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We are bound to make mistakes while measuring anything in an experiment. Most measurement inaccuracies are unavoidable. This often happens because your equipment is inaccurate, your hands shake, or your instruments cannot measure accurately or because of random errors. After detecting the causes of the first three types of errors, they can be removed, but the random errors remain. It is impossible to assign a specific cause to such errors.

When an experiment is performed numerous times, the random errors might be positive or negative. As a result, the average of many repeated experiment findings is near to the genuine value. However, there is still considerable doubt about how accurate this average is.

The percentage errors inform you how large or small your errors are. Smaller numbers indicate that you are getting nearer to the acceptable or true value. A 1% inaccuracy, for example, suggests that you were exceptionally near to the approved number, but a 48% error indicates that you were fairly far off from the genuine figure.

The percentage error formula will tell you how much these unavoidable mistakes influenced your results.

Percentage error =Absolute error/True value* 100%

## Absolute error

Absolute error is the number of errors that occur during a measurement. It aids us in understanding the level of inaccuracy being measured.

Absolute error is defined mathematically as

Absolute Error = (Measured value - Accepted x)

## Error in Relative Measurement( Relative error)

The relative error of measurement is defined as the ratio of the absolute error to the accepted measurement. The relative error expresses the extent of the absolute inaccuracy in terms of the object's actual measurement. When the true measurement of the object is unknown, the measured value is frequently used to compute the relative error.

The following is the mathematical expression for relative error:

Relative Error =Absolute Error/Accepted Value

Relative Error=measured value - actual value/actual value

### In other words, percent error is the relative error multiplied by 100

Percentage error is calculated by taking the difference between the precise and estimated values of a number, dividing it by the exact value, then multiplying it by 100 to express it as a percentage of the exact value.

## FORMULAS TO CALCULATE PERCENT ERROR

Percentage error = |Approximate value -Exact Value|/|Exact Value|* 100%

OR

Percentage Error= |accepted value -experimental value|/|accepted value| * 100%

Because accepted value is sometimes known as "true" or "theoretical" value, you may see the formula stated in somewhat various ways:

Percentage Error= |true value -experimental value|/|accepted value| * 100%

OR

Percentage Error= |theoratical value-experimental value|/|accepted value| * 100%

In all the above formulas, "|" symbols mean absolute value, so negatives become positive)

In all versions of the formula, the same thing is meant - it's just that the wording is different.

## What Is The Significance of Calculating The Percentage of Error?

1. A percentage error calculation is used to determine how near a measured value is to an actual value.

2. Percent error is always stated as a positive figure in some sectors. In others, either a positive or negative number is acceptable. The sign can be retained to see if recorded values frequently go above or below predicted values.

3. One sort of error computation is percent error. Other typical estimates include absolute and relative error. A full error analysis consists of a percentage error calculation.

## How To Apply The Percentage Error Formula To Calculate Percentage Error?

### Steps for Calculating Percent Error

- Subtract one value from another. If you omit the sign (take the absolute value), the order is irrelevant. If you're maintaining negative signs, subtract the theoretical value from the experimental value. This is your "Error."
- Divide the error by the actual value. This will result in a decimal number.
- To get the percentage multiple by 100
- To represent the percentage error value, add a percentage or percentage sign.

## Solved Examples on Percent Error

### Example 1

John measured himself and discovered that he was 5 feet tall. However, after a thorough investigation, he found that his true height was 4.5 ft. Determine the percentage error he made when measuring his height.

Solution:

Before we begin to solve the problem, let us first identify the information:

- Actual value: 4.5 feet, estimated value: 5 feet

**Step 1**: Subtract one value from the others to obtain the absolute value of the mistake.

|4.5 - 5| = 0.5 Error

**Step 2**: Subtract the mistake from the actual amount.

0.5/4.5 is 0.1111 (up to 4 decimal places)

**Step 3**: To represent the answer as a percentage, multiply the number by 100 and add the percent sign.

100 x 0.111 = 11.11

**Percent Error = 11.11 %**

### Example 2

Helen's Science class yesterday had 36 pupils. She miscounted the number of pupils in the class and entered it as 30. What is Helen's margin of error?

Solution:

The real number of pupils was 36, whereas the recorded number of students was 30.

Asolute Error = 36 - 30 = 6

Percent error =6/36 = 0.167

= 0.25 x 100 = 16.67%

Helen's percent error is 16.67%.

### Example 3

John determines the radius of a circular sheet of paper to be 20 cm long. The packaging label shows that the radius is 24 cm. Calculate the measurement error as a percentage.

Solution:

20 cm is the measured value.

Accepted measurement = 24 cm

Step 1: Subtract the measured value from the acceptable value in step one.

4 cm = 24 cm – 20 cm

Step 2: Determine the absolute value of step 1 |4 cm| = 4 cm.

Step 3: Subtract the answer from the acceptable value.

4/24 = 0.166=0.17 (by rounding off to two significant figures)

**Step 4**: To represent the answer as a percentage, multiply the number by 100 and add the percentage sign.

0.17 x 100 = 17 %

The measurement's percentage error was 17%.

## CONCLUSION

Now you know what percentage error, relative error, and absolute error are. You may very well be aware that you have a problem where you have the real value and the estimated value. Calculate the percentage error using the formula of percentage error.