The percentage error value is crucial when performing calculations in experiments. It enables us to observe the percentage difference between the exact result and our guesses. Therefore, in many cases, we must compute the percentage inaccuracy. Don’t worry if you are new to this topic. Here, we will be covering we will discuss the Percent Error Formula with examples.
What is Percent Error?
The difference between an observed and a true or acceptable value is measured as a percent error. The outcome of data measurement often deviates from the actual value. Errors can occur for a variety of reasons, such as estimations and limitations of the measurement devices. However, they are more commonly related to human mistakes. Still, it becomes critical to determine the percentage of mistakes in certain situations. Simply said, the absolute error is the difference between the true value and the observed value and is used in the computation of percentage error. The percentage error is then calculated by multiplying the relative error by 100 after dividing the absolute error by the real number.
Formula for Percent Error
A percent error formula is necessary whenever you need to calculate the expectations vs. facts ratio. The percent error computation procedure is simple to follow:
- Take the genuine value and subtract it from the estimated value. If there is a negative sign, ignore it as the number is regarded as an absolute value.
- The number should be divided by the actual value. Thus, you get a frac or a decimal number.
- Put the “%” symbol after multiplying the integer by 100.
You will get the formula like this:
Per cent error = (Approximate or experimental Value – Exact or known Value/Exact or known Value) ∗ 100
The Advantages of Calculating Percent Error
Determining the percent errors has many advantages. Here are a few advantages of calculating percent errors:
It’s crucial to understand the accuracy in terms of percent inaccuracy. The degree of a measured value’s similarity to its original value is called accuracy. One can compute the percent error by multiplying the original value by 100 and dividing the difference between the estimated and original values.
Knowing your proximity to the correct value is the primary advantage of calculating the percent error. The percent error could be as low as insignificant or as high as quite high depending on your observations. Therefore, you can ignore it if the percent mistake is very small. However, if the percent error is large, you must recalculate or measure the data to obtain the absolute value.
Solved Examples on Percent Error
Example 1: The concert’s organizers had anticipated 90 attendees, but 120 individuals showed up. Determine the percent error in the organizers’ estimation value.
Solution: The percent error formula is
(Approximate or experimental Value – Exact or known Value/Exact or known Value) ∗ 100
When we enter the data above in the given formula,
we obtain: % error = ∣90−120∣120∗100=30120∗100 = 25%
Example 2: Despite your suggestion that the mass would be 350 grams, the actual mass was 170 grams.
Solution: Once more, we begin by subtracting the values: 170 – 350 = 180
This time, the result is positive. Therefore, we keep track of the ratio of the measured value to the absolute error: 180/170 = 2.57
Lastly, we convert the amount to a percentage (2.57 * 100% = 257%)
And that demonstrates a mistake rate that exceeds 100%.
Example 3: A few small inaccuracies cause a scale to measure a value of 14 cm incorrectly. If the value is 10 cm in measurement, get the percentage inaccuracy.
Solution: Considering the problem,
Value of experiment = 14 cm
Theoretical value = 10 cm
By using the calculation’s formula,
Percentage Error = (experimental value–theoretical value) Theoretical value×100
= 14−10/10×100
= 4/10×100
40% is the calculated percentage error.
Relationship Between Percent Error as a Percent Difference, Absolute Error, and Relative Error
There is a relationship between all three of those figures. But it is crucial to comprehend the difference in order to make an appropriate computation.
The discrepancy between the measured and theoretical values is known as absolute error. It normally has a positive value, although occasionally a negative error might be obtained.
In any case, the absolute value of the error—ignoring the negative sign—is all you’ll need for any consecutive computations.
The ratio of the absolute difference to the known value is known as the relative error. Usually, it is either a decimal or a frac number. Estimating the relative error size in relation to the accepted value is helpful.
The percent error illustrates the percent variation. Before calculating it, the absolute and relative errors must be calculated. The relative error is multiplied by 100 to get the percentage error.
Conclusion
A calculation of errors is the percent error. Absolute error and relative error are two other popular forms of error computations. We can make mistakes when performing the analysis. The percent error helps us figure out where our errors are when we measure something. Our calculations were fairly accurate if the percent error was low.
The presence of imperfect components can lead to percent mistakes. Sometimes, experimenters may not have the right supplies on hand, which can result in a percent mistake. Inaccurate instruments used for computations can also lead to errors since they might not be able to precisely measure a given object.
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