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Unit Two

Unit Two. Math and Measurement. Introduction: The Metric System. The Metric System. In 1960, the scientific community adopted a subset of the metric system to use as the standard scientific system of measurement units. (SI= Systeme International) Features seven base units

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Unit Two

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  1. Unit Two Math and Measurement

  2. Introduction: The Metric System

  3. The Metric System • In 1960, the scientific community adopted a subset of the metric system to use as the standard scientific system of measurement units. (SI= Systeme International) • Features seven base units • Only five of these are used extensively in chemistry

  4. The Metric System • Any SI unit can be modified with prefixes to match the scale of the object being measured. • Would you use millimeters to measure a persons height?

  5. The Metric System • The metric system is based on the powers of 10 • Basic Units • Length – Meters (m) • Distance traveled by light in a during a time interval of second. • Mass – kilogram (kg) • Basic unit is the gram (g) • platinum-iridium chunk is kept in France

  6. The Metric System • Time - seconds (s) • The “duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom”. • Volume - liters (L) • 1000 cm3

  7. The Metric System • How do we measure temperature? • Using Kelvins (K) • Notice there is no degree sign () • The Celsius scale designates 0 as the freezing point of water. • Absolute zero, or 0 K, is the coldest temperature theoretically possible.

  8. The Metric System • The equation we use to convert between the Celsius and Kelvin scales is: • C + 273.16 =K or K- 273.16 = C • For Example: • What is 37C in K? • 310K (normal body temperature) • What is 373 K in C? • 100C (boiling point of water)

  9. Using the scientific measurements • Measurement = the comparison of a physical quantity to a known standard. • Scientists measure things as precisely as possible without misrepresenting what their instrument can do. • Tolerance = the smallest division on an instrument that can be represented as a power of 10.

  10. How good is your measurement? • Accuracy = how close you are to the accepted value. • This will be determined by calculating percent error. • Precision = how close measurements are to each other.

  11. How good is your measurement?

  12. How good is your measurement?

  13. Metric Conversions

  14. Derived Units & Conversions Move decimal to the LEFT. Divide by 10. Your “number” will decrease. Move decimal to the RIGHT. Multiply by 10. Your “number” will increase.

  15. What do derived units look like? *Common derived units. (We’ll use these the most!)

  16. Remember: The base unit can be grams (g), liters (L), or meters (m)! Kilo- Hecto- Deka- BASE UNIT deci- centi- milli-

  17. 1 2 3 MetersLitersGrams Starting Point Ending Point __. __. __. 2 3 1 KILO1000 HECTO100 DEKA10 deci- 0.1 centi-0.01 milli-0.001 4 Km= _______ m 4. = 4000 m

  18. Metric Conversions Find the spot (unit) on the ladder that has the same prefix as the measurement you are starting with. Locate the spot on the “ladder” that you want to convert your number to. Count the number of “steps” you move on the ladder to make your conversion Move the decimal in your original number this same number of steps and in the same direction.

  19. Metric Conversions LETS PRACTICE! 2000 mg = _____ g 104 km = ______ m 480 cm = ______m 5.6 kg = ______ g 8 mm = ______cm 5 L = ______ mL 120 mg = ______kg 6.3 mL = _______L 50 cm = _______m 2500 m = _______cm

  20. Metric Conversions LETS PRACTICE! 2000 mg = 2.0 g 104 km = 104000.0 m 480 cm = 4.8 m 5.6 kg = 5600 g 8 mm = .8 cm 5 L = 5000 mL 120 mg = .000120 kg 6.3 mL =.0063 L 50 cm = .50 m 2500 m = 250000 cm

  21. Metric Conversions Factor Label Method: • The fundamental principle at work here is “cancellation of units”.

  22. Metric Conversions Factor Label Method: • 5cm  m

  23. Metric Conversions Factor Label Method: • 1. If an axle spins at 12 revolutions per second, how many revolutions per minute does it spin? • 2. If an axle spins at 58 revolutions per minute, how many revolutions per second does it spin?

  24. Metric Conversions Factor Label Method: • 1. If an axle spins at 12 revolutions per second, how many revolutions per minute does it spin? • 720 Revolutions per minute • 2. If an axle spins at 58 revolutions per minute, how many revolutions per second does it spin? • 0.97 revolutions per second

  25. Tolerance of Equipment

  26. Tolerance of Equipment What is tolerance? • the smallest division on an instrument that can be represented as a power of 10.

  27. Significant Figures If a measurement is reported with either too many or too few digits, it is not possible to tell how precise the measurement really is. Significant figures are those digits in a measurement that have actually been measured by comparison with a scale, plus one estimated digit.

  28. Significant Figures By comparing the length of the pen to the scale on the ruler; you can see that the pen is more than 4.72cm long, but less than 4.8cm. To report this measurement in sig figs you would write 4.7 (which are the numbers actually measured), then you would estimate the final number as 2 or 3 So your final measurement would be 4.72 or 4.73 cm

  29. Determining Significant Figures “Rule 4: zeros at the end of a number without a decimal point are not significant” (This rule depends on the piece of equipment you are using to measure)

  30. Determining Significant Figures

  31. Practice Determine the number of significant figures in the following numbers: 0.02 0.020 501 501.0 5,000 6) 5,000. 7) 6,051.00 8) 0.0005 9) 0.1020 10) 10,001 Determine the location of the last significant place value by placing a bar over the digit. (EX: 1.700) 8040 0.0300 699.5 0.90100 5) 90,100 6) 10,800,000 7) 0.000410

  32. Practice Determine the number of significant figures in the following numbers: 0.02 = 1 (leading 0’s don’t count) 0.020 = 2 (all 0’s following a digit to the right of a decimal are significant) 501= 3 501.0 = 4 (if there are digits before the decimal all 0’s to the right of a decimal are sig figs) 5,000 = 1 (no decimal point, zeros are not sig figs) 6) 5,000. = 4 (0’ are sandwiched between a digit and a decimal) 7) 6,051.00 = 6 (all 0’s following a digit to the right of a decimal are significant) 8) 0.0005 = 1 (leading 0’s don’t count) 9) 0.1020 = 4 (all 0’s following a digit to the right of a decimal are significant) 10) 10,001 = 5 (all sandwiched 0’s count)

  33. Practice Determine the location of the last significant place value by placing a bar over the digit. (EX: 1.700) 1) 8040 2) 0.0300 3) 699.5 4) 0.90100 5) 90,100 6) 10,800,000 7) 0.000410

  34. Calculations with Sig Figs • Addition and Subtraction: • Your result should have the same number of DECIMAL PLACES as the quantity with the least number of decimal places. • Multiplication and Division: • Your result should have the same number of SIG FIGS as the quantity with the least sig figs. • When cutting off numbers to reduce sig figs, make sure to follow proper rounding rules!

  35. Calculations with Sig Figs Multiplication and Division: 23.0 cm x 432 cm x 19 cm = 188,784 cm3 Multiply numbers Count sig figs Round answer to have correct sig figs The answer is expressed as 190,000 cm3 since 19 cm has only two sig figs. 3 sig figs 3 sig figs 2 sig figs

  36. Calculations with Sig Figs Addition and Subtraction: 123.25 mL + 46.0 mL + 86.257 mL = 255.507 mL Add numbers Count decimal places Move decimal in answer The answer is expressed as 255.5 mL since 46.0 mL only has one decimal place. 2 3 1

  37. Practice 465.89+9.6+.001= 1000-54.78-7.6484= 5.4+8.99-.7896= 15.4 x 6.553 = 2000 x 4.89/.25 = 0.0207 x .100001 x 1.210 =

  38. Practice 465.89+9.6+.001= 475.5 1000-54.78-7.6484= 938 5.4+8.99-.7896= 15.2 15.4 x 6.553 = 101 2000 x 4.89/.25 = 40 0.0207 x 1.00001 x 1.210 = 0.0251

  39. Scientific Notation • Scientific notation is the way that scientists easily handle very large or very small numbers. • For example, instead of writing 0.0000000056, we write • The exponent of 10 is the number of places the decimal point must be shifted to give the number in long form. • A positive exponent shows that the decimal point is shifted that number of places to the right • A negative exponent shows that the decimal point is shifted that number of places to the left.

  40. Scientific Notation • 0.00000000001 = When moving the decimal to the left, your exponent will be positive. When moving the decimal to the right, your exponent will be negative. Don’t mix up your negative and positive exponents! Remember, in scientific notation, -11 would mean to move the decimal point to the left 11 place; however, when trying to turn a number into scientific notation moving the decimal to the right will result in a -11 exponent!

  41. Scientific Notation • Here are a few examples: • = 602,000,000,000,000,000,000,000 • = 482 • = 0.053 • =0.0078 • = 0.00044

  42. Scientific Notation • Scientific notation will make determining significant figures easier: • Focus on the number, not the exponent. 46600000 = 4.66 x 107 3 Sig Figs 0.00053 = 5.3 x 10-4 2 Sig Figs

  43. Scientific Notation Lets Practice! • Write the following terms in scientific notation! • 12,000,000 • .00230 • .000006 • 1,275 • 150.00

  44. Scientific Notation • How do you enter numbers into your calculator in scientific notation? • Using the EE button • Using the SCI function • Solving equations with your calculator

  45. Math Mania! • Randomly choose partners! • As a pair you will be competing with the other pairs in the classroom to answer all of the questions correctly in the shortest amount of time! • You will need two sheets of paper (one for you and one for your partner). • I will hand you an envelop with questions written on it, you will need to write the question down, show your work, and circle your answer. • When you think you have all the problems answered correctly come check them with me. • If you get them all correct, I will hand you the next envelope. • The team to work through all envelopes in the fastest amount of time wins!

  46. Math Mania! • YOU MUST: • Write the question. • Show all of your work • Circle your answer • ALL NOTES SHOULD BE PUT AWAY! • Everyone who finishes will earn 2 extra credit points! • The team to finish first will earn 4 extra credit points!

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