Units of Measurement. There are two types of units: fundamental (or base) units; derived units. There are 7 base units in the SI system.
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1 Units of Measurement There are two types of units: fundamental (or base) units; derived units. There are 7 base units in the SI system. SI Units 2:00:07 PM
2 Units of Measurement Powers of ten are used for convenience with smaller or larger units in the SI system. 2:00:09 PM
3 Units of Measurement SI Units 2:00:10 PM
4 EXAMPLE Convert the following: 60 mm to pm 60 mm to nm 1m to dm 1m 2 to dm 2 1m 3 to dm 3 Wednesday, February 22, 8:52:20 AM
5 Units of Measurement 2:00:12 PM SI Units Note the SI unit for length is the meter (m) whereas the SI unit for mass is the kilogram (kg). Temperature There are three temperature scales: Kelvin Scale Used in science. Same temperature increment as Celsius scale. Lowest temperature possible (absolute zero) is zero Kelvin. Absolute zero: 0 K = o C.
6 Units of Measurement Celsius Scale Also used in science. Water freezes at 0 o C and boils at 100 o C. To convert: K = o C Temperature Fahrenheit Scale Not generally used in science. Water freezes at 32 o F and boils at 212 o F. To convert: 2:00:14 PM 5 C F F C
7 Units of Measurement Temperature Wednesday, February 22, 8:52:45 AM
8 Units of Measurement Derived Units Derived units are obtained from the 7 base SI units. Example: Units of velocity units of distance units of time meters seconds m/s Wednesday, February 22, 8:52:46 AM
9 What is the derived unit for Joule? What is the derived unit for Pascal? 1:54:42 PM
10 Units of Measurement Volume The units for volume are given by (units of length) 3. SI unit for volume is 1 m 3. We usually use 1 ml = 1 cm 3. Other volume units: 1 L = 1 dm 3 = 1000 cm 3 = 1000 ml. 2:00:15 PM
11 Units of Measurement Volume 1:54:43 PM
12 Units of Measurement Used to characterize substances. Defined as mass divided by volume: mass Density volume Density Units: g/cm 3. 2:00:16 PM
13 Uncertainty in Measurement Uncertainty in Measurement All scientific measures are subject to error. These errors are reflected in the number of figures reported for the measurement. These errors are also reflected in the observation that two successive measures of the same quantity are different. Precision and Accuracy Measurements that are close to the correct value are accurate. Measurements that are close to each other are 2:00:18 precise. PM
14 Uncertainty in Measurement Precision and Accuracy Wednesday, February 22, 8:54:19 AM
15 A way of measuring accuracy and precision The set which is more accurate can be obtained from the average of a data set and compared with the true value. Precision can be judged from the average of the deviations from the average value of a data set. (Calculate the average value for each data set and then calculate the average value of the absolute deviations of each measurement from the average.) 2:00:19 PM
16 EXAMPLE Two students determine the average percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52% The students results for three determinations are as follows: Set Set Wednesday, February 22, 8:55:12 AM
17 Which set is more accurate? Which set is more precise? Wednesday, February 22, 8:55:14 AM
18 For accuracy. Compare each average with true value 2:00:21 PM
19 For Precision: Average deviation gives an indication of the closeness of data points Average deviation={/(σx i-n )/N - x i-n /}/N 2:00:26 PM
20 Set 2 Average deviation: 1:54:56 PM
21 Significant Figures Significant figures reflect uncertainty in measurement. All the figures known with certainty plus one extra figure are called significant figures. Example Manufacturer guarantees balance to 0.01 g This measurement has 3 significant figures 1:54:57 PM
22 Uncertainty in Measurement Non-zero numbers are always significant. 1:54:59 PM Significant Figures Zeros between non-zero numbers are always significant. Zeros before the first non-zero digit are not significant. (Example: has one significant figure.) Zeros at the end of the number after a decimal place are significant.(eg: 2.00 has three significant figures) Zeros at the end of a number are ambiguous (e.g. 10,300 g). Exponential form removes ambiguity.
23 Uncertainty in Measurement Significant Figures All the figures known with certainty plus one extra figure are called significant figures. In any calculation, the results are reported to the fewest significant figures (for multiplication and division) or fewest decimal places (addition and subtraction). 1:55:00 PM
24 Significant figures Measured quantities are generally reported in such a way that only the last digit is uncertain. All digits including the uncertain one are called significant figures Exact numbers have infinite significant numbers. E.g Numbers by definition Rounding off numbers to 2 sigf to 3 sigf 4.74 since leftmost digit is 5 or greater 1:55:01 PM
25 Significant figures in calculations In multiplication and division, the result must be repeated with the same number of significant figures as the measurement with the fewest significant figures Example: (6.221cm)(5.2cm) = cm 2 =32cm 2 1:55:03 PM
26 In addition and subtraction the results cannot have more digits to the right of the decimal point than any of the original numbers Example: = = :55:04 PM
27 In equations such as E = k mv V= πr and d = 2πr the numbers 1 / 2, 4 / 3 and 2 are exact numbers; they are known with infinite precision and hence have an infinite number of significant figures. 3 2 Wednesday, February 22, 9:01:40 AM
28 EXAMPLE How many significant figures are there in the following: x and Wednesday, February 22, 9:01:57 AM
29 Give the answer to the correct number of significant figures. 3.0 x 2= 3.0x2.0= 3.000/4.000 x100= = 3.00/ = Wednesday, February 22, 9:03:13 AM
30 Dimensional Analysis Dimensional analysis the method of calculation in which one carries along the units for quantities The advantages of this are: The correct units for the answer follow automatically. Errors are more easily identified. eg. when the final units are nonsense 1:55:06 PM
31 Dimensional Analysis Dimensional Analysis Method of calculation utilizing a knowledge of units. Given units can be multiplied or divided to give the desired units. Conversion factors are used to manipulate units: Desired unit = given unit (conversion factor) The conversion factors are simple ratios: Conversion 1:55:08 PM factor desired unit given unit
32 EXAMPLE Perform the following conversion: a L to ml b. km/h to m/s a L = L X 1000mL/1L b.1km/h =760mL = 0.76 x10 2 ml = 1km/h x (0.278 m/s)(h/km) = 0.278m/s =0.3m/s 1:55:10 PM
33 Dimensional Analysis Using Two or More Conversion Factors Example to convert length in meters to length in inches: Number of in number of m conversion m cm conversion cm in Number of in number of m 100 cm m 1in 2.54 cm 1:55:11 PM
34 Dimensional Analysis Using Two or More Conversion Factors In dimensional analysis always ask three questions: What data are we given? What quantity do we need? What conversion factors are available to take us from what we are given to what we need? Thursday, March 3, 3:24:47 PM
35 1:55:14 PM End
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