Calculating percentages, significant digits, averages, MEAN values, rounding
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EXAMPLE PROBLEM for PERCENTAGE: A student is at the end of a class. There were three 100 point exams and homework assignments worth 100 points. The student earned 368 points. What is the student's percentage of the total possible points? SOLUTION: 1. Write out what the question asks for as an answer. 2. Write out the definition for figuring percentage. % = 100 x ( part / total ) 3. Write out the given information.
4. Relate given values with definition for %
5. Figure percentage % = 100 x ( part / total) =100 x [ 368 We see that there are no units for the answer because the labels cancelled. |
| AVERAGE VALUES and MEAN VALUES Average values are used frequently. The average is also known as the "mean". The average for a set of measurements is figured by adding up all the values a dividing the total by the count of the number of measurements. Average value = Total for all values / count of number of values. EXAMPLE A series of volume lung capacity measurements were made for a patient. The measurements are listed here. 2300 ml, 2400 ml, 2500 ml, 2200 ml, 2700 ml. What is the average volume? Note the values do not agree in the second digit. This is the first uncertain digit and the last significant figure. The average has only two significant figures. Total = 2300 ml + 2400 ml + 2500 ml + 2200 ml + 2200 ml = 13100 ml Average = total / number of measurements Average = the 'mean' = 11600 ml / 5 = 2320 ml rounded off to 2300 ml with 2 significant figures. The measurements agree in only one digit. The last sf is the number where the measurements begin to differ. The count, 5, is an exact number with no uncertainty. This does not change the number of significant figures in the average. The answer can only be as good as the poorest number in the calculation. The measurements originally had only 2 sf because they agreed only in the first digit and were different in the second digit. |
