Measures and solids · Ages 13–14

Absolute, relative and percentage errors worksheet

Part of: Errors in measurement

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Measures and solids · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A towel's length is measured as 29 cm to the nearest 1 cm. What is the relative error of this measurement, as a fraction?
Answer in simplest form
Answer:
2.A parcel is weighed as 36.5 kg to the nearest 0.5 kg. What is the greatest absolute error of this measurement, in kg?
Answer:
3.A parcel is weighed as 6.7 kg to the nearest 0.1 kg. What is the greatest absolute error of this measurement, in kg?
Answer:
4.A plant is 10 cm tall, to the nearest 1 cm. What is the percentage error of this measurement?
Answer:
5.A pen is 40 cm long, to the nearest 0.1 cm. The greatest absolute error is cm, the relative error , the percentage error %.
Fill in each blank
Answer:
6.A pen is 4 cm long, to the nearest 0.1 cm. The greatest absolute error is cm, the relative error , the percentage error %.
Fill in each blank
Answer:
7.A strip of wood is measured to the nearest 1 cm with a percentage error of 2%. What length was measured, in cm?
Answer:
8.A measurement's true value x lies in 153 ≤ x < 155. What is its relative error, as a fraction?
Answer in simplest form
Answer:
9.A measurement's true value x lies in 7.35 ≤ x < 7.45. What is its relative error, as a fraction?
Answer in simplest form
Answer:

10.Of these four measurements, which is the most accurate (the smallest relative error)?
- A. 21 mm (to the nearest 1 mm)
- B. 93 mm (to the nearest 10 mm)
- C. 452 mm (to the nearest 1 mm)
- D. 47 mm (to the nearest 10 mm)
Choose the right answer
Answer:
11.Measurement A: 11 cm, to the nearest 0.1 cm; measurement B: 676 cm, to the nearest 10 cm. A is more accurate than B.
True or false?
Answer:
12.Measurement A: 50 cm, to the nearest 0.1 cm; measurement B: 782 cm, to the nearest 10 cm. A is more accurate than B.
True or false?
Answer:

13.Ming weighs a sack of rice on a scale as 100 kg, to the nearest 1 kg. What is the percentage error of this measurement?
Working:
Answer:
14.A measurement correct to the nearest 5 cm has a relative error of 1125. What value was measured, in cm?
Working:
Answer:
15.A track is 61 m long, to the nearest 0.1 m; a pen is 23 cm long, to the nearest 0.1 cm. Which measurement is more accurate?
- A. Equally: both are to the nearest 0.1
- B. The pen: its greatest absolute error is smaller
- C. The track: its relative error is smaller
- D. The pen: its unit, cm, is smaller than m
Choose the right answer
Working:
Answer:
16.A cup is 8 cm tall, to the nearest 1 cm. Find the percentage error: put the steps in order.
- A. Percentage error = 0.0625 × 100% = 6.25%
- B. Relative error = 0.5 ÷ 8 = 0.0625
- C. Greatest absolute error = 1 ÷ 2 = 0.5
Write the letters in the right order
Working:
Answer:
17.Ming measures a rope as 500 cm long, to the nearest 10 cm; Chi-keung measures a coin as 2.4 cm across, to the nearest 0.1 cm. Ming's measurement is more accurate than Chi-keung's.
True or false?
Working:
Answer:
18.A cake needs 125 g of flour, weighed on a kitchen scale to the nearest 10 g. The greatest absolute error is g, the relative error , the percentage error %.
Fill in each blank
Working:
Answer:

Show the answers and working

Absolute, relative and percentage errors worksheet: Answers and working

1. 158
The greatest absolute error is 0.5 cm, so the relative error = 0.5 ÷ 29 = 158.
2. 0.25 kg
The greatest absolute error is half the unit: 0.5 ÷ 2 = 0.25 kg.
3. 0.05 kg
The greatest absolute error is half the unit: 0.1 ÷ 2 = 0.05 kg.
4. 5%
Relative error 0.5 ÷ 10 = 0.05, percentage error = 0.05 × 100% = 5%.
5. 0.05, 0.00125, 0.125
0.1 ÷ 2 = 0.05 cm; 0.05 ÷ 40 = 0.00125; 0.00125 × 100% = 0.125%.
6. 0.05, 0.0125, 1.25
0.1 ÷ 2 = 0.05 cm; 0.05 ÷ 4 = 0.0125; 0.0125 × 100% = 1.25%.
7. 25 cm
Percentage error = 0.5 ÷ value × 100%, so the value = 0.5 × 100 ÷ 2 = 25 cm.
8. 1154
The value is halfway: (153 + 155) ÷ 2 = 154; the greatest absolute error 155 − 154 = 1; relative error 1 ÷ 154 = 1154.
9. 1148
The value is halfway: (7.35 + 7.45) ÷ 2 = 7.4; the greatest absolute error 7.45 − 7.4 = 0.05; relative error 0.05 ÷ 7.4 = 1148.

10. C. 452 mm (to the nearest 1 mm)
Work out each relative error = half the unit ÷ the value: the smallest is 1904. A small absolute error alone doesn't make a measurement the most accurate.
11. True
Compare the relative errors: A's is 0.05 ÷ 11 = 1220, B's 5 ÷ 676 = 5676; the smaller is the more accurate.
12. True
Compare the relative errors: A's is 0.05 ÷ 50 = 11000, B's 5 ÷ 782 = 5782; the smaller is the more accurate.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 0.5%
The greatest absolute error is 0.5 kg: 0.5 ÷ 100 × 100% = 0.5%.
14. 312.5 cm
The greatest absolute error is 5 ÷ 2 = 2.5 cm; relative error = 2.5 ÷ value = 1125, so the value = 2.5 × 125 = 312.5 cm.
15. C. The track: its relative error is smaller
Relative errors: the track 0.05 ÷ 61 = 11220, the pen 0.05 ÷ 23 = 1460; the track's is smaller, so it is more accurate.
16. C → B → A
The greatest absolute error, then ÷ the value, then × 100%: 6.25%.
17. True
Compare the relative errors: the rope's 5 ÷ 500 = 1100, the coin's 0.05 ÷ 2.4 = 148; the smaller is the more accurate.
18. 5, 0.04, 4
10 ÷ 2 = 5 g; 5 ÷ 125 = 0.04; 0.04 × 100% = 4%.

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