Percent Error Worksheet with Answer Key (Free, Printable)

1.

Let

M

be the measured value and

A

the actual value. Which formula gives the percent error?

a) $|M - A| \times 100\%$
b) $\frac{A}{M} \times 100\%$
c) $\frac{|M - A|}{M} \times 100\%$
d) $\frac{|M - A|}{A} \times 100\%$

Answer: $\frac{|M - A|}{A} \times 100\%$

Percent error divides the absolute error $|M - A|$ by the actual value $A$ and multiplies by $100\%$ .

2.

A board is actually 50 cm long. You measure it as 45 cm. What is the percent error? Give your answer in %.

Answer: 10

$\frac{|45 - 50|}{50} \times 100\% = \frac{5}{50} \times 100\% = 10\%$

3.

A test weight has an actual mass of 50 g. A scale shows 52 g. What is the absolute error?

a)2 g
b)-2 g
c)0.04 g
d)4 g

Answer: 2 g

$|52 - 50| = 2$ , so the absolute error is 2 g. It is always positive and keeps the unit. (The percent error would be $4\%$ .)

4.

You guess that a jar holds 240 candies. It actually holds 300. What is your percent error?

Answer: 20

What is the absolute error $|240 - 300|$ ? 60
Divide by the actual value: $60 \div 300$ 0.2
Multiply by 100. What is the percent error (in %)? 20

5.

A thermometer reads

98\ °\text{C}

in boiling water at sea level, where the actual boiling point is

100\ °\text{C}

. What is the percent error? Give your answer in %.

Answer: 2

$\frac{|98 - 100|}{100} \times 100\% = \frac{2}{100} \times 100\% = 2\%$

6.

A book is actually 20 cm wide. Lea measures 21 cm. What is her percent error?

Answer: 5

What is the absolute error in cm? 1
Divide by the actual width: $1 \div 20$ 0.05
Multiply by 100. What is the percent error (in %)? 5

7.

The actual value is 40 and the measured value is 48. Which calculation gives the percent error?

a) $\frac{48}{40} \times 100\%$
b) $\frac{8}{48} \times 100\%$
c) $\frac{8}{40}$
d) $\frac{8}{40} \times 100\%$

Answer: $\frac{8}{40} \times 100\%$

The absolute error is $|48 - 40| = 8$ . Divide by the actual value 40 and multiply by 100: $\frac{8}{40} \times 100\% = 20\%$ . $\frac{8}{40}$ alone is only the decimal $0.2$ .

8.

Noah guesses that 75 people will come to a party. Exactly 60 people come. What is his percent error? Give your answer in %.

Answer: 25

$\frac{|75 - 60|}{60} \times 100\% = \frac{15}{60} \times 100\% = 25\%$ . Dividing by 75 would give $20\%$ , which is wrong.

9.

In a pendulum lab you measure gravity as

9.32\ \text{m/s}^2

. The accepted value is

9.81\ \text{m/s}^2

. What is the percent error, rounded to one decimal place?

a)5.3%
b)4.99%
c)5.0%
d)4.9%

Answer: 5.0%

$|9.32 - 9.81| = 0.49$ and $\frac{0.49}{9.81} \times 100\% = 4.9949\ldots\%$ . The second decimal is 9, so round up: $5.0\%$ . $4.9\%$ cuts the digits off instead of rounding, $4.99\%$ has two decimal places, and $5.3\%$ comes from dividing by $9.32$ .

10.

Zoe guesses that a box holds 90 buttons. It actually holds 40. What is her percent error?

a)50%
b)225%
c)55.6%
d)125%

Answer: 125%

$\frac{|90 - 40|}{40} \times 100\% = \frac{50}{40} \times 100\% = 125\%$ . $55.6\%$ comes from dividing by 90, which is the wrong reference.

11.

Kai measures a 25 m swimming pool as 25.5 m. Lena measures a 5 m rope as 5.5 m. How many times larger is Lena's percent error than Kai's?

Answer: 5

What is Kai's percent error (in %)? 2
What is Lena's percent error (in %)? 10
How many times larger is Lena's percent error? 5

12.

A bottle actually holds 2.5 liters. A measuring jug shows 2.4 liters. What is the percent error of the jug? Give your answer in %.

Answer: 4

$\frac{|2.4 - 2.5|}{2.5} \times 100\% = \frac{0.1}{2.5} \times 100\% = 0.04 \times 100\% = 4\%$

13.

A map app estimates that a walk will take 68 minutes. The walk actually takes 80 minutes. What is the app's percent error?

Answer: 15

What is measured minus actual, $68 - 80$ ? -12
What is the absolute error $|-12|$ ? 12
Divide by the actual time: $12 \div 80$ 0.15
Multiply by 100. What is the percent error (in %)? 15

14.

A student measures the density of copper as

8.512\ \text{g/cm}^3

. The accepted value is

8.96\ \text{g/cm}^3

. What is the percent error?

Answer: 5

What is the absolute error $|8.512 - 8.96|$ ? 0.448
Divide by the accepted value: $0.448 \div 8.96$ 0.05
Multiply by 100. What is the percent error (in %)? 5

15.

The actual value is 80. A measurement has a percent error of 5%, and it is smaller than the actual value. What was the measured value?

Answer: 76

The absolute error is $0.05 \times 80 = 4$ . The measurement is too small, so it is $80 - 4 = 76$ . Check: $\frac{|76 - 80|}{80} \times 100\% = 5\%$ .

16.

A class measures the speed of sound as

352\ \text{m/s}

. The accepted value is

343\ \text{m/s}

. Find the percent error rounded to two decimal places, then rounded to the nearest whole percent.

Answer: 3

What is the absolute error in m/s? 9
Compute $9 \div 343 \times 100$ and round to two decimal places 2.62
Now round the same result to the nearest whole percent 3

17.

Ana measured 40, but the actual value is 50. She wrote

\frac{|40 - 50|}{40} \times 100\% = 25\%

. What is the correct percent error?

a)25%
b)20%
c)80%
d)10%

Answer: 20%

Ana divided by the measured value. Correct: $\frac{|40 - 50|}{50} \times 100\% = \frac{10}{50} \times 100\% = 20\%$ .

18.

The actual mass of a parcel is 250 g. A scale has a percent error of 8% and shows too much. What does the scale show?

Answer: 270

Divide 8 by 100 to write the percent error as a decimal: $8 \div 100$ 0.08
What is the absolute error in grams, $0.08 \times 250$ ? 20
The scale shows too much. What does it show, in grams? 270