Percent Error

Percentage error

LO: Calculate percentage error in a measurement.

Error does not necessarily mean mistake

Errors arise because no measurement can be absolutely
accurate or exact.

Error

The difference between an estimated or approximate
value and the exact value is called the error

Measuring instruments and human limitations cause
measurements to deviate from the “exact values”.

Error = vA - vE

Where vA is the approximate value

and vE is the exact value

Example 1:
Leslie and Alfred each went to a basketball match.

Error

Calculate the errors Leslie and Alfred made in their estimations.

In the match that Leslie attended there were 1450 people
and Leslie estimated that there were 1300.

In the match that Alfred attended there were 1950
people and Alfred estimated that there were 1800.

Alfred:

Exact value: 1950
Approximate value: 1800

Error = vA - vE
Error = 1800 - 1950

Error = -150

Leslie:

Exact value: 1450
Approximate value: 1300

Error = vA - vE
Error = 1300 - 1450

Error = -150

​Note: Approximate is the same as esitmated.

Error

Error = -150

Leslie:

Error = -150

Alfred:

Leslie and Alfred made the same error.

However, Alfred’s estimate is more accurate.

Why would we say so?.

Error

Error = -150

Leslie:

Error = -150

Alfred:

If we calculate the percentage error
we can see that there is a difference..

Percentage Error =

Alfred:

vE = 1950
vA = 1800

vE = 1450

Leslie:

vA = 1300

The bars | | mean that is the modulus, which means the value will be always positive. It represents the absolute value. The percentage error will ALWAYS be POSITIVE.

Leslie:

Alfred:

Percentage Error = 10.3%

Percentage Error = 7.69%

​Find this formula on your formula sheets! You will never have to memorize formulas!

​Alfred
had a
lower %
error.

Example 2: The size of the angle A is 34.6°. Fahad
measure the angle A with his protractor and found that
the size was 34°. Find the percentage error made by
Fahad when measuring the angle A.

Error

Calculate the errors Fahad made in his estimation.

vE = 34.6

vA = 34

Percentage Error =

Percentage Error = 1.73%

And now it is your turn!
Record your work on paper.
If you get the answer incorrect,
revisit your work and make corrections.
You can retake this Quizizz
as many times as you like!
Go for the 100%!

Multiple Choice

An object is measured to be 3.12 g.  The exact value is 4.50 g.  What is the percentage error for this measurement correct to 3 significant figures?

• 43.1%

• 30.7%

• 30.666%

• 25.1%

Multiple Choice

A chemist measured the amount of caffeine in a new energy drink called FlipOUT to be 84.20 mg. The correct amount of caffeine is 87.10 mg. Calculate the percent error correct to 3 significant figures.

• 9.6%

• 3.4%

• 3.33%

• 0.033%

Multiple Choice

The deer population is estimated to be 17,600 in northern Illinois, but an actual count was 21,300. What is the percent error correct to 3 significant figures?

• 21%

• 17.37%

• 17.4%

• 21.02%

Multiple Choice

The students measured length during a science experiment, they got 12 cm. But the actual measurement was 14.25 cm. What was the percent error correct to 3 significant figures?

• 15.79%

• 18.75%

• 15.8%

• 18%

Multiple Choice

Round 0.010229 to four sig figs

• 0.0102

• 0.010

• 0.01023

• 0.01022

Multiple Choice

Round 1047.78 to three sig figs

• 1048

• 105

• 1050

• 1050.00

Multiple Choice

How many significant figures are in the number 0.01630

• 6

• 3

• 4

• 5

Multiple Choice

What is 78.5 rounded to one significant figure?

• 79

• 8

• 78

• 80