Percent Error Examples

Example 1: The actual length of a straight line is 8cm and when we measured with a scale it was 7cm (Wrong value) due to some marginal error. What is the percentage error?

Solution:

Given,

• Measured value = 7 cm
• Actual Value = 8 cm

Percent Error(PE) = (|Measured Value-Actual Value| / Actual Value) x 100

⇒ PE = (|7-8| / 8) x 100

⇒ PE = (|-1| / 8) x 100

⇒ PE = (1/8) x 100

⇒ PE = 12.5%

So, Percent Error is 12.5%

Example 2: What is the percentage error if the measured value is 40cm and the Actual value is 50cm?

Solution:

Given,

• Measured Value = 40 cm
• Actual Value = 50 cm

Percent Error = (|Measured Value-Actual Value| / Actual Value) x 100

⇒ PE = (|40-50| / 50) x 100

⇒ PE = (|-10| / 50) x 100

⇒ PE = (10/50) x 100

⇒ PE = 20%

So, Percent Error is 20%

Example 3: A scale measures wrongly a value as 15 cm due to some marginal errors. Find the percentage error if the actual measurement of the value is 14 cm.

Solution:

Given,

• Measured Value = 15 cm
• Actual Value = 14 cm

Percent Error(PE) = ( |Measured Value-Actual Value| / Actual Value ) x 100

⇒ PE = ( |15-14| / 14 ) x 100

⇒ PE = ( |1| / 14 ) x 100

⇒ PE = 100/14

⇒ PE = 7.14%

So, Percent Error is 7.14%

Example 4: What is the percentage error if the measured value is 11cm and the Actual value is 10cm?

Solution:

Given,

• Measured Value = 11 cm (Wrongly Measured)
• Actual Value = 10 cm (Exact value)

Percent Error(PE) = ( |Measured Value-Actual Value| / Actual Value ) x 100

⇒ PE = ( |11-10| / 10 ) x 100

⇒ PE = ( |1| / 10 ) x 100

⇒ PE = 100/10

⇒ PE = 10%

So, Percent Error is 10%

Example 5: Find the percentage error if the wrongly measured value is 100 cm and the Actual value is 105 cm?

Solution:

Given,

• Wrongly Measured Value = 100 cm
• Actual Value = 105 cm

Percent Error(PE) = (|Measured Value-Actual Value| / Actual Value) x 100

⇒ PE = (|100-105| / 105) x 100

⇒ PE = (|-5| / 105) x 100

⇒ PE = (5/105) x 100

⇒ PE = 100/21

⇒ PE = 4.76%

So, Percentage Error is 4.76%

Percent Error Formula is the percentage difference between the actual value and the measured value in any measurement. Percent Error is very useful because in all the measuring and manufacturing processes there is a possibility of slight error because of Human Error then the percent error is what tells us how a measurement differs from the original or estimated value.

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