Measures and solids · Ages 13–14

Errors in measurement worksheet

Covers: Upper and lower limits, Absolute, relative and percentage errors, Errors in measurement at work, Planning a 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 distance was measured to some unit, and its true value x lies in 7.55 km ≤ x < 7.65 km. What was the distance measured, in km?
Answer:
2.A measurement correct to 3 significant figures is 5.62 m. What is its lower limit, in m?
Answer:
3.A measurement has a lower limit of 1.75 mL and an upper limit of 1.85 mL. To the nearest how many mL was it measured?
Answer:
4.A towel's length is measured as 115 cm to the nearest 1 cm. What is the relative error of this measurement, as a fraction?
Answer in simplest form
Answer:
5.A rectangular sheet is 30 cm by 21 cm, each to the nearest 1 cm. Its area A lies in cm² ≤ A < cm².
Fill in each blank
Answer:
6.A triangle's sides, each to the nearest 1 cm, are 15 cm, 20 cm and 11 cm. What is the upper limit of its perimeter, in cm?
Answer:
7.A pendulum is timed for 10 swings, taking 22.6 seconds in all. On average, how many seconds does one swing take?
Answer:
8.20 identical coins are stacked, and a ruler correct to the nearest 1 mm measures the stack as 28 mm tall. One coin is mm thick, with a greatest absolute error of mm.
Fill in each blank
Answer:

9.Measurement A: 56 cm, to the nearest 0.1 cm; measurement B: 527 cm, to the nearest 1 cm. A is more accurate than B.
True or false?
Answer:
10.Of these four measurements, which is the most accurate (the smallest relative error)?
- A. 41 mm (to the nearest 10 mm)
- B. 465 mm (to the nearest 100 mm)
- C. 28 mm (to the nearest 0.1 mm)
- D. 111 mm (to the nearest 10 mm)
Choose the right answer
Answer:
11.7 books each weigh 24 g to the nearest 1 g. Their total weight could be 171.5 g.
True or false?
Answer:
12.With a ruler correct to the nearest 1 mm, a stack of identical sheets is measured and divided by the number of sheets to find one sheet's thickness. Which way gives the most accurate thickness?
- A. Measure 2 sheets
- B. Measure 80 sheets
- C. Measure 100 sheets
- D. Measure 16 sheets
Choose the right answer
Answer:

13.Ming's height is 149 cm to the nearest 1 cm. Which of these gives Ming's true height x correctly?
- A. 148.5 < x ≤ 149.5
- B. 148.5 ≤ x < 149.5
- C. 148 ≤ x < 150
- D. 148.5 ≤ x ≤ 149.5
Choose the right answer
Working:
Answer:
14.A measuring jug can only be read correct to some unit. The reading's upper limit is 387.5 mL and its lower limit 382.5 mL. The reading was mL, to the nearest mL.
Fill in each blank
Working:
Answer:
15.Ka-yee measures a rope as 490 cm long, to the nearest 10 cm; May measures a coin as 1.7 cm across, to the nearest 0.1 cm. Ka-yee's measurement is more accurate than May's.
True or false?
Working:
Answer:
16.Tsz-hin weighs a sack of rice on a scale as 80 kg, to the nearest 1 kg. What is the percentage error of this measurement?
Working:
Answer:
17.7 tiles each weigh 56 g to the nearest 1 g. Which of these could be their total weight?
- A. 388 g
- B. 395.5 g
- C. 393.25 g
- D. 396 g
Choose the right answer
Working:
Answer:
18.To measure a thin copper wire's diameter, Ka-yee winds it tightly round a pencil 50 times, and a ruler correct to the nearest 1 mm measures the coil as 32 mm long. The wire's diameter is about mm, with a greatest absolute error of mm.
Fill in each blank
Working:
Answer:

Show the answers and working

Errors in measurement worksheet: Answers and working

1. 7.6 km
The measured value sits halfway between the limits: (7.55 + 7.65) ÷ 2 = 7.6 km.
2. 5.615 m
The third significant figure of 5.62 is in the 0.01 place, so the unit is 0.01 m and half of it 0.005: 5.62 − 0.005 = 5.615 m.
3. 0.1 mL
The limits are one unit apart: 1.85 − 1.75 = 0.1 mL.
4. 1230
The greatest absolute error is 0.5 cm, so the relative error = 0.5 ÷ 115 = 1230.
5. 604.75, 655.75
Least: the lower limits multiplied, 29.5 × 20.5 = 604.75; greatest: the upper limits, 30.5 × 21.5 = 655.75 (the true area is less).
6. 47.5 cm
Each side's upper limit is 0.5 cm more, three of them 3 × 0.5: 15 + 20 + 11 + 3 × 0.5 = 47.5 cm.
7. 2.26 s
22.6 ÷ 10 = 2.26 seconds. Timing many and dividing shares the stopwatch's error among them.
8. 1.4, 0.025
28 ÷ 20 = 1.4 mm; the stack's 0.5 mm error is shared among 20 coins: 0.5 ÷ 20 = 0.025 mm.

9. True
Compare the relative errors: A's is 0.05 ÷ 56 = 11120, B's 0.5 ÷ 527 = 11054; the smaller is the more accurate.
10. C. 28 mm (to the nearest 0.1 mm)
Work out each relative error = half the unit ÷ the value: the smallest is 1560. A small absolute error alone doesn't make a measurement the most accurate.
11. False
The total lies in 7 × (24 − 0.5) = 164.5 ≤ W < 7 × (24 + 0.5) = 171.5.
12. C. Measure 100 sheets
The stack's error is always 0.5 mm, so the more sheets, the smaller each one's share: 0.5 ÷ 100 = 0.005 mm is the least.

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

13. B. 148.5 ≤ x < 149.5
Lower limit 149 − 0.5 = 148.5 (in), upper limit 149 + 0.5 = 149.5 (not in): 148.5 ≤ x < 149.5.
14. 385, 5
The reading is halfway between the limits: (382.5 + 387.5) ÷ 2 = 385; the limits are one unit apart: 387.5 − 382.5 = 5.
15. True
Compare the relative errors: the rope's 5 ÷ 490 = 198, the coin's 0.05 ÷ 1.7 = 134; the smaller is the more accurate.
16. 0.625%
The greatest absolute error is 0.5 kg: 0.5 ÷ 80 × 100% = 0.625%.
17. C. 393.25 g
The total lies in 7 × (56 − 0.5) = 388.5 ≤ W < 7 × (56 + 0.5) = 395.5.
18. 0.64, 0.01
The coil is 50 diameters long: 32 ÷ 50 = 0.64 mm; its 0.5 mm error is shared among 50 turns: 0.5 ÷ 50 = 0.01 mm.

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