Scientific Measurement and Conversions / Dimensional Analysis

1. Scientific Measurement and Conversions / Dimensional Analysis

2. Using and Expressing Measurements • Measurement • A quantity that has both a NUMBER and a UNIT • From now on: units are metric* • Scientific Notation • Product of a coefficient and 10 raised to a power • Coefficient must be 1 ≤ # ≥ 9 • 100 = 1 • 101 = 10 • Use “EE” or “EXP” or “E” button • means “times 10 to the”

3. Accuracy, Precision, and … • Accuracy • How close a measurement comes to the actual or true value of whatever is measured • How close to the bulls-eye did your dart(s) land? • Precision • How close a series of measurements are to one another • How close together are all your darts? (regardless of proximity to bulls-eye)

4. What darts?

5. And …. Error • Error = experimental value – accepted value • Exp value = measured in lab • Accepted value = correct value based on references or math (formulas) • % error = l error l x 100 % accepted • % error = (the absolute value of experimental error – accepted value) divided by the accepted value, times 100 to make it a %

6. Significant Figures  • ALL “known” digits + 1 “estimated” digit • Known are digits clearly marked by instrument increments • Estimated is the smallest increment divided by 10 • So if ruler marks off millimeters (0.001 m) then the unknown digit will be the ten-thousandths’ place (0.0001 m)… or 0.1 mm • Sig figs can be annoying, but it is important to only record measurements to the most or least precise it can be…

7. Visual example…

8. Rules  … you’re given a measurement, are the digits sig? • NONZERO digits are significant – always! • 1998 m = 4 sig figs • EMBEDDED zeros are significant – always! • 2002 L = 4 sig figs • LEADING zeros are NEVER significant • 0.08 g = 1 sig fig • (because could be written as 8 X 10-2 g…clearly 1 sig fig) • Trailing zeros are NOT sig, UNLESS a decimal point is involved • 2010 mg = 3 sig figs, BUT 201.0 cg = 4 sig figs; • 2010. mg = 4 sig figs • although that format is frowned upon because it could and should be written as 2.010 x 103 mg (obviously 4 sig figs still)

10. Unlimited number of sig figs? Woohoo! • Counted numbers • 24 students in the classroom • 5 “digits” on my hand • Defined quantities • 60 minutes = 1 hour • 100 pennies = 1 dollar • 100 cm = 1 m

11. Rounding- you’re not in math class anymore… • If digit ≤4, truncate (drop) • 2.22 cm  2.2 cm • If digit > 5, round up • 1.68 cm  1.7 cm • If digit = 5, look at numbers after OR before • If there is a NONZERO digit AFTER a 5, round the 5 up (ex: 1.251 cm  1.3 cm) • If there is a ZERO or NO DIGIT after a 5, look at the digit BEFORE • If digit is EVEN, truncate 5 (ex: 1.250 cm  1.2 cm) • If digit is ODD, round up (ex: 1.15 cm  1.2 cm)

13. Mo Rounding!

14. Sig Figs in calculations = more rules • A calculated answer can NEVER be more precise than the least precise measurement from which it is calculated • Think “a chain is only as strong as its weakest link” • Addition & Subtraction • Keep the LEAST number of DECIMAL PLACES • 1.8 mL + 2 mL = 3.8 mL 4 mL (must round to “ones”) • Multiplication & Division • Keep the LEAST number of SIGNIFICANT FIGURES • 1.8 m X 2.71 m = 4.878 m2  4.9 m2 (must round to 2 figures) • Yes, PEMDAS is still in effect

16. Addition & Subtraction practice

18. Mult & Div practice

19. QUESTIONS??

20. Dimensional Analysis Dimensional Analysis uses MULTIPLICATION and SIMPLE CONVERSION FACTORS to move from one unit to another. Convert 2 feet to inches We need a conversion factor, a relationship between the units

21. Dimensional Analysis These both give us a relationship between in. and ft. We use D.A. to cancel units

22. Dimensional Analysis The units cancel out leaving only Giving us an answer of 24 in.

23. Dimensional Analysis Convert 48 inches to feet.

24. Dimensional Analysis Convert 5 days to hours.

25. Dimensional Analysis How many seconds are there in 4 minutes?

26. Dimensional Analysis Sometimes our conversion requires more than 1 step. Convert 1 Ms to hr.

27. Dimensional Analysis Convert 60 miles/hour to feet/second

28. Other Common Chemistry Conversions…Temperature K = C + 273 K  Kelvin – SI Base unit of temp. 0 Kelvin = Absolute Zero – point at which all motion ceases!!

29. Questions??

30. What is Density?

31. Density = Mass / Volume

32. Table 3.6 (3.7 DNE) page 90

33. Metric (goes hand-in-hand with SI: The International System of Units) • Based on powers of 10 • Common units [with prefixes if needed] • Meter (length) • Gram (mass) • Second (time) • Liter (volume) • If measuring a large item, use a larger unit • If measuring tiny item, use a smaller unit

35. “Ken Hates Dates because Dates Cost MONEY!”Strategy 1: Stair-Step Method

36. How Do I Use This? • The first letter tells you which step to start on. • The first letter tells you which step to stop on. • Count the number of steps to get to where you need to stop. • If you went downstairs the decimal moves that many places to the right

37. How Do I Use This (cont.)? • If you went upstairs the decimal moves to the left. Fill any empty places with zeros. • If there is only one letter in the unit of measurement, then you start or stop on the base unit step. Now let’s look at our examples…..

38. 525568 mm = ? m

39. .00654 km = ? m

40. Strategy 2: Conversion Factors (YOU MUST KNOW HOW TO DO IT THIS WAY!) • Used to convert the same quantity of something to a new unit • Ex: 1 mL = 1 cm3 (or 1 cc)

41. Practice Writing Conversion Factors:

43. Mo metric conversion

45. Again, again!

46. Questions??