1. Ch. 3, Scientific Measurement

2. Measurement Measurement: A quantity that has a number and a unit. Like 52 meters.

3. D. Scientific Notation Converting into Sci. Notation: –Move decimal until there’s 1 digit to its left. –Any number other than 0. –Places moved = exponent. –Large # (>1)  positive exponent Small # (<1)  negative exponent –Only include sig figs. 65,000 kg  6.5 × 10 4 kg

4. D. Scientific Notation 7. 2,400,000  g 8. 0.00256 kg 9. 7  10 -5 km 10.6.2  10 4 mm Practice Problems 2.4  10 6  g 2.56  10 -3 kg 0.00007 km 62,000 mm

5. D. Scientific Notation Calculating with Sci. Notation (5.44 x 10 7 g) / (8.1 x 10 4 mol) = Type of your calculator: 5.44 EE 7 / 8.1 EE 4 = 671.6049383 = 670 g/mol = 6.7 x 10 2 g/mol

6. A. Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

7. Accuracy vs. Precision *Accuracy: How close a measurement comes to the correct value. *Precision: How close a series of measurements are to one another. – Consistency

8. Determining Error of a measurement Error = Experimental Value - Accepted Value – Can be positive or negative Percent Error = error / accepted value * 100% – or – Always positive Example, you measured 99 cm, but it is 100 cm. 99 cm – 100 cm 100 cm x 100 x 100 = 1% error

9. C. Significant Figures Indicate precision of a measurement. Recording Sig Figs –Sig figs in a measurement include the known digits plus a final estimated digit –(See page 24) 2.32 cm

10. 1) How many sig figs after we estimate? –3.2 2) Now how many? –3.13

11. Rules for Sig Figs Non-Zero Numbers are always significant – Ex).236 m has 3 sig figs. Zeros between non-zero numbers are significant. – Ex) 7003 m and 40.79 m each have 4 sig figs. Leftmost zeros are not significant – Ex).000099 m, 0.42 m, and.073 m each have 2 sig figs. Rightmost zeros are significant IF they come before or after a decimal. – Ex) 9000. m, 90.00 m, and 9.090 m each have 4 sig figs. Rightmost zeros with no decimal points are not significant. Ex) 300 m has 1 sig fig. **The number of left handed people in the class is insignificant compared to the number of right handed people

12. 4. 0.080 3. 5,280 2. 402 1. 23.50 C. Significant Figures Counting Sig Fig Examples 1. 23.50 2. 402 3. 5,280 4. 0.080 4 sig figs 3 sig figs 2 sig figs

13. Is a Zero a Significant Number or Not? 504 L.06 mL 50.0 m 7,000 km YES – 3 sig figs NO – 1 sig figs YES – 3 sig figs NO – 1 sig fig

14. C. Significant Figures Calculating with Sig Figs –Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm 3 )(23.3cm 3 ) = 324.103g 324 g 4 SF3 SF

15. C. Significant Figures Calculating with Sig Figs (con’t) –Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL + 4.1 mL 7.85 mL  7.9 mL 3.75 mL + 4.1 mL 7.85 mL

16. C. Significant Figures Calculating with Sig Figs (con’t) –Exact Numbers do not limit the # of sig figs in the answer. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

17. In this class, delay rounding until the very end. 1.8 × 2.10 × 1.542 Rounding: 1.8 x 2.10 = 3.8 x 1.542 = 5.9 Round at end: 1.8 x 2.10 x 1.542 = 5.82876 = 5.8

18. C. Significant Figures 5. (15.30 g) ÷ (6.4 mL) Practice Problems = 2.390625 g/mL  18.1 g 6.18.9g - 0.84 g 18.06 g 4 SF2 SF  2.4 g/mL 2 SF

19. E. SI Units QuantityBase UnitAbbrev. Length Mass Time Temp meter kilogram second kelvin m kg s K Amountmolemol Symbol l m t T n Volume V liter L

20. Temperature: Celsius and Kelvin are units of temperature that are the same, just shifted. K = C + 273 Water freezes at 0 C and at 273 K. Absolute Zero = 0 K; K will never be negative. Convert 15 C to K = Convert 321 K to C = 288 K 48 C

21. E. SI Units mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  10 -6 nano-n10 -9 pico-p10 -12 kilo-k10 3 BASE UNIT---10 0

22. Different way of looking at it… 1 km = 1000 m 1 m = 10 dm 1 m = 100 cm 1 m = 1000 mm 1 mm = 1000 um

23. F. Derived Units Combination of base units. Volume (m 3 or cm 3 ) –length  length  length D = MVMV 1 cm 3 = 1 mL 1 dm 3 = 1 L  Density (kg/m 3 or g/cm 3 )  mass per volume

24. Problem-Solving Steps 1. Analyze 2. Plan 3. Compute 4. Evaluate

25. Basic Algebra Review Whatever you do to one side, you do to the other. 6 + 6 = 12 + 22 + 3 3

26. Density An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. GIVEN: V = 825 cm 3 D = 13.6 g/cm 3 M = ? WORK : M = DV M = (13.6 g/cm 3 )(825cm 3 ) M = 11,220g  11,200 g

27. Density A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK : V = M D V = 25 g 0.87 g/mL V = 28.7356  29 mL

28. SI Prefix Conversions mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  10 -6 nano-n10 -9 pico-p10 -12 kilo-k10 3 move left move right BASE UNIT---10 0

29. = SI Prefix Conversions NUMBER UNIT NUMBER UNIT 532 m = _______ km 0.532

30. SI Unit Conversions King __doofus can milk many newts. k__ d c m m n kilo, deci, centi, milli, micro, nano What’s yours?

31. Dimensional Analysis Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

32. Dimensional Analysis Lining up conversion factors: 1 in = 2.54 cm 2.54 cm 1 in = 2.54 cm 1 in 1 in = 1 1 =

33. Dimensional Analysis 5)Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? (1 in=2.54cm) 8.0 cm1 in 2.54 cm = 3.2 in cmin

34. Dimensional Analysis How many milliliters are in 1.00 quart of milk? (1L = 1.057 qt) 1.00 qt 1 L 1.057 qt = 946 mL qtmL 1000 mL 1 L 

35. Dimensional Analysis You have 1.5 pounds of gold. Find its volume in cm 3 if the density of gold is 19.3 g/cm 3. (1 kg = 2.2 lbs) lbcm 3 1.5 lb 1 kg 2.2 lb = 35 cm 3 1000 g 1 kg 1 cm 3 19.3 g

36. Dimensional Analysis Convert 60.0 km/hr into m/sec 60.0 km 1000 m 1 km = 16.7 m/sec 1 hr 60 min 1 min 60 sec 1 hr

37. SI Prefix Conversions 1) 20 cm = ______________ m 2) 0.032 L = ______________ mL 3) 45 m = ____ mm 4) 805 dm = ______________ km 0.2 0.0805 45,000 32

38. Example Problems!!!

39. 1. How many sig figs in: 1.480*10 5.00070 1.000080 3.00E3 2. Perform these calculations and come up with answers that have the correct number of sig figs: 5.667 +.34 5.007E3 / 1.20 4.3 - 1.3590 5.309E3 * 3 3. Convert 3.4 ug into kg. 4. Convert 7E3 cm into Mm. 5. What is the mass if a substance with a density of 4.5 g/L has a volume of 3 L?

40. 6. How many sig figs in: 1010 3000 3000. 3000.0 7. Convert 3 kg into g. Convert 34 cm into m. Convert 4 m into cm. 8. You have a 4 kg box. You measure it to be 5.8 kg. What is the error? The % error? 9. What is the difference between accuracy and precision?

41. 11. Put 5,009,000,000 into Scientific Notation 12. Put 0.00007890 into Scientific Notation. 13. Put 8.7 * 10 -4 into a regular number.

42. 14. Which is the largest amount? A. 2*10 2 g B. 30 kg C. 45 mg D. 190 g 15. Convert 40 Kelvin into Celsius 16. Convert 99 Celsius into Kelvin.