1. 1 Chapter 1B Measurement

2. 2 CHAPTER OUTLINE  SI Units SI Units  Scientific Notation Scientific Notation  Error in Measurements Error in Measurements  Significant Figures Significant Figures  Rounding Off Numbers Rounding Off Numbers  Conversion of Factors Conversion of Factors  Conversion of Units Conversion of Units  Volume & Density Volume & Density

3. 3 SI UNITS  Measurements are made by scientists to determine size, length and other properties of matter.  For measurements to be useful, a measurement standard must be used.  A standard is an exact quantity that people agree to use for comparison.  SI is the standard system of measurement used worldwide by scientists.

4. 4 SI BASE UNITS Quantity MeasuredUnitsSymbol LengthMeterm MassKilogramkg TimeSecondss TemperatureKelvinK Amount of substanceMolemol Electric currentAmpereA Intensity of lightCandelacd

5. 5 DERIVED UNITS Quantity MeasuredUnitsSymbol VolumeLiterL Densitygrams/ccg/cm 3  In addition to the base units, several derived units are commonly used in SI system.

6. 6 SCIENCTIFIC NOTATION  Scientific Notation is a convenient way to express very large or very small quantities.  Its general form is A x 10 n coefficient 1  A < 10 n = integer

7. 7 SCIENTIFIC NOTATION To convert from decimal to scientific notation:  Move the decimal point in the original number so that it is located after the first nonzero digit.  Follow the new number by a multiplication sign and 10 with an exponent (power).  The exponent is equal to the number of places that the decimal point was shifted. 7 5 0 0 0 0 0 0 7.5 x 10 7

8. 8 SCIENTIFIC NOTATION  For numbers smaller than 1, the decimal moves to the left and the power becomes negative. 0 0 0 6 4 2 6.42 x 10 33

9. 9 1. Write 6419 in scientific notation. 64196419.641.9x10 1 64.19x10 2 6.419 x 10 3 decimal after first nonzero digit power of 10 Examples:

10. 10 2. Write 0.000654 in scientific notation. 0.000654 0.00654 x 10 -1 0.0654 x 10 -2 0.654 x 10 -3 6.54 x 10 -4 decimal after first nonzero digit power of 10 Examples:

11. 11 CALCULATIONS WITH SCIENTIFIC NOTATION  To perform multiplication or division with scientific notation: 1.Change numbers to exponential form. 2.Multiply or divide coefficients. 3.Add exponents if multiplying, or subtract exponents if dividing. 4.If needed, reconstruct answer in standard exponential form.

12. 12 Multiply 30,000 by 600,000 Example 1: Convert to exponential form (3 x 10 4 )(6 x 10 5 ) = Multiply coefficients 18 x 10 Add exponents 9 Reconstruct answer 1.8 x 10 10

13. 13 Divided 30,000 by 0.006 Example 2: Convert to exponential form (3 x 10 4 ) (6 x 10 -3 ) Divide coefficients = 0.5 x 10 Subtract exponents 7 Reconstruct answer 5 x 10 6 4 – (-3)

14. 14 Follow-up Problems: (5.5x10 3 )(3.1x10 5 ) =17.05x10 8 = 1.7x10 9 (9.7x10 14 )(4.3x10  20 ) = 41.71x10  6 = 4.2x10  5 0.4483x10 4 = 4.5x10 3 0.2073x10 3 = 2.1x10 2 (3.7x10  6 )(4.0x10 8 ) = 14.8x10 2 = 1.5x10 3

15. 15 Follow-up Problems: (8.75x10 14 )(3.6x10 8 ) =31.5x10 22 = 3.2x10 23 0.2041x10  41 = 2.04x10  42

16. 16 ERROR IN MEASUREMENTS  Two kinds of numbers are used in science: Counted or defined: exact numbers; have no uncertainty Measured: are subject to error; have uncertainty  Every measurement has uncertainty because of instrument limitations and human error.

17. 17 ERROR IN MEASUREMENTS What is this measurement? 8.65 certainuncertain What is this measurement? 8.6 certain uncertain  The last digit in any measurement is the estimated one.

18. 18 SIGNIFICANT FIGURES RULES  Significant figures are the certain and uncertain digits in a measurement.  Significant figures rules are used to determine which digits are significant and which are not. 1.All non-zero digits are significant. 2.All sandwiched zeros are significant. 3.Leading zeros (before or after a decimal) are NOT significant. 4.Trailing zeros (after a decimal) are significant. 0. 0 0 4 0 0 4 5 0 0

19. 19 Examples: Determine the number of significant figures in each of the following measurements. 461 cm 3 sig figs 1025 g 4 sig figs 0.705 mL 3 sig figs 93.500 g 5 sig figs 0.006 m 1 sig fig 5500 km 2 sig figs

20. 20 ROUNDING OFF NUMBERS  If rounded digit is less than 5, the digit is dropped. 51.234Round to 3 sig figs Less than 5 1.875377 Round to 4 sig figs Less than 5

21. 21 ROUNDING OFF NUMBERS  If rounded digit is equal to or more than 5, the digit is increased by 1. 51.369Round to 3 sig figs More than 5 4 5.4505 Round to 4 sig figs Equal to 5 1

22. 22 SIGNIFICANT FIGURES & CALCULATIONS  The results of a calculation cannot be more precise than the least precise measurement.  In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures.  For addition and subtraction, the answer must have the same number of decimal places as there are in the measurement with the fewest decimal places.

23. 23 (9.2)(6.80)(0.3744) = 23.4225 Calculator answer 3 sig figs 4 sig figs The answer should have two significant figures because 9.2 is the number with the fewest significant figures. The correct answer is 23 2 sig figs MULTIPLICATION & DIVISION

24. 24 Add 83.5 and 23.28 83.5 23.28 106.78 Calculator answer Least precise number 106.8 Correct answer ADDITION & SUBTRACTION

25. 25 Example 1: 5.008 + 16.2 + 13.48 =34.688 Least precise number Round to 34.7

26. 26 Example 2: 6.1788 2 sig figs 3 sig figs Round to 6.2

27. 27 SI PREFIXES  The SI system of units is easy to use because it is based on multiples of ten.  Common prefixes are used with the base units to indicate the multiple of ten that the unit represents. SI Prefixes PrefixesSymbolMultiplying factor mega-M 1,000,000 kilo-k 1000 centi-c 0.01 milli-m 0.001 micro-  0.000,001 10 6 10 3 10 -2 10 -3 10 -6

28. 28 SI PREFIXES How many mm are in a cm?10How many cm are in a km?10x10x10x10x10 100000 or 10 5

29. 29 CONVERSION FACTORS  Many problems in chemistry and related fields require a change of units.  Any unit can be converted into another by use of the appropriate conversion factor.  Any equality in units can be written in the form of a fraction called a conversion factor. For example: 1 m = 100 cmEquality Conversion Factors 1 m 100 cm 1 m or Metric-Metric Factor

30. 30 CONVERSION FACTORS 1 kg = 2.20 lbEquality Conversion Factors 1 kg 2.20 lb 1 kg or Metric-English Factor Percent quantity:  Sometimes a conversion factor is given as a percentage. For example: 18% body fat by mass Conversion Factors 18 kg body fat 100 kg body mass 18 kg body fat or Percentage Factor

31. 31 CONVERSION OF UNITS beginning unit final unit Conversion factor  Problems involving conversion of units and other chemistry problems can be solved using the following step-wise method: 1. Determine the intial unit given and the final unit needed. 2.Plan a sequence of steps to convert the initial unit to the final unit. 3. Write the conversion factor for each units change in your plan. 4. Set up the problem by arranging cancelling units in the numerator and denominator of the steps involved.

32. 32 Example 1: Convert 164 lb to kg (1 kg = 2.20 lb) Step 1:Given: 164 lb Need: kg Step 2: English-Metric factor lbkg Step 3: 1 kg 2.20 lb or 2.20 lb 1 kg Step 4:

33. 33 Example 2: The thickness of a book is 2.5 cm. What is this measurement in mm? Step 1:Given: 2.5 cm Need: mm Step 2: Metric-Metric factor cmmm Step 3: 1 cm 10 mm or 10 mm 1 cm Step 4:

34. 34 Example 3: How many centimeters are in 2.0 ft? (1 in=2.54 cm) Step 1:Given: 2.0 ft Need: cm Step 2: English-English factor ftin Step 3: 1 ft 12 in and 1 in 2.54 cm Step 4: cm English-Metric factor 60.96 cm61 cm

35. 35 Example 4: Bronze is 80.0% by mass copper and 20.0% by mass tin. A sculptor is preparing to case a figure that requires 1.75 lb of bronze. How many grams of copper are needed for the brass figure? Step 1:Given: 1.75 lb bronze Need: g of copper Step 2: English-Metric factor lb brz g brz g Cu Percentage factor

36. 36 Example 4: Step 3: 1 lb 454 g and 80.0 g Cu 100 g brz Step 4:= 635.6 g= 636 g 1.75 lb brz x 454 g 1 lb x 80.0 g Cu 100 g brz

37. 37 VOLUME  Volume is the amount of space an object occupies.  Common units are cm 3 or liter (L) and milliliter (mL). 1 L = 1000 mL1 mL = 1 cm 3

38. 38 DENSITY  Density is mass per unit volume of a material.  Common units are g/cm 3 (solids) or g/mL (liquids). Which has greatest density? Density is directly proportional to the mass of an object. Density is indirectly proportional to the volume of an object.

39. 39 Example 1: A copper sample has a mass of 44.65 g and a volume of 5.0 cm 3. What is the density of copper? m = 44.65 g V = 5.0 cm 3 d = ??? d = m V = 44.65 g 5.0 mL = 8.93 g/cm 3 = 8.9 g/cm 3

40. 40 Example 2: A silver bar with a volume of 28.0 cm 3 has a mass of 294 g. What is the density of this bar? m = 294 g V = 28.0 cm 3 d = ??? d = m V = 294 g 28.0 mL = 10.5 g/cm 3

41. 41 Example 3: If the density of gold is 19.3 g/cm 3, how many grams does a 5.00 cm 3 nugget weigh? Step 1:Given: 5.00 cm 3 Need: g Step 2: density cm 3 g Step 3: 19.3 g 1 cm 3 or 1 cm 3 19.3 g Step 4:

42. 42 Example 4: If the density of milk is 1.04 g/mL, what is the mass of 0.50 qt of milk? (1L = 1.06 qt) Step 1:Given: 0.5 gt Need: g Step 2: English-metric Factor qt mL Step 3: and 1.04 g 1 mL Step 4: g density 1L 1.06 qt 1000 mL = 490.57 g= 490 g

43. 43 Example 5: What volume of mercury has a mass of 60.0 g if its density is 13.6 g/mL? g mL 60.0 g 4.41 1 13.6 inverse of density

44. 44 DENSITY & FLOATING  Objects float in liquids when their density is lower relative to the density of the liquid.  The density column shown was prepared by layering liquids of various densities.  See demo See demo Honey Syrup Soap Water Vegetable oil Isopropyl alcohol less dense more dense

45. 45 IS UNIT CONVERSION IMPORTANT?  In 1999 Mars Climate orbiter was lost in space because engineers failed to make a simple conversion from English units to metric, an embarrassing lapse that sent the $125 million craft fatally close to the Martian surface.  Further investigation showed that engineers at Lockheed Martin, which built the aircraft, calculated navigational measurements in English units. When NASA’s JPL engineers received the data, they assumed the information was in metric units, causing the confusion.

46. 46 THE END