1. Error in Measurement There are different ways to calculate and represent errors in measurement.

2. Absolute Error The absolute error is the difference between the measured value and the accepted (known) value. If x is the actual value of a quantity and x 0 is the measured value of the quantity, then the absolute error value can be calculated using the formula Δx = x 0 - x Here, Δx is called an absolute error.

3. Example 24.13 is the actual value of a quantity and 25.09 is the measure or inferred value, then the absolute error will be: Absolute Error = 25.09 – 24.13 = 0.86 Most of the time it is sufficient to record only two decimal digits of the absolute error. Thus, it is sufficient to state that the absolute error of the approximation 4.55 to the correct value 4.538395 is 0.012.

4. Mean Absolute Error The Mean Absolute Error(MAE) is the average of all absolute errors.average The formula is: Where: n = the number of errors, Σ = summation symbol (which means “add them all up”),summation symbol |x i – x| = the absolute errors.

5. Relative Error The relative error is defined as the ratio of the absolute error of the measurement to the actual measurement. Using this method we can determine the magnitude of the absolute error in terms of the actual size of the measurement. If the true measurement of the object is not known, then the relative error can be found using the measured value. The relative error gives an indication of how good measurement is relative to the size of the object being measured.

6. If x is the actual value of a quantity, x 0 is the measured value of the quantity and Δx is the absolute error, then the relative error can be measured using the below formula. Relative error = (x 0 -x)/x = (Δx)/x An important note that relative errors are dimensionless. When writing relative errors it is usual to multiply the fractional error by 100 and express it as a percentage.

7. Percent error Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.relative error Percent Error Formula: % Error = (x 0 -x)/x*100 = (Δx)/x*100

8. Example 1. Find the absolute and relative errors of the approximation 125.67 to the value 119.66. Solution: Absolute error = |125.67-119.66|=6.01 Relative error = |125.67- 119.66|/119.66 = 0.05022

9. 2. A student measures the radius of a circular sheet of paper and finds that it is 15 cm long. The label on the package indicates that the radius is is 17 cm. Calculate the percentage error in the measurement. Solution: Measured value = 15 cm Accepted value = 17 cm Percent error = |17-15|/17*100 = 0.12

10. Exercise 1.Rohan weighed an object on her balance and recorded a mass of 13.62 grams. Her teacher told her that there was obviously something wrong with her balance because it was giving her a reading which was 22.22% too high. Find the actual mass of the object? 2.Another student was experimentally determining the boiling point of water. They reported it to be 99.5° C. The accepted value for the boiling point of water is 100° C. What is the percent error?

11. Minimize errors when taking measurements: 1. Be familiar with the measuring instrument. Be sure you know how to correctly use the measuring device. Always take readings by looking straight at the measuring device. Avoid looking at the scale from a position to the left or the right of the measuring device, as this causes an error know as parallax (a distorted view). 2. Repeat the measurement. Repeating the measurement will allow you to take an average of the measurement which will most likely be a more accurate indication of the true measurement. 3. Use the most accurate measuring instrument possible. A more accurate measuring device will have a smaller unit division (or fraction of a unit division) on the scale of the device. 4. Be aware of your surroundings when measuring. Be aware that conditions such as temperature may cause the object (or even the measuring device) to swell or shrink, making your measurements less accurate.

12. Thank You!!!