 ## How to Solve Percent Error

Percent Error is a mathematical concept used in statistics and science to determine the accuracy of an experimental or observed value in comparison to a true or accepted value. It is essentially a measure of how off a particular measurement or calculation might be from the actual or expected value. The percent error formula involves subtracting the true value from the experimental value, dividing the result by the true value, and then multiplying by 100 to convert it to a percentage. A higher percent error means a larger deviation from the true value, indicating a lesser degree of accuracy.

## Step 1: Understand Percent Error

Percent Error is a statistical concept used to compare the accuracy of an experimental value to a true or accepted value. It is often used in science to report the difference between experimental values and expected values.

The formula to calculate percent error is:

$\text{Percent Error} = \frac{{(\text{Observed} - \text{Expected})}}{{\text{Expected}}} * 100$

## Step 2: Identify Your Values

Identify the Observed (Experimental) and Expected (True) values in the problem. The Observed value is the result that you obtain from your experiment or test, while the Expected value is the theoretical, known, or accepted value.

## Step 3: Subtract the Expected Value from the Observed Value

Subtract the Expected value from the Observed value. This difference represents the error in the experiment.

## Step 4: Divide by the Expected Value

Next, divide the result from step 3 by the Expected value. This gives you the fractional error.

## Step 5: Multiply by 100 to Get Percentage

Multiply the result from step 4 by 100. This converts the fractional error into a percentage, providing your percent error.

## Step 6: Consider the Result's Significance

Interpret the result. A high percent error indicates a large deviation from the expected value, suggesting that the experimental design or execution may need to be reviewed.

Keep in mind that in some fields, the absolute value of the result is taken to discard the direction of the error. This depends on whether overestimation or underestimation impacts the overall interpretation of the data.

### Example

Suppose you're conducting an experiment where the expected or "true" value is 150 units.

In your experiment, the observed value turns out to be 135 units.

We can now calculate the percent error using the formula:

$\text{Percent Error} = \frac{{(\text{Observed} - \text{Expected})}}{{\text{Expected}}} * 100$

Plugging in our values:

$\text{Percent Error} = \frac{{(135 - 150)}}{{150}} * 100$

First, subtract 150 from 135 to get -15. This is your error, which is negative because the observed value is less than the expected value.

Next, divide this -15 by the expected value of 150. This equals -0.1.

Finally, multiply -0.1 by 100 to convert it to a percentage. This equals -10%.

So, the percent error in this case is -10%, indicating that the observed value was 10% less than the expected value.

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