Error is the difference between a measured value and the actual value.

Percentage error is the ratio of the measured value to the actual value. Mathematically, it is represented as:

$P.E=\frac{Error}{actual value}\times100$

Using this fact, let's solve the following examples.

__Example 1__

__Example 1__

A pen is 18cm long, Daniel estimated its length to be 20cm. Find the percentage error in the conclusion

**Solution:**

$Error=20-18=2$

$P.E=\frac{2}{18}\times100$

$P.E=11.1\%$

__Example 2__

Instead of recording the 1.23cn of the radius of a tube, a student recorded 1.32cm. Find the percentage error correct to one decimal.

**Solution:**

$Error=1.32-1.23=0.09$

$P.E=\frac{0.09}{1.23}\times100$

$P.E=7.3\%$

__Example 3__

While doing his physics practical, Samuel recorded a reading of 1.12cm instead of 1.21cm. Calculate his percentage error?

**Solution:**

$Error=1.21-1.12=0.09$

$P.E=\frac{0.09}{1.21}\times100$

$P.E=7.44\%$

__Example 4__

Mrs Daniel sold a book for €7.5 instead of €12.75. Calculate his percentage error correct to one decimal place.

**Solution:**

$Error=12.75-7.5=5.25$

$P.E=\frac{5.25}{12.75}\times100$

$P.E=41.2\%$

__Example 5__

A bricklayer measured the length of a walk and obtained 4.1cm. If the actual length of the walk is 4.25cm, Calculate his percentage error.

**Solution:**

$P.E=\frac{4.25-4.1}{4.25}\times100=3.53\%$

__Example 6__

A stick of length 1.75m was measured by a boy as 1.8cm. Find the percentage error in his measurement

**Solution:**

$P.E=\frac{0.05}{1.75}\times100=2.9\%$

__Example 7__

James estimated his transport fare as €190 instead of €200. Find the percentage error?

**Solution:**

$P.E=\frac{200-190}{200}\times100=\frac{10}{200}\times100=5\%$

READ ALSO: **SOLVING PROPORTION**

__Example 8__

Rather than subtract 15 from a certain number, I mistakenly added 25 and got 145. Find the percentage error

**Solution:**

The actual error is 40 because 25 which should otherwise not be added, was added and 15, which was supposed to be subtracted, was not subtracted.

The actual number is 105 because if we remove subtract 25 added, and remove 15 that is supposed to be subtracted.

$\frac{40}{105}×100=38.1\%$

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