Worksheet on percent error word problems for math practice.

To solve the problems involving percent error, we use the formula for percent error:

\[
\text{Percent Error} = \left| \frac{\text{Experimental Value} - \text{Actual Value}}{\text{Actual Value}} \right| \times 100
\]

Let's solve each problem step by step.

---

Problem 1:

Gabrielle calculated the volume of the cube as 125 cubic feet. The actual volume of the cube is 184 cubic feet. What was the percent error in Gabrielle's calculation?

#### Step-by-Step Solution:
1. Identify the values:
- Experimental Value (Gabrielle's calculation): \( 125 \) cubic feet
- Actual Value: \( 184 \) cubic feet

2. Apply the percent error formula:
\[
\text{Percent Error} = \left| \frac{125 - 184}{184} \right| \times 100
\]

3. Calculate the difference:
\[
125 - 184 = -59
\]

4. Take the absolute value:
\[
\left| -59 \right| = 59
\]

5. Divide by the actual value:
\[
\frac{59}{184} \approx 0.32065
\]

6. Multiply by 100 to get the percentage:
\[
0.32065 \times 100 \approx 32.1
\]

#### Final Answer:
\[
\boxed{32.1}
\]

---

Problem 2:

Fiona uses a thermometer to measure the boiling point of methanol and finds it to be 70 degrees Celsius. But the actual boiling point is 64.7 degrees Celsius. What is Fiona's percent error?

#### Step-by-Step Solution:
1. Identify the values:
- Experimental Value (Fiona's measurement): \( 70 \) degrees Celsius
- Actual Value: \( 64.7 \) degrees Celsius

2. Apply the percent error formula:
\[
\text{Percent Error} = \left| \frac{70 - 64.7}{64.7} \right| \times 100
\]

3. Calculate the difference:
\[
70 - 64.7 = 5.3
\]

4. Take the absolute value:
\[
\left| 5.3 \right| = 5.3
\]

5. Divide by the actual value:
\[
\frac{5.3}{64.7} \approx 0.0819
\]

6. Multiply by 100 to get the percentage:
\[
0.0819 \times 100 \approx 8.2
\]

#### Final Answer:
\[
\boxed{8.2}
\]

---

Problem 3:

Ken thought that the distance between his new home and work was 32 miles. Upon verifying it, he found the distance was 41.5 miles. Find Ken's percent error.

#### Step-by-Step Solution:
1. Identify the values:
- Experimental Value (Ken's estimate): \( 32 \) miles
- Actual Value: \( 41.5 \) miles

2. Apply the percent error formula:
\[
\text{Percent Error} = \left| \frac{32 - 41.5}{41.5} \right| \times 100
\]

3. Calculate the difference:
\[
32 - 41.5 = -9.5
\]

4. Take the absolute value:
\[
\left| -9.5 \right| = 9.5
\]

5. Divide by the actual value:
\[
\frac{9.5}{41.5} \approx 0.2289
\]

6. Multiply by 100 to get the percentage:
\[
0.2289 \times 100 \approx 22.9
\]

#### Final Answer:
\[
\boxed{22.9}
\]

---

Problem 4:

Yvonne is training for the marathon. She calculates to see whether she can cover 9 miles in 10 minutes. But she completes the distance in 8 minutes. What is the percent error in Yvonne's calculation?

#### Step-by-Step Solution:
1. Identify the values:
- Experimental Value (Yvonne's estimate): \( 10 \) minutes
- Actual Value: \( 8 \) minutes

2. Apply the percent error formula:
\[
\text{Percent Error} = \left| \frac{10 - 8}{8} \right| \times 100
\]

3. Calculate the difference:
\[
10 - 8 = 2
\]

4. Take the absolute value:
\[
\left| 2 \right| = 2
\]

5. Divide by the actual value:
\[
\frac{2}{8} = 0.25
\]

6. Multiply by 100 to get the percentage:
\[
0.25 \times 100 = 25
\]

#### Final Answer:
\[
\boxed{25}
\]

---

Problem 5:

Derek filled the pitcher with 8 fluid ounces of lemonade. What was the percent error if the actual measurement was 10 fluid ounces?

#### Step-by-Step Solution:
1. Identify the values:
- Experimental Value (Derek's measurement): \( 8 \) fluid ounces
- Actual Value: \( 10 \) fluid ounces

2. Apply the percent error formula:
\[
\text{Percent Error} = \left| \frac{8 - 10}{10} \right| \times 100
\]

3. Calculate the difference:
\[
8 - 10 = -2
\]

4. Take the absolute value:
\[
\left| -2 \right| = 2
\]

5. Divide by the actual value:
\[
\frac{2}{10} = 0.2
\]

6. Multiply by 100 to get the percentage:
\[
0.2 \times 100 = 20
\]

#### Final Answer:
\[
\boxed{20}
\]

---

Final Answers:

1. \(\boxed{32.1}\)
2. \(\boxed{8.2}\)
3. \(\boxed{22.9}\)
4. \(\boxed{25}\)
5. \(\boxed{20}\)