The approximate value is your estimated value, and the exact value is the real value. For example, if you guess that there will be 9 oranges in a bag, but there are actually 10, 9 is the approximate value, and 10 is your exact value.
This difference is considered the magnitude of difference in approximate and estimated values. This begins to tell you how far off the results were from what they were expected to be.
In the oranges example, 9 - 10 = -1. The absolute value of -1, written as |-1|, is 1. If your result is positive, leave the number as it is. For example, 12 apples (approximate) - 10 apples (exact) = 2. The absolute value of 2 (|2|) is just 2. In statistics, taking the absolute value simply means you don’t care which direction your guess was off (either too high—positive—or too low—negative). You just want to know how far off the estimate was from the exact value.
For this example, 1/|10| = 1/10. In some cases, the exact value might be a negative number to begin with. If this is the case, you want to ignore the negative (i. e. take the absolute value of the exact number). [5] X Research source
If you cannot use a calculator, it may take using long division to convert the fraction to a decimal. Usually, about 4 or 5 digits past the decimal place will be sufficient to round to. You should always be dividing a positive number by a positive number when converting to decimal form.
In this example, 0. 1 x 100 = 10. Add the percent sign to get 10%, your percentage error.
In our example, we want to make sure that our approximation of 9 oranges is off by 10% of the actual value of oranges. 10% (10% = 0.
- of 10 oranges is 1 (0. 1 x 10 = 1). 9 oranges + 1 = 10 oranges. This confirms that the guess of 9 was indeed off by just 1 oranges or 10% of the actual value of 10 oranges.
