Given below are some examples based on percentage error:

**Example 1:** Calculate the percentage error if the approximate value and observed value is 45 and 35 respectively?

**Solution:**

__Given:__ Approximate value = 45,

Observed value = 35

Percentage Error = $\frac{|Approximate\ Value - Observed\ Value|}{Observed\ Value|}$ $\times$ 100 %

= $\frac{|45 - 35|}{|35|}$

= $\frac{|10|}{|35|}$ $\times$ 100 %

= 28.57 %

Percentage error is found to be 28.57%.

**Example 2:** A measuring scale wrongly measures an value as 9 cm due to some marginal errors. Calculate the percentage error if the actual measurement of the value is 15.3 cm?

**Solution:**

__Given:__ Approximate value = 9cm

Observed value = 15.3 cm

Percentage Error = $\frac{|Approximate\ Value - Observed\ Value|}{Observed\ Value|}$ $\times$ 100 %

= $\frac{|9 - 15.3|}{|15.3|}$

= $\frac{|-63|}{|15.3|}$ $\times$ 100 %

= 41.18 %

Percentage error is found to be 41.18%.

**Example 3:** According to a study in a report it was mentioned that the car parking held 5600 cars, but after careful investigation it was found that there were 5650 parking spaces. What is the percentage error?

**Solution:** Given Approximate Value : 5600 cars

Observed Value = 5650 cars

Percentage Error = $\frac{|Approximate\ Value - Observed\ Value|}{Observed\ Value|}$ $\times$ 100 %

= $\frac{|5600 - 5650 |}{|5650|}$

= $\frac{|-50|}{|5650|}$ $\times$ 100 %

= 0.885 %

For the given problem, percentage error is found to be 0.885%.