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Problem Solving Ch. 2

Problem Solving Ch. 2. Take out materials for notes – believe me, you’ll want to take them. Sig Figs!. Significant figures = important numbers 0.01 vs. 0.010 vs. 0.0100 Which number is more precise? Deals with measured or computed values (as opposed to exact values like 2 eyes, 12 eggs).

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Problem Solving Ch. 2

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  1. Problem SolvingCh. 2 Take out materials for notes – believe me, you’ll want to take them

  2. Sig Figs! • Significant figures = important numbers • 0.01 vs. 0.010 vs. 0.0100 Which number is more precise? • Deals with measured or computed values (as opposed to exact values like 2 eyes, 12 eggs)

  3. Remember the measurement lab? • To what place can we record measurements on this graduated cylinder? • It is given to the ones place, so we estimate to the tenths place • Sig figs explain why 50 mL is not the same as 50.0 mL

  4. Rules RULE 1: All nonzero digits are significant: RULE 2: Zeroes between nonzero digits are significant. RULE 3: Leading zeros to the LEFT of the first nonzero digits are NOT significant; such zeroes merely indicate the position of the decimal point. RULE 4: Trailing zeroes that are also to the RIGHT of a decimal point in a number ARE significant. RULE 5: When a number ends in zeroes that are not to the right of a decimal point, the zeroes are NOT necessarily significant

  5. See if you can figure out when numbers are significant… • Based on these • Can you guess how many are in the following #s? • 4301 • 1.05 • 0.568 • 0.00798 • 12000 • 515 3 sig figs • 5050 3 sig figs • 0.5050 4 sig figs • 0.05050 4 sig figs • 5000 1 sig fig • 0.0500 3 sig figs • 505.0 4 sig figs

  6. Or, you can try it this way… • Figure out which side of the number to start from (Absent or Present) • Start counting at your first non-zero number • KEEP COUNTING!!!

  7. Rounding • If digit next to last significant figure is: 0-4 don’t round 5-9, then round up 12488 (3 sig figs) 0.008209 (2 sig figs) 2.77549 (4 sig figs) 0.352 (1 sig fig) Make sure your new rounded number is close to your original number!!!!

  8. Calculating with sig figs • Adding/subtracting – line up the numbers, add ‘em up, and cut off at the shortest tail (round if necessary) 3.31 + 12.565 + 25.0915 147.3 + 29.12 + 0.115 178.1 – 92.67 1505.22 – 500

  9. Multiplication/Division • Count number of sig figs in each of your numbers – the lowest number of sig figs is the number of sig figs that will be in your answer 32.7 x 2.5 19.9 x 100 135.5  5.7 281  9.341

  10. Let’s practice… 3.461728 + 14.91 + 0.980001 + 5.2631 0.04216 - 0.0004134 2.3 x 3.45 x 7.42 =   208 / 9.0 =   

  11. WARM-UP Calculate, using sig figs 0.00783 + 0.022 + 1.057 225.112 ÷ 14.78

  12. Record your answer using the correct number of significant figures and proper units. a. 7.55 m x 0.34 m _____ b. 2.10 m x 0.700m ____ c. 2.4526 m / 8.4 sec _____ d. 0.365 m / 0.0200 hr _____ e. 8432 m / 12.5 hr _____ f. 7 m x 1.22 m ____

  13. What’s the point? A student once needed a cube of metal that had to have a mass of 83 grams. He knew the density of this metal was 8.67 g/mL, which told him the cube's volume. Believing significant figures were invented just to make life difficult for chemistry students and had no practical use in the real world, he calculated the volume of the cube as 9.573 mL. He thus determined that the edge of the cube had to be 2.097 cm. He took his plans to the machine shop where his friend had the same type of work done the previous year. The shop foreman said, "Yes, we can make this according to your specifications - but it will be expensive." "That's OK," replied the student. "It's important." He knew his friend has paid $35, and he had been given $50 out of the school's research budget to get the job done.

  14. He returned the next day, expecting the job to be done. "Sorry," said the foreman. "We're still working on it. Try next week." Finally the day came, and our friend got his cube. It looked very, very smooth and shiny and beautiful in its velvet case. Seeing it, our hero had a premonition of disaster and became a bit nervous. But he summoned up enough courage to ask for the bill. "$500, and cheap at the price. We had a terrific job getting it right -- had to make three before we got one right." "But--but--my friend paid only $35 for the same thing!" "No. He wanted a cube 2.1 cm on an edge, and your specifications called for 2.097. We had yours roughed out to 2.1 that very afternoon, but it was the precision grinding and lapping to get it down to 2.097 which took so long and cost the big money. The first one we made was 2.089 on one edge when we got finished, so we had to scrap it. The second was closer, but still not what you specified. That's why the three tries." Oh!"

  15. There are 4 graduated cylinders and 4 triple beams (with objects) around the room… You’ll be going to each graduated cylinder and triple beam Record the number graduated cylinder and its volume (be sure to estimate an extra place) Record the letter of the triple beam, and find the mass of the object (be sure to estimate an extra place)

  16. Perform the following operations with the data you just found… Be sure to use sig figs in your answers! 2 + A - 1 = B ÷ 3 = 4 x D ÷ C =

  17. You need a non-graphing calculator for today…. If you don’t have one, I have ones in the box at the front – just sign one out Warm up: Calculate, using sig figs 25.978 + 5.901 + 139.8 250 ÷ 9.25

  18. Review • Write the following numbers in scientific notation: 840,000 3500 0.0000785 0.008812

  19. Multiplying/Dividing • Perform function with base numbers Multiplying = add exponents Dividing = subtract exponents Putting answer in correct scientific notation: decimal Left = exponent Larger decimal Right = exponent Reduced

  20. Estimate your answer before using a calculator Now let’s learn about the EE button! (2.0 x 10 -1) x (8.5 x 105) (4.42 x 10-3) x (4 x 10-2) (9.4 x 10 2)  (1.24 x 10-5) (9.2 x 10-3)  (6.3 x 106)     

  21. Adding/Subtracting Calculate, using the EE button (2.5 x 102 ) + (5.2 x 104 ) (4.1 x 103) + (3.25 x 102) (9.86 x 104) - (1.2 x 102) How many sig figs should be in each answer?

  22. Answers Multiplication/Division 8) 2.6 x106 9) -1.31 x 1014 10) 3.74 x 10-9 11) -2.1 x 1016 12)-8.9 x 1020 13) 4.3 x 1016 14) 1.4 x 1045 Addition/Subtraction i) 4.01 x 10-9 j) 9.4 x 1010 k) -2.8 x 107 l) 4.62 x 10-1 m) 2.5 x 106 n) 6.6 x 1018

  23. Warm up Calculate, with correct number of sig figs: 8.56 x 0.030 x 12.15 (198.1 – 7.82) / 2.5

  24. Precision and Accuracy

  25. Accuracy= measurements are close to the given, accepted value • Precision = getting the same measurement each time; also pertains to the number of places you use in a measurement 9.52 cm is more precise than 9.5 cm • If I said I was 6 feet, 5 inches, 2.38 cm tall, I would be ________________ but not _________________.

  26. Percent Error- how wrong were you? • A way to report how far off your values were from the accepted value • The closer you are to 0%, the better your results |measured - accepted| x 100 accepted

  27. Examples • A student measures the volume of a 2.50 liter container to be 2.38 liters. What is the percent error in the student's measurement? • Don’t forget about sig figs! • 4.8% error

  28. Precision and Accuracy activity Carefully read and follow the instructions Percent error calculations – use absolute value | 5.00 – measure | x 100 5.00

  29. Turn in Accuracy and Precision activity and try warm up… The melting point of a chemical is 53.0oC. In a lab, two students try to verify this value. The first student records 51.5oC, 53.5oC, 55.0oC and 54.2oC. The second student records 52.3oC, 53.2oC, 54.0oC and 52.5oC. 1. Calculate the average value for each student 2. Calculate the % error for each average 3. Which student is most precise? Most accurate? How do you know?

  30. Temperature conversions Celsius or Kelvin 0 Co = 273 K Guess how you 10 Co = 283 K 100 Co = 373 K solve for Kelvin Fahrenheit to Celsius is a little harder Fo = 1.8(Co) + 32

  31. Temperature conversions Convert 60o C to Kelvin Convert 75o F to oC Convert 323 K to oC Convert 10o C to oF Convert 90o F to K Convert 400 K to oF

  32. Try this recipe… Chocolate chip cookies: 1 sugar 1 brown sugar 1 ½ butter 2 ½ all purpose flour ½ salt 1 baking soda 2 semisweet chocolate chips

  33. Units – annoying but important SI Units – Systeme Internationale d’Unites A universal system of measurement that allows people all over to discuss and trade without confusion kilogram = kilogram

  34. Base units Second (s) Meter (m) Kilogram (kg) Kelvin (K) mole (mol) The standard kilogram kept in a vacuum sealed container in France. Time Length Mass Temperature Amount of a substance

  35. Derived Units An SI unit that is defined by a combination of base units Density = g/mL Volume = cm3 If you know the units, you can figure out the formula, or vice versa What is the unit for speed? What is the formula for speed then?

  36. Dimensional Analysis A way of converting from one unit to another Conversion factors 1 min = 60 sec 12 in = 1 foot 16 oz = 1 lb

  37. Warm up Convert the following using the provided formulas: 65 oF to oC 393 K to oF Formulas: K = oC + 273 oF = 1.8(oC) + 32

  38. Convert: • 45 inches to miles 1. Start with your given 2. Figure out which conversion factors you need 3. Set it up so units cancel 4. Do the calculations • Multiply across the top, divide across the bottom • 3.6 miles to centimeters • 1450 minutes to days • 0.8 days to seconds • 1.3 x 1010 seconds to years

  39. WARM-UP Using dimensional analysis, solve the following: If 25 zags = 1 zangdoodle, and 3.5 zangdoodles = 1 raz, and 1.75 raz = 1 zoom, how many zags would you have if you had 8.9 zooms?

  40. Warm up: Convert 450.0 oz to tons 1 ton = 2000 lbs 1 oz = 28.3 g 1 pound = 454 g Let’s rewrite our answers with sig figs! Only base the number of sig figs off of the given, NOT the conversion factors

  41. Dimensional Analysis with derived units The average student is in class 330 min/day. • How many hours/day is the average student in class? What is changing? What conversion factors do I need? b. How many seconds is the average student in class per week?

  42. Practice How many mph is 23 km/hr? How many mph is 459 ft/sec? How many ft/hr is 4515 cm/min?

  43. What floats? Why does the tiny golf ball sink, and the much larger bowling ball floats? What 2 things does density take into consideration? What is the unit for density? (You can figure this out from the formula) What units must you be in to calculate density?

  44. Things you might need… Density = Mass/Volume Volume = l x w x h 1 m = 100 cm = 1000 mm 1 km = 1000 m 1 inch = 2.54 cm 1 lb = 16 oz 1 lb = 454 g

  45. Density problem An oddly shaped piece of iron has a mass of 45.8 g. A graduated cylinder contains 35.0 mL of water. After dropping the iron in to the water, the level rises to 43.6 mL. What is the density of iron?

  46. Three cubes, same size… • What do these 3 blocks have the same amount of? • Volume • Which one has more “stuff” in it? Which is the least dense? Most dense? If you were to draw what the atoms look like in each of the blocks, what would they look like?

  47. Candle trick Why does the candle sink more in one of the graduated cylinders than in the other? Something will float if it is (more, less) dense than the substance it is in. Rank the densities of the liquids in relation to the candle

  48. Any progress reports? Warm up: If the following items were combined (and did not mix) put them in order from top to bottom densities alcohol 0.79 g/mL corn syrup 1.36 g/mL dishwashing liquid 1.03 g/mL vegetable oil 0.9 g/mL rubber stopper 1.5 g/cm3 cork 0.2 g/cm3

  49. Density of water Using the provided equipment (and water from the sink), find and record the mass and volume of 4 different amounts of water Be sure to use an estimated digit in your measurements Make sure you are finding the mass of just the water

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