Determining the Ratio of Circumference to Diameter of a Circle
In determining the ratio of the circumference to the diameter I began by measuring the diameter of one of the si objects which contained circles, then using a string, I wrapped the string around the circle and compared the length of the string, which measured the circumference, to a meter stick. With this method I measured all of the six circles. After I had this data, I went back and rechecked the circumference with a tape measure, which allowed me to make a more accurate measure of the objects circumferences by taking away some of the error that mymethod of using a string created.
After I had the measurements I layed them out in a table. The objects that I measured were a small flask, a large flask, a tray from a scale, a roll of tape, a roll of paper towels, and a spraycan.
By dividing the circumference of the circle by the diameter I was able to calculate the experimental ratio, and I knew that the accepted ratio was pi.
Then I put both ratios in the chart.
By subtracting the accepted ratio from the experimental you find the error. Error is the deviation of the experimental ratio from the accepted ratio.
After I had the error I could go on to find the percentage error. The equation I used was, error divided by the accepted ratio times 100. For example, if I took the error of the experimental ratio for the paper towels, which was 0.12. I took that and divided it by the accepted ratio giving me .03821651. Then I multiplied that by 100 giving me about 3.14. Using these steps I found the percentage error for all of the objects measured.
The next step was to graph the results. I was able to do this very easily with spreadsheet. I typed in all of my data and the computer gave me a nice scatter block graph. I also made a graph by hand. I set up the scale by taking the number of blocks up the side of my graph and dividing them by the number of blocks across. I placed my points on my hand drawn graph. Once I did this I drew a line of best representation because some of the points were off a little bit due to error.
By looking at my graph I can tell that these numbers are directly proportional to each other. In this lab it was a good way to learn about error
The results of this experiment are shown in the compiled student data in Table 1 below.
...e been beneficial to the experiment. An error may have occurred due to the fact that measurements were taken by different individuals, so the calculations could have been inconsistent.
In my experiment, I will use an overall volume of 50 cm³ of 2moles of
2 + 0.75(100) = 77. However, in any particular year when sales X = 100, the actual cost of goods sold can deviate randomly around 77. This deviation from the average is called the “disturbance” or the “error” and is represented by “e”.
In this experiment, there were several objectives. First, this lab was designed to determine the difference, if any, between the densities of Coke and Diet Coke. It was designed to evaluate the accuracy and precision of several lab equipment measurements. This lab was also designed to be an introduction to the LabQuest Data and the Logger Pro data analysis database. Random, systematic, and gross errors are errors made during experiments that can have significant effects to the results. Random errors do not really have a specific cause, but still causes a few of the measurements to either be a little high or a little low. Systematic errors occur when there are limitations or mistakes on lab equipment or lab procedures. These kinds of errors cause measurements to be either be always high or always low. The last kind of error is gross errors. Gross errors occur when machines or equipment fail completely. However, gross errors usually occur due to a personal mistake. For this experiment, the number of significant figures is very important and depends on the equipment being used. When using the volumetric pipette and burette, the measurements are rounded to the hundredth place while in a graduated cylinder, it is rounded to the tenth place.
words the points all lie on a straight line that goes up from left to
Above is my original data. In the graph, it can be seen that there are
The question that was proposed for investigation was: Can the theoretical, actual, and percent yields be determined accurately (Lab Guide pg. 83)?
F = x/y = lFl x ((δx/IxI) + (δy/lyl)) was used for the error propagation of 1/d where x = 1 and y = d. This equation was also used for the error propagation of κ = slope/ ε0A where x = slope and y = A.
IOS 5725 “Accuracy (trueness and precision) of measurement methods and results” Part 2 to 5: 1994
Step 3: Draw a straight line through the two marks to obtain an approximate east-west line.
You will need to sum down for the first four orientations and sum across some of the rows, then sum down and divide by two for the last orientation. The chart should make it clear.
by selecting four points a planet could be and then drawing a line to the center of the
Possible sources of error in this experiment include the inaccuracy of measurements, as correct measurements are vital for the experiment.