### Percent Error

```Percent Error
Percent Error
The percent error can be determined when the
experimental value is compared to the accepted value
according to the equation below:
What you got.
A percent error can be either positive or negative.
If the measured value is greater than the accepted
value, the difference (measured value – accepted
value) will be positive, and the percent error will be
positive.
If the measured value is less than the accepted
value, the difference will be negative and the
percent error will be negative.
Example:
The accepted value for the density of copper is 8.93 g/cm3. In a
laboratory setting, three students are asked to experimentally
determine the density of copper. Their results are
Student 1: 8.91 g/cm3
Student 2: 8.23 g/cm3
Student 3: 8.99 g/cm3
Calculate the percent error associated with each student’s
reported density.
Experimental value: Student 1: 8.91 g/cm3
Accepted value: 8.93 g/cm3
( 8.91 g/cm3
-
8.93 g/cm3 )
X 100
=
-0.2% error
8.93 g/cm3
Always put a
box around
Note that there are no units associated with percent error; g/cm3, present in both
numerator and denominator, cancel.
Experimental value: Student 2: 8.23 g/cm3
Accepted value: 8.93 g/cm3
( 8.23 g/cm3
-
8.93 g/cm3 )
X 100
=
-7.8%error
8.93 g/cm3
Always put a
box around
Experimental value: Student 3: 8.99 g/cm3
Accepted value: 8.93 g/cm3
( 8.99 g/cm3
-
8.93 g/cm3 )
X 100
=
0.7% error
8.93 g/cm3
Always put a
box around
Problems
1. A student calculated the volume of a test tube
to be 10.3 mL. The true volume is 10.0mL.
( 10.3 mL
-
10.0 mL
)
X 100
10.0 mL
=
3% error
2. A student determines the density of gold to
be 18.98 g/L. The true density of gold is 19.30 g/L.
( 18.98 g/L
-
19.30 g/L )
X 100
19.30 g/L
=
-1.66% error
3. An equation was solved using 299,000,000 m/s as the speed of
light. Actually the speed of light in a vacuum is
exactly 299,792,458 m/s.
( 299,000,000 m/s
-
299,792,458 m/s )
X 100 =
299,792,458 m/s
-0.26434 % error
4. A group of students using a triple beam balance found the mass of a
copper sample to be 2.40 g. The actual mass of the copper sample
is 2.41 g.
( 2.40 g
-
2.41 g )
X 100
2.41 g
=
-0.415% error
5. Working in the laboratory, a student find the density of a piece of
pure aluminum to be 2.85 g. The accepted value for the
density of aluminum is 2.69 g.
( 2.85 g
-
2.69 g )
X 100
2.69 g
=
5.95% error
6. A group of students using a triple beam balance found the mass of an
aluminum sample to be 1.90 g. The actual mass of the aluminum
sample is 2.01 g.
( 1.90 g
-
2.01 g )
X 100
2.01 g
=
-5.47% error
7. A student experimentally determines the specific heat of water to
be 4.29 J/g Co. He then looks up the specific heat of water
on a reference table and finds that is 4.18 J/g Co.
( 4.29 J/g
-
4.18 J/g )
X 100
4.18 J/g
=
2.63% error
8. A student takes an object with an accepted mass of 200.00 grams
and masses it on his own balance. He records the mass of the object
as 196.5 g.
( 196.5 g
-
200.00 g )
X 100
200.00 g
=
-1.75% error
9. A student measured the length of a line to be 23 cm long.
The actual length of the line is 23.101 cm long.
( 23 cm
-
23.101 cm )
X 100
23.101 cm
=
-0.437% error
10. A person was traveling 65 mph in a 55 mph zone. After being
stopped by an officer, the person claimed his speedometer said
55 mph not 65 mph.
( 65 mph
-
55 mph
)
X 100
55 mph
=
18% error
```