Everyday Conversion: Money

Transcription

1

2 Everyday Conversion: Money

3 Everyday Measurement: Water

4 Everyday Measurement: Water

5 Everyday Accuracy: Weighing Scales

6 The need to measure correctly and convert!

7 Some Interesting Quantities Length Volume Mass

8 Significant Figures The number of significant figures in a measurement depends upon the measuring device C C

9 Issues Concerning Significant Figures Electronic Calculators be sure to correlate with the problem FIX function on some calculators Choice of Measuring Device graduated cylinder < buret pipet Exact Numbers numbers with no uncertainty 60 min = 1 hr 1000 mg = 1 g These have as many significant digits as the calculation requires.

10 Significant Figures Rules All digits are significant! except zeros that are used only to position the decimal point. Start at the left of the number and move right until you reach the first nonzero digit. Count that digit and every digit to it s right as significant.

11 Sample Problem PROBLEM: Number of significant figures Determine the right number of significant figures in the following numbers a) 45 b) 504 c) 5634

12 Significant Figures Rules: Zeros Zeros that end a number and lie either after or before the decimal point are significant; ml has four significant figures, and L has four significant figures also. Numbers such as 5300 L are assumed to only have 2 significant figures. A terminal decimal point is often used to clarify the situation, but scientific notation is the best!

13 Sample Problem PROBLEM: Number of significant figures Determine the right number of significant figures in the following numbers a) b) c) 5.0

14 Rounding Off Rules 1. If the digit removed is more than 5, the preceding number increases by rounds to 5.38 if three significant figures are retained and to 5.4 if two significant figures are retained. 2. If the digit removed is less than 5, the preceding number is unchanged rounds to if three significant figures are retained and to 0.24 if two significant figures are retained.

15 Rounding Off Rules 3.If the digit removed is 5, the preceding number increases by 1 if it is odd and remains unchanged if it is even rounds to 17.8, but rounds to If the 5 is followed only by zeros, rule 3 is followed; if the 5 is followed by nonzeros, rule 1 is followed: rounds to 17.6, but rounds to Be sure to carry two or more additional significant figures through a multistep calculation and round off only the final answer.

16 Sample Problem Rounding off and Reporting the Right Number of Significant Figures PROBLEM: Round off each number to the indicated number of significant figures (sf): a) (to 2 sf) b) (to 4 sf) c) (to 3 sf) Answers: a) b) c) 22.5

17 Scientific Notation Mass of Sun: 2,000,000,000,000,000,000,000,000,000,000 kg Distance to Alpha Centauri: 43,000,000,000 km Number of Stars in Milky Way Galaxy: 400,000,000,000 Age of Universe: 13,000,000,000 years Size of the atom: m

18 Scientific Notation In Scientific Notation: Mass of Sun: 2 x kg Distance to Alpha Centauri: 4.3 x km Number of Stars in Milky Way Galaxy: 4 x Age of Universe: 1.3 x years Size of the atom: 2.3 x pm

19 Scientific Notation In Scientific Notation: Mass of Sun: 2,000,000,000,000,000,000,000,000,000,000 Mass of Sun: 2 x kg

20 Scientific Notation In Scientific Notation: Size of the atom: m Size of the atom: 2.3 x pm

21 Sample Problem Scientific Notation PROBLEM: Report the following numbers in scientific notation and with the proper number of significant figures: a) m b) kg c) g/ml

22 Worksheet #1-1 Number Scientific Notation Number of Significant Figures x x x 10 3

23 Worksheet #1-1: Answers Number Scientific Notation Number of Significant Figures x x x x x x

24 Significant Figures in Calculations General Rule: The least certain measurement sets the limit on certainty for the entire calculation and determines the number of significant figures in the final answer.

25 Significant Figures in Calculations Addition and Subtraction The answer has the same number of decimal places as there are in the measurement with the fewest decimal place. Example: ml of water from the graduated cylinder ml of water from the beaker ml ml ml Answer: 93.4 ml (reported answer!)

26 Significant Figures in Calculations Multiplication and Division The answer contains the same number of significant figures as in the measurement with the fewest significant figures. Ex. Volume of a wooden block: length = 9.2 cm Volume = (l) (w) (t) width = 7.30 cm = cm 3 thickness = 2.56 cm = 170 cm 3 (reported answer!)

27 Sample Problem Significant Figures and Rounding PROBLEM: Perform the following calculations and round the answer to the correct number of significant figures. 1) ) ) [78.2 x32]/22.5 4) 98.6/[87.2 x 25.97] 5) [ ]/7.09 Answers: 1) 9.1 2) 80 3) 110 4) ) /7.09 = 2.10

28 Worksheet # 1-2 Perform the following operations and express the answer in the correct number of significant figures. 1) = 2) = 3) x 3.2 x = 4) (4.5 x 6.78)/12.3 = 5) ( ) x 8.23 =

29 Worksheet # 1-2: Answers Perform the following operations and express the answer in the correct number of significant figures. 1) = ) = 41 3) x 3.2 x = 6.7 4) (4.5 x 6.78)/12.3 =2.5 5) ( ) x 8.23 = 81

30 Unit Conversion Mass kilograms, grams, pounds, etc. Volume liter, milliter, gallon, tablespoon, etc. Temperature o C, o F, K Time second, minutes, day, year, lightyear, etc.

31 SI Base Units Physical Quantity (Dimension) mass length Unit Name kilogram meter Unit Abbreviation kg m time second s temperature kelvin K electric current ampere A amount of substance mole mol luminous intensity candela cd

32 Common Decimal Prefixes Used with SI Units Prefix Prefix Symbol Word Conventional Notation Exponential Notation tera T trillion 1,000,000,000,000 1x10 12 giga G billion 1,000,000,000 1x10 9 mega M million 1,000,000 1x10 6 kilo k thousand 1,000 1x10 3 hecto h hundred 100 1x10 2 deka da ten 10 1x one 1 1x10 0 deci d tenth 0.1 1x10-1 centi c hundredth x10-2 milli m thousandth x10-3 micro millionth x10-6 nano n billionth x10-9 pico p trillionth x10-12 femto f quadrillionth x10-15

33 SI English Unit Conversion

34 Dimensional Analysis Conversion: Within the same system, English Metric General Formula: = final unit Conversion Factor

35 Example: Same System km to m? km to cm? Conversion Factor Conversion Factor Conversion Factor

36 Example: English - Metric km to inch? Conversion Factor Conversion Factor Conversion Factor

37 Sample Problem Converting Units of Length, Volume and Mass PROBLEM: Convert the following units: a) 1.5 km to in and mm b) 2.75 m 3 to liter c) 3.45 kg to pounds and Mg Answers: a) 5.91 x 10 4 in, mm b) 2750 L c) 7.61 lb, Mg

38 Sample Problem Converting Units and Reporting Numbers PROBLEM: Convert the following units and report the result in scientific notation with the right number of significant figures: a) kilometers to centimeter b) 6.3 x 10 5 liters to milliliters c) 2.50 nanograms to kilograms Answers: a) x 10 5 cm b) 6.3 x 10 8 ml c) 2.50 x kg

39 Worksheet # 1-3 Solve the following problems. Write the answers in proper number of significant figures. 1) mg = cg 2) 7.5 x 10 3 ml = liters 3) 3.45 km = mm 4) MHz = mhz 5) 5.5 kg = lbs 6) yards = m

40 Worksheet # 1-3: Answers Solve the following problems. Write the answers in proper number of significant figures. 1) mg = 3.5 x 10-3 cg 2) 7.5 x 10 3 ml = 7.5 liters 3) 3.45 km = 3.45 x 10 6 mm 4) MHz = x 10 9 mhz 5) 5.5 kg = 12 lbs 6) yards = m

41 The freezing and boiling points of water.

42 The freezing and boiling points of water.

43 Temperature Scales and Inter-conversions Kelvin ( K ) - The Absolute temperature scale begins at absolute zero and only has positive values. Celsius ( o C ) - The temperature scale used by science, formally called centigrade, most commonly used scale around the world; water freezes at 0 o C, and boils at 100 o C. Fahrenheit ( o F ) - Commonly used scale in the U.S. for our weather reports; water freezes at 32 o F and boils at 212 o F.

44 Temperature Scales and Inter-conversions T (in K) = T (in o C) T (in o C) = T (in K) T (in o F) = 9/5 T (in o C) + 32 T (in o C) = [ T (in o F) - 32 ] 5/9

45 Sample Problem PROBLEM: Converting Units of Temperature Perform the following conversions: a) 72 F (a pleasant spring day) to C and K. b) -164 C to K and F. c) 0 K (absolute zero) to C and F. Answers: a) 22 C, 295 K b) 109 K, F c) C, F

46 Some interesting temperatures.

47 Worksheet # 1-4 Celcius Kelvin Fahrenheit 145 C 359 K 98.6 F K C

48 Worksheet # 1-4: Answers Celcius Kelvin Fahrenheit 145 C 418 C 293 F K 187 F 37.0 C 310 K 98.6 F 21.5 C K 70.6F C 263 K 13.1 F

49 Precision and Accuracy Precision - Refers to reproducibility or how close the measurements are to each other. Accuracy - Refers to how close a measurement is to the real value.

50 Precision and Accuracy

51 Precision and accuracy in the laboratory precise and accurate precise but not accurate