample of matter.

  41. Density The ratio of mass to volume, or mass divided by volume. mass m Density = D = volume V

  42. Density • A measure of how closely matter is packed into a volume. • Unique for each compound. • Density of water is 1.00 g/mL at 25˚C. • Increasing temperature decreases the density, so densities are given with temperatures. • An intensive property. • Substances that are less dense float in substances more dense.

  43. Density Problems A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the density of aluminum. 8.4 g 8.4 g Don’t forget units! Given: m = D = V = 3.1 cm3 3.1 cm3 Unknown: D = ? Equation: Box answer! D = 2.7 g/cm3 m D = v Don’t forget units!!!

  44. You try! An unknown liquid is discovered at a crime scene. A volume of 2.3 mL has a mass of 4.1 grams, what the liquid’s density?

  45. Density Problems Diamond has a density of 3.26 g/cm3. What is the mass of a diamond that has a volume of 0.350 cm3?

  46. Density Problems A sample of metal is found to have a mass of 4.56 g and a density of 1.98 g/mL. What is the volume of this metal?

  47. Density Problem (No calculator) The typical battery in a car is filled with a solution of sulfuric acid, which is approximately 39.9% sulfuric acid. If the density of this solution is 1.3 g/mL, determine the number of grams of acid present in 500.0 mL of battery solution.

  48. What is the volume of 5 grams of this substance? • What is the approximate density of the substance?

  49. Converting Temperatures C = 5/9 (F-32) F = K = C + 273 C =

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