Measurement and Calculations

1. Measurement and Calculations

2. the science that deals with the materials of the universe and the changes these materials undergo • Chemistry – • Qualitative Measurement – • Quantitative Measurement – Qualities or observations that can be made about a substance ex: the substance is a yellow solid a measurement that consists of a number and a unit ex: the substance weighs 3.45 grams

3. Units • tells what scale or standard is being used to represent the measurement • International System (SI) • SI Base Units: • Length: • measures distance • Mass: • quantity of matter present in an sample • Volume: • 1 mL = 1 cm3 • three-dimensional space occupied by a sample • Temperature: • TK = T°C + 273 • Time: • Pressure: • Energy/Heat: • Counting Atoms: meter grams Liter, centimeter cubed, decimeter cubed 1 L = 1 dm3 Kelvin, Celsius second Pascals Joules moles

4. Units Common metric prefixes (MEMORIZE) Giga 1 x 109 _ = 1 G_ Mega 1 x 106 _ = 1 M_ Kilo - 1000 _ = 1 k_ Hecto - 100 _ = 1 H_ Deka - 10 _ = 1 D_ (base) – meter, liter, gram… deci- 1 _ = 10 d_ centi- 1 _ = 100 c_ milli- 1 _ = 1000 m_ micro- 1 _ = 1 x 106_ ( = lowercase Greek Mu) nano- 1 _ = 1 x 109 n_ pico- 1 _ = 1 x 1012 p_ * * * * *

5. 2 1 1 2 3 Scientific Notation Expresses a number as a product of a number between 1 and 10 and the appropriate power of 10 If you move the decimal point- left  positive exponent right  negative exponent Ex: 200 g .00314 mL 2 x 102 g 3.14 x 10-3 mL

6. 1 2 3 1 Converting from Scientific Notation to Ordinary Numbers move the decimal point- positive exponent  right negative exponent  left Ex: 6.32 x 101 cm 3.92 x 10-3 m 63.2 cm .00392 m

7. Learning Check Try these: • 657000000000 m • 0.000000235 g • 9.34 x 102 cL • 3.35 x 10-3 L 6.57 x 1011 m 2.35 x 10-7 g 934 cL 0.00335 L

8. Limits to Measurements estimate last • When measuring you should always ______________ the _______ digit of your measurement • Your measurement should be recorded to ONE PLACE VALUE BEYOND the ______________marking • Your Estimate (or _____________ number) should be the final one on the right. • If the tool is digital, _________ the given number– no estimated number. • Measurements always have some degree of uncertainty (estimation) calibration uncertain record

9. Ex 3: Measure the volume of liquid in the buret. Ex 1: Measure the volume of liquid in the Graduated cylinder. Remember: The volume is read at the bottom of the liquid curve (called the meniscus). Ex 2: Measure the line using both rulers. 7.5 cm 42.8 mL 15.75 mL 7.56 cm

10. Learning check Read the following pieces of equipment, record your answer with the estimated digit and units. 1. 4. 5. 2. 3.

11. Significant Figures All certain numbers plus first uncertain digit Rules for counting Sig. Figs. 3578 = 4 SF 1. All nonzero numbers are significant. 236 = 3 SF • 2. Zeros • a. Leading Zeros – precede all nonzero digits, they NEVER COUNT .0025 = 2 SF .0009 = 1 SF • b. Captive (Trapped) Zeros – fall between two nonzero digits, they ALWAYS COUNT .00705 = 3 SF 20502 = 5 SF 6008 = 4 SF c. Trailing Zeros – come at the end of a number and count IF there is a DECIMAL POINT .001500300 = 7 SF 2580.0 = 5 SF 3000. = 4 SF 3000 = 1 SF 3. Exact numbers – have infinite number of sig. figs., they arise from definitions 1 inch = 2.54 cm, 1 g = 1000 mg

12. Rounding If the digit to be removed is – • less than 5, the preceding digit stays the same • equal or greater than 5, increase the preceding digit by 1 When rounding off, use ONLY the first number to the right of the last significant figure Ex:Round to 3 SF$ 10,079 0.002978 g 0.03296 cm 1000. mL = $10,100 = 0.00298 g = 0.0330 cm = 1.00 x 103 mL

13. Learning Check Determine the number of significant figures in the following numbers: • 0.00340 g • 9.00 mm • 30.390 mL Round each number to 2 significant figures. • 0.00340 g • 9.00 mm • 30.390 mL

14. Calculations Notes

15. Uncertainty in Measurement close • Accuracy: - How _________ a measurement is to the actual or _________value. To evaluate accuracy you must __________ the true value. For example, knowing a watch is 5 min fast…The time on the watch is ________ accurate and you know it is not accurate b/c you know the real time and can make an ________. • Shooting Free Throws - Accuracy can be measured by how many are __________. accepted know not adjustment baskets

16. Precision: set 1st Meaning of Precision How close a ____________ of measurements are to the _________________. To evaluate precision you must compare the values of 2 or more _______________ measurements. • Ex. Measure the temperature of water three times. Which set of measurements are more precise? Thermometer 1: 22.3oC, 22.3oC, 22.4oC Thermometer 2: 24.5oC, 20.1oC, 18.7oC • Shooting Free Throws - Precision can be measured by how many _______ in the same _________. Ex. Consistently hitting the ___________ of the rim and missing. Not accurate b/c not making the shots, but precise b/c results are repeated. • Science – should be both accurate (___________) and precise (can ____________ it consistently) actual value similar shots spot side right repeat

17. precise places 2nd Meaning of Precision • Precision can also refer to how __________ a measurement is (more decimal __________ = more precise) Consider mass of sugar in bubble gum • 5 g - wide range of values that it could be! - Could be between 4.5 g and 5.4 g and rounded to 5 g. • 5.0 g gives you more information – Could be between 4.95 g and 5.04 g. • 5.00 g gives you even more information – Could be between 4.995 g and 5.004 g • More numbers to ______________ of decimal, more precise the measurement is! right

18. Learning Check Think of an example, from your life, of accuracy and precision.

19. Multiplication and Division Number of the sig. figs. is the result of the measurement with the smallest number of sig. figs. (least accurate). LEAST NUMBER OF SIG FIGS! Ex 1: 4.63 m x 7.5 m Ex. 2: 8.460 m2 / 2.1 m 4 sf 2 sf 3 sf 2 sf 4.0285714286 34.725 35 m2 4.0 m

20. 6.341 .789 4.2 6.799 2.41 Addition and Subtraction Align the decimal points and carry out the calculation. First column from the leftwith an uncertain digit determines the number of sig. figs. in your answer (Chop & round at the GAP) LEAST NUMBER of DECIMAL PLACES! Ex 1: 6.341 g + .789 g + 4.2 g Ex. 2: 6.799 m - 2.41 m 11.3 g 4.39 m GAP GAP 11.330 4.389

21. Learning Check • 22.4 L x 9.3 L 2. 9.63 g + 17.3251 g

22. Scientific Notation and Multiplication and Division Multiplication – Multiply coefficients, ADD exponents, multiply units, round to proper S.F. Division - Divide coefficients, SUBTRACT exponents, divide units, round to proper S.F. Ex 1: (1.00 x 103 m)(3.2 x 102 m) Ex. 2: (3.00 x 104 g)/(1.0 x 102 cm3) 3.2 x 105 m2 3.0 x 102 g/cm3

23. 3.0 .10 1 Scientific Notation and Addition and Subtraction must be in the same power of ten and same unit before you add or subtract coefficients, convert to larger exponent Ex 1: 3.0 x 1023 m + 1.0 x 1022 m 3.0 x 1023 m + .10 x 1023 m 3.1 x 1023 m GAP 3.10

24. Learning Check 1. 2.29 x 105 g - 9.3 x 104 g 2. 6.02 x 1023 m ÷ 1.7 x 1022 m

25. 2.54 cm 1 inch 1 inch 2.54 cm 100 cm 1 m 1 m 100 cm Problem Solving and Dimensional Analysis Conversion factor – ratio of two parts of the statement that relates the two units Equivalence Statement – true statement in fraction form Dimensional Analysis – when used properly all units will cancel out except the desired unit 2.54 cm = 1 inch 100 cm = 1 m or or Wanted UNIT Desired UNIT # # Given with UNITS x ________________ x ______________ = # Given UNIT # Wanted UNIT

26. 1 g = 1000 mg 1 g = 1000 mg 1 km = 1000 m 1 kg = 1000 g Ex. 1: 250 m = ___________ km Ex. 2: 3.54 g = ___________ mg Ex. 3: 0.542 kg = __________ mg 250 m 1 km x ___________ .25 km = 1000 m 1000 mg 3.54 g x ___________ 3540 mg = 1 g 0.542 kg 1000 g 1000 mg x ________ x __________ = 542000 mg 1 kg 1 g

27. Learning Check 1. 0.542 mm = __________ km 2. 0.542 g = __________ µg

28. Determining Error accepted ___________________value - correct value based on reliable references ___________________value - value measured in the lab Error = experimental value – accepted value (Note: error can be positive or negative) You will take the ___________ value of this when you calculate percent error. experimental absolute

29. % error = (91.1 oC – 100 oC) x 100% 100 oC Determining Percent (%) Error Percent error = absolute value of error divided by accepted value and multiplied by 100% % error = (experimental value – accepted value) x 100% accepted value Example: You take three temperature readings of a beaker of boiling water and record: 91.3oC, 90.9oC, and 91.1oC. Evaluate accuracy, precision, and error. No, water boils at 100oC Accurate? Precise? Yes, values are close to each other Error • Find average experimental data • Use formula (91.3oC + 90.9oC + 91.1oC)/3 = 91.1oC = 8.90 %

30. Learning Check 1. At a track meet, you time a friend running 100 m in 11.00 seconds. The officials time her at 10.67 seconds. What is your percentage error?

31. For Fun! Hagrid instructed Harry to give the delivery owl five Knuts for a newspaper (p. 62). A weekday newspaper costs $0.25. At Gringots, Harry learned that there are seventeen Sickles to a Galleon and twenty-nine Knuts to a Sickle (p. 75). Harry then paid seven Galleons for his new wand-Holly and phoenix feather (p. 85). Use dimensional analysis to calculate how much Harry’s wand would cost in dollars? On the train, Harry paid eleven Sickles and seven Knuts for junk food from the snack trolley. How much money did he spend? Sickles 7 Galleons 17 29 Knuts .25 dollars $172.55 x ___________ x ______________ = x ___________ 1 Galleon Knuts 1 Sickles 5 29 Knuts .25 $ 15.95 dollars 11 Sickles = x __________ x ___________ 5 $16.30 Sickle 1 Knuts 7 Knuts dollars .25 = $ 0.35 x ___________ 5 Knuts