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Error intervals practice questions with answers

Foundation and Higher · Grade 3 · Non-calculator

A second set of error intervals questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

A length is 8 cm to the nearest 0.1 cm. Give the lower bound, then the upper bound.

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Answer: 7.95, 8.05

  1. Half the unit is 0.05.
  2. The bounds are 7.95 and 8.05.
  • Method (1): Half the unit is 0.05.
  • Accuracy (1): Answer 7.95, 8.05

Question 2 Easy

A length is 200 m to the nearest 100 m. Give the lower bound, then the upper bound.

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Answer: 150, 250

  1. Half the unit is 50.
  2. The bounds are 150 and 250.
  • Method (1): Half the unit is 50.
  • Accuracy (1): Answer 150, 250

Question 3 Medium

The lower bound is 7.5 and the upper bound is 8.5. The value was rounded to the nearest whole number. What value was recorded?

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Answer: 8

  1. The recorded value is halfway between the bounds.
  2. 7.5 + 0.5.
  • Method (1): The recorded value is halfway between the bounds.
  • Accuracy (1): Answer 8

Question 4 Medium

A length is given as 6 cm to the nearest cm. How large is the error, in cm?

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Answer: 0.5

  1. The rounding unit is 1 cm.
  2. The error is half of that unit.
  • Method (1): The rounding unit is 1 cm.
  • Accuracy (1): Answer 0.5

Question 5 Hard

A distance of 10 m and a time of 2 s are both given to the nearest whole unit. What is the upper bound of the speed, in m/s?

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Answer: 7

  1. The greatest speed uses the greatest distance and the least time.
  2. 10.5 ÷ 1.5 = 7.
  • Method (1): The greatest speed uses the greatest distance and the least time.
  • Accuracy (1): Answer 7

Question 6 Hard

40 has already been rounded to the nearest 10. A second measurement is 50, also to the nearest 10. What is the least possible difference between the true values?

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Answer: 0

  1. The higher value can be as low as its lower bound.
  2. The lower value can be as high as its upper bound.
  • Method (1): The higher value can be as low as its lower bound.
  • Accuracy (1): Answer 0

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

A square is 11 cm by 11 cm, both to the nearest cm. What is the upper bound of the area?

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Answer: 132.25

  1. Each upper bound is 11.5.
  2. The area upper bound is 132.25.
  • Method (1): Each upper bound is 11.5.
  • Accuracy (1): Answer 132.25

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

A length L is 30 cm to the nearest cm. Write the error interval for L.

  1. 29.5 ≤ L < 30.5
  2. 29 ≤ L < 31
  3. 29.5 ≤ L ≤ 30.5
Show answer

29.5 ≤ L < 30.5 The result is 29.5 ≤ L < 30.5.

Check 2

A number n is 240 to the nearest 10. Write the error interval for n.

  1. 235 ≤ n < 245
  2. 230 ≤ n < 250
  3. 235 ≤ n ≤ 245
Show answer

235 ≤ n < 245 The result is 235 ≤ n < 245.

Check 3

A mass x is 8.6 kg to 1 decimal place. Write the error interval for x.

  1. 8.55 ≤ x < 8.65
  2. 8.5 ≤ x < 8.7
  3. 8.55 ≤ x ≤ 8.65
Show answer

8.55 ≤ x < 8.65 The result is 8.55 ≤ x < 8.65.

Check 4

A rope is 29 m long to the nearest metre. What is the lower bound of its length in metres?

  1. 28.5
  2. 28
  3. 29.5
Show answer

28.5 The result is 28.5.

Check 5

A length L is 34 cm to the nearest cm. Write the error interval for L.

  1. 33.5 ≤ L < 34.5
  2. 33 ≤ L < 35
  3. 33.5 ≤ L ≤ 34.5
Show answer

33.5 ≤ L < 34.5 The result is 33.5 ≤ L < 34.5.

Check 6

A number n is 280 to the nearest 10. Write the error interval for n.

  1. 275 ≤ n < 285
  2. 270 ≤ n < 290
  3. 275 ≤ n ≤ 285
Show answer

275 ≤ n < 285 The result is 275 ≤ n < 285.

Check 7

A mass x is 9.8 kg to 1 decimal place. Write the error interval for x.

  1. 9.75 ≤ x < 9.85
  2. 9.7 ≤ x < 9.9
  3. 9.75 ≤ x ≤ 9.85
Show answer

9.75 ≤ x < 9.85 The result is 9.75 ≤ x < 9.85.

Check 8

A rope is 33 m long to the nearest metre. What is the upper bound of its length in metres?

  1. 33.5
  2. 34
  3. 32.5
Show answer

33.5 The result is 33.5.

Check 9

A length L is 38 cm to the nearest cm. Write the error interval for L.

  1. 37.5 ≤ L < 38.5
  2. 37 ≤ L < 39
  3. 37.5 ≤ L ≤ 38.5
Show answer

37.5 ≤ L < 38.5 The result is 37.5 ≤ L < 38.5.

Check 10

A number n is 320 to the nearest 10. Write the error interval for n.

  1. 315 ≤ n < 325
  2. 310 ≤ n < 330
  3. 315 ≤ n ≤ 325
Show answer

315 ≤ n < 325 The result is 315 ≤ n < 325.

Check 11

A mass x is 11.0 kg to 1 decimal place. Write the error interval for x.

  1. 10.95 ≤ x < 11.05
  2. 10.9 ≤ x < 11.1
  3. 10.95 ≤ x ≤ 11.05
Show answer

10.95 ≤ x < 11.05 The result is 10.95 ≤ x < 11.05.

Check 12

A rope is 37 m long to the nearest metre. What is the lower bound of its length in metres?

  1. 36.5
  2. 36
  3. 37.5
Show answer

36.5 The result is 36.5.

Check 13

A length L is 42 cm to the nearest cm. Write the error interval for L.

  1. 41.5 ≤ L < 42.5
  2. 41 ≤ L < 43
  3. 41.5 ≤ L ≤ 42.5
Show answer

41.5 ≤ L < 42.5 The result is 41.5 ≤ L < 42.5.

Check 14

A number n is 360 to the nearest 10. Write the error interval for n.

  1. 355 ≤ n < 365
  2. 350 ≤ n < 370
  3. 355 ≤ n ≤ 365
Show answer

355 ≤ n < 365 The result is 355 ≤ n < 365.

Check 15

A mass x is 12.2 kg to 1 decimal place. Write the error interval for x.

  1. 12.15 ≤ x < 12.25
  2. 12.1 ≤ x < 12.3
  3. 12.15 ≤ x ≤ 12.25
Show answer

12.15 ≤ x < 12.25 The result is 12.15 ≤ x < 12.25.

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