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Unit 1 Part 2: Measurement

Unit 1 Part 2: Measurement. Mr. Gates Chemistry. Measurement. Measurement is a quantitative description of both a number and a unit. Ex. 6 feet and 2 inches. Standards. There needs to be standards in order for units to work. The King’s foot. Accuracy vs. Precision.

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Unit 1 Part 2: Measurement

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  1. Unit 1 Part 2:Measurement Mr. Gates Chemistry

  2. Measurement • Measurement is a quantitative description of both a number and a unit. • Ex. 6 feet and 2 inches

  3. Standards • There needs to be standards in order for units to work. • The King’s foot.

  4. Accuracy vs. Precision • Accuracy describes how close a measurement is to the accepted value • Precision describes how close a measurement is to other measurements taken.

  5. Significant Figures All numbers in a measurement that can be known precisely plus one additional number that is estimated. Digits in a measurement that indicate the precision of an instrument used to take a measurement.

  6. Examples (going for a walk) • 3 miles (3 estimated) • 1.9 miles (9 estimated) • 1.918 miles (8 estimated) • 1.91 miles (1 estimated)

  7. Which Figures are Significant? • All nonzero digits are significant • Ex. 5.3 has two significant figures • Zeroes appearing in front (to the left) of a nonzero digit are NOT significant • Ex. 0.0275 has three significant figures • Zeroes appearing in between two nonzero digits are ALWAYS significant • Ex. 2.054 has four significant figures • Zeroes appearing to the right of a nonzero number and after the decimal place are significant. • Ex. 32.810 has five significant figures • Zeroes to the right of nonzero digits and to the left of a decimal place are ambiguous. • Ex. 300 has ?? … it depends

  8. Ambiguous Numbers??? • 200 miles • 200 miles • 200.0 miles • 200. miles

  9. Practice • How many significant figures are in the following numbers? • .0891 • 109.3 • 6.0 • 0.0005 • 1.089 • 7.0020 • .08340

  10. Rules for Rounding • If the number to the right of the last significant figure is from 0-4, round down. • If the number to the right of the last significant figure is from 5-9, round up. • Examples: 26.819 • rounded to three significant figures is 26.8 • Rounded to four significant figures is 26.82 • Practice: 0.01037 • Rounded to three significant figures? • Rounded to two significant figures?

  11. Practice • Round the number 34.1050 to: • 2 sig figs • 34 • 5 sig figs • 34.105 • 4 sig figs • 34.11 • 3 sig figs • 34.1 • Round the number 0.0539801 to: • 2 sig figs • 0.054 • 5 sig figs • 0.053980 • 4 sig figs • 0.05398 • 3 sig figs • 0.0540

  12. Exceptions that Make the Rule • There is an UNLIMITED amount of sig figs in two circumstances. • Counted numbers • 23 students in class (can’t have a fraction of a person) • Exact/defined quantities • 12 inches in a foot • Like 12.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000… (catching my breath)…000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000…. To infinity and beyond zeroes

  13. Sig Figs w/ Calculations Addition or Subtraction The answer can have no more decimal places than the number with the least decimal places in the calculation. Ex. 4.56-1.2= 3.36, but with proper sig figs the answer is… =3.4 Ex. 9.64+1.751= 11.391, but with proper sig figs the answer is… = 11.39

  14. Sig Figs w/ Calculations • Multiplication and Division • The answer can have no more sig figs than the number with the least amount of sig figs in the calculation. Ex. 1.24 x 2.6 = 3.224, but with proper sig figs the answer is... = 3.2 Ex. 5.11 x 6.551 = 33.47561, but with proper sig figs the answer is… = 33.5

  15. Scientific Notation • Scientific notation is a number written as the product of two numbers. • Follows the following format: M x 10N • M is some number between 1 and 10 • N is the amount of times the decimal places had to be moved. • N ≠ decimals

  16. Putting #’s in Sci. Notation • Every time the decimal place is moved the exponent must move too. M x 10N If the decimal moves  then the exponent goes down If the decimal moves  then the exponent goes up

  17. In and Out Put into scientific notation: 0.0000361 9,840,000,000 Take out of scientific notation: 3.65 x 107 2.49 x 10-4

  18. Sig Figs and Sci. Notation • All of the numbers in proper scientific notation are significant… No ambiguous numbers!!! 2000 is 2.00 x 103 with three sig figs.

  19. Addition/Subtraction in Sci. Notation • Adding and Subtracting: • Exponents must be the same!!! • EX: 5.1 x 105 + 6.07 x 105 11.17 x 105 (not correct sig figs) 11.2 x 105 (not correct sci not.) 1.12 x 106

  20. Multiplying/Dividing in Sci. Notation • Multiplying and Dividing: • EX: 7.2 x 102 x 4.2 x 103 30.24 x 105 (not correct sig figs) 30. x 105 (not correct sci. not.) 3.0 x 106

  21. International System of Measurement • Internationally used system of measurement known as the “Metric System”

  22. Benefits of Using the Metric System • Scientist all over the world use this system. • They can share and understand each other’s work. • Based on multiples of ten. Makes for easier conversions.

  23. SI Base units

  24. Volume • The amount of space an object takes up. • Base unit is cm3

  25. Mass • The amount of matter in an object. • Base unit is the kg because the gram is too small.

  26. Weight • The pull gravity has on the mass of an object.

  27. Fluid Volume • When dealing with a fluid (gas or liquid) the most commonly used unit is the liter (L) • 1ml = 1cm3

  28. SI Prefixes

  29. Dimensional Analysis • Method of converting from one unit to another of equal value using conversion factors.

  30. Conversion Factors • These are fractions that are equal to one because the top is equal to the bottom despite the differing units. • Multiplying anything by one will not change the number. • Conversion factors spawn from two numbers that are equal to each other. • Ex. 100cm = 1m • or

  31. Using Dimensional Analysis • How many mg are in 1.32kg? • How many seconds are in your lifetime? • How many cases of pop will you drink in your lifetime?

  32. Converting Complex Units • What is 19 in2 in ft2?

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