Exams Prep Master
Percent Error refers to the difference between the exact or known value of something and its measured value, in percentage form. We use it to report the difference between the experimental value to its true or exact value. For example, if we look at a gumball machine and make an estimate of how many gumballs there are and then we actually go ahead and calculate the number of gumballs, then we will be able to measure the percent error in our guess. This concept lets you see how far off you are in estimating the value of something from its exact value. Percent errors could happen due to the imprecision of equipment, measurement (human error or tool error), or some adjustments done in calculation methods. Here we’ll discuss the formula for calculating the percent error and solve some related questions.
| Table of Content |
Key Takeaways: Percentage, Experimental value, Exact value, Absolute value.
Also read: Isosceles Triangle Theorems
Formula of Percent error
[Click Here for Sample Questions]
Percent Error refers to the difference between the exact or known value of something and its measured value, expressed as a percentage. To put it in a simple manner, the percent error is the relative error multiplied by 100. If it is close to 0, then our approximation is very close to the actual or true value. The percent Error formula is very important to determine the precision of our calculations. Generally, the percent error is represented as a positive number, but for some sciences like chemistry, it is customary to express it as a negative number. This is because a positive value in chemistry would point to a potential problem with the experiment or reactions which are not accounted for.
The formula for percent error = Percent error = (Approximate or experimental Value - Exact or known Value / Exact or known Value) x 100
The video below explains this:
Percentage Error Formula Detailed Video Explanation:
Also read: Determinant Formula
Calculation of Percent Error
[Click Here for Sample Questions]
Finding percent error is a simple process. We need to know a few important things in order to find a percent error. We should know the estimated value and original value to find the percent error. Firstly, we need to find the difference between the estimated value and the original value. We can ignore the negative sign in case we get a negative result.
The steps given below describe how to obtain the percent error in detail.
Step 1: Calculate the difference between one value from the other. The order does not matter since we are ignoring the sign. However, we need to subtract the original value from the determined value if we are keeping negative signs. The value which we get is the “error.”
Step 2: Here we need to perform a division operation for the error by the accurate or ideal value (not estimated or measured value), this results in a decimal number.
Step 3: Multiply the decimal by 100 to transform it into percentage form.
Step 4: Put the percentage symbol (%) to represent the percent error value.
Also read: Differentiation and Integration Formula
Things to Remember
- The difference of the original value from the determined is called the “error.”
- Percent error = (Approximate or experimental Value - Exact or known Value / Exact or known Value) x 100
- We use it to report the difference between the experimental value to its true or exact value.
- If we get a negative value, we take the absolute value, ignoring the negative symbol.
- We calculate percent error to analyze how close the measured value is to an actual value.
- Percent error is part of comprehensive error analysis.
Also read: First Order Differential Equation
Sample Questions
Ques. We know that the estimated distance to the moon is 235,755 miles on a particular day. But we find that the actual distance is 250,655 miles. Find the percent error. (2 marks)
Ans. The percent error can be calculated as: 235, 755 - 250, 655 / 250, 655 = 0.059 x 100 = 5.9%
Ques. Jimmy was planning to go hiking. The estimated height of the hiking trail was 215 ft, but when he went with his friends, he found the actual height of the trail was 230 ft. Find the percent error in Jimmy’s calculation. (2 marks)
Ans. (215 − 230) / 230
= 15 / 230
= 0.065 x 100
= 6.5 %
Ques. A fest was organized which was open for all. The organizers estimated that 1000 people will visit every day. However, the actual number of people visiting the fest was 1050. Find the percent error. (2 marks)
Ans. (1000 − 1050) / 1050
= 50 / 1050
= 0.047 x 100
= 4.7 %
Ques. Chandler wanted to prepare a square lawn. The estimate was that it would cover 450 square meters of area. When he started digging, the actual area to be covered was 470 meters square. Calculate the percent error. (2 marks)
Ans. (450 − 470) / 470
= 20 / 470
= 0.042 x 100
= 4.2 %
Ques. State the uses of calculating percent error? (2 marks)
Ans. The Percent error is a system to measure how accurate and close the estimate is to the exact value of any given experiment or quantity. The Percent error method lets us determine if the collection of data is progressing in the right direction or not. This method is mostly used by statistics experts and corporate companies. Percent error is also of high importance to students who want to pursue economics.
Ques. What are some of the reasons for percent error? (2 marks)
Ans. There are a number of reasons for a difference in the measured value from the known value. Some of the general reasons for the percent error may be human error, issue with experiment, calculation error (like rounding off, etc.), systematic error, precision error, etc.
Ques. What is an absolute error and how is it different from percent error? (2 marks)
Ans. Absolute error refers to the difference between the known and measured values. And when it is divided by the known value and then multiplied by 100, it becomes a per cent error.
Hence: Absolute error = |Approximate value – Exact Value|
Percent error = |Approximate value – Exact Value| / Exact value * 100.
Ques. The area of a rectangle plot is measured to be 468 cm2. Whereas the actual area of the plot has been recorded as 470 cm2. Find the percent error of measurement. (2 marks)
Ans. We know, Measured area value = 468 cm2
Actual area value = 470 cm2
Steps of calculation:
Step 1: Subtract one value from another; 468 – 470 = -2
Here we ignore the negative sign and the difference is 2, which is the error.
Step 2: Now we divide the error by actual value; 2/470 = 0.0042531
Multiply this value by 100; 0.0042531 × 100 = 0.42% (expressing it in two decimal points) Hence, 0.42% is the percent error.
Also Read:
Comments