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Percent Error worksheet

Grade 7 · CCSS 7.RP.A.3

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Measured (experimental) value: 55
- True (theoretical) value: 52
- Report as: Signed (+ over, − under)
Find: Percent error (signed)
Answer
2.
Problem 2.
- Measured (experimental) value: 45
- True (theoretical) value: 40
- Report as: Signed (+ over, − under)
Find: Percent error (signed)
Answer
3.
Problem 3.
- Measured (experimental) value: 48
- True (theoretical) value: 56
- Report as: Absolute (always positive)
Find: Percent error
Answer
4.
Problem 4.
- Measured (experimental) value: 62
- True (theoretical) value: 60
- Report as: Absolute (always positive)
Find: Percent error
Answer
5.
Problem 5.
- Measured (experimental) value: 47.5
- True (theoretical) value: 45
- Report as: Absolute (always positive)
Find: Percent error
Answer
6.
Problem 6.
- Measured (experimental) value: 40
- True (theoretical) value: 58
- Report as: Absolute (always positive)
Find: Percent error
Answer
7.
Problem 7.
- Measured (experimental) value: 75
- True (theoretical) value: 74
- Report as: Absolute (always positive)
Find: Percent error
Answer
8.
Problem 8.
- Measured (experimental) value: 62.5
- True (theoretical) value: 55
- Report as: Absolute (always positive)
Find: Percent error
Answer
9.
Problem 9.
- Measured (experimental) value: 47.5
- True (theoretical) value: 40
- Report as: Signed (+ over, − under)
Find: Percent error (signed)
Answer
10.
Problem 10.
- Measured (experimental) value: 50
- True (theoretical) value: 38
- Report as: Signed (+ over, − under)
Find: Percent error (signed)
Answer

Answer key: Percent Error worksheet

1. Percent error (signed): 5.77%
1. Find the error: subtract the true value from the measured value
  $55 - 52$ $= 3$
2. Divide by the size of the true value to get the relative error
  $\frac{3}{52}$ $= 0.0576923077$
3. Multiply by 100 to express it as a percent
  $0.0576923077 \times 100$ $= 5.7692307692%$
2. Percent error (signed): 12.5%
1. Find the error: subtract the true value from the measured value
  $45 - 40$ $= 5$
2. Divide by the size of the true value to get the relative error
  $\frac{5}{40}$ $= 0.125$
3. Multiply by 100 to express it as a percent
  $0.125 \times 100$ $= 12.5%$
3. Percent error: 14.29%
1. Find the error: subtract the true value from the measured value
  $48 - 56$ $= −8$
2. Take the absolute value, since only the size of the error matters here
  $| −8 |$ $= 8$
3. Divide by the size of the true value to get the relative error
  $\frac{8}{56}$ $= 0.1428571429$
4. Multiply by 100 to express it as a percent
  $0.1428571429 \times 100$ $= 14.2857142857%$
4. Percent error: 3.33%
1. Find the error: subtract the true value from the measured value
  $62 - 60$ $= 2$
2. Take the absolute value, since only the size of the error matters here
  $| 2 |$ $= 2$
3. Divide by the size of the true value to get the relative error
  $\frac{2}{60}$ $= 0.0333333333$
4. Multiply by 100 to express it as a percent
  $0.0333333333 \times 100$ $= 3.3333333333%$
5. Percent error: 5.56%
1. Find the error: subtract the true value from the measured value
  $47.5 - 45$ $= 2.5$
2. Take the absolute value, since only the size of the error matters here
  $| 2.5 |$ $= 2.5$
3. Divide by the size of the true value to get the relative error
  $\frac{2.5}{45}$ $= 0.0555555556$
4. Multiply by 100 to express it as a percent
  $0.0555555556 \times 100$ $= 5.5555555556%$
6. Percent error: 31.03%
1. Find the error: subtract the true value from the measured value
  $40 - 58$ $= −18$
2. Take the absolute value, since only the size of the error matters here
  $| −18 |$ $= 18$
3. Divide by the size of the true value to get the relative error
  $\frac{18}{58}$ $= 0.3103448276$
4. Multiply by 100 to express it as a percent
  $0.3103448276 \times 100$ $= 31.0344827586%$
7. Percent error: 1.35%
1. Find the error: subtract the true value from the measured value
  $75 - 74$ $= 1$
2. Take the absolute value, since only the size of the error matters here
  $| 1 |$ $= 1$
3. Divide by the size of the true value to get the relative error
  $\frac{1}{74}$ $= 0.0135135135$
4. Multiply by 100 to express it as a percent
  $0.0135135135 \times 100$ $= 1.3513513514%$
8. Percent error: 13.64%
1. Find the error: subtract the true value from the measured value
  $62.5 - 55$ $= 7.5$
2. Take the absolute value, since only the size of the error matters here
  $| 7.5 |$ $= 7.5$
3. Divide by the size of the true value to get the relative error
  $\frac{7.5}{55}$ $= 0.1363636364$
4. Multiply by 100 to express it as a percent
  $0.1363636364 \times 100$ $= 13.6363636364%$
9. Percent error (signed): 18.75%
1. Find the error: subtract the true value from the measured value
  $47.5 - 40$ $= 7.5$
2. Divide by the size of the true value to get the relative error
  $\frac{7.5}{40}$ $= 0.1875$
3. Multiply by 100 to express it as a percent
  $0.1875 \times 100$ $= 18.75%$
10. Percent error (signed): 31.58%
1. Find the error: subtract the true value from the measured value
  $50 - 38$ $= 12$
2. Divide by the size of the true value to get the relative error
  $\frac{12}{38}$ $= 0.3157894737$
3. Multiply by 100 to express it as a percent
  $0.3157894737 \times 100$ $= 31.5789473684%$