Error intervals Quiz (Grade 3)

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Error intervals — Notes & Worked Examples Show / Hide

Explanation:

An error interval shows the range of possible actual values of a number before it was rounded or truncated. For a rounded measurement, find half of the degree of accuracy and subtract it for the lower bound, then add it for the upper bound.

For a value x, the error interval is always written using the inequalities LB ≤ x < UB. If a number is truncated (chopped off without rounding), the lower bound is the truncated number itself and the upper bound is the next unit up.

Example 1: A length, L cm, is 8.4 cm rounded to 1 d.p. Write down the error interval for L.

Half of 0.1 cm = 0.05 cm → LB = 8.4 − 0.05 = 8.35, UB = 8.4 + 0.05 = 8.45

Answer: 8.35 ≤ L < 8.45

Example 2: A number, y, is truncated to 2 decimal places to give 4.72. Write down the error interval for y.

Solution:

Truncated at 2 d.p. means digits after 0.01s were cut off.

Smallest possible value = 4.72

Upper bound (next hundredth up) = 4.72 + 0.01 = 4.73

Answer: 4.72 ≤ y < 4.73

One Page Guide (PDF) Error intervals Worksheets

Question 1

[2 marks]

Karim rounds a number, n, to 1 decimal place.
The result is 23.8

Complete the error interval for n.

Worked Solution & Answer

Half the unit of rounding: 0.1 ÷ 2 = 0.05 M1
Lower bound = 23.8 – 0.05 = 23.75
Upper bound = 23.8 + 0.05 = 23.85. A1

Answer: 23.75 ≤ n < 23.85

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Question 2

[2 marks]

Work out
A number, d, is rounded to 1 decimal place.
The result is 12.7
Complete the error interval for d.

Worked Solution & Answer

12.65 ⩽ d < 12.75 M1 A1

Answer: 12.65, 12.75

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Question 3 AQA Nov 2023 3H Q3

[2 marks]

The length of a line is 8 cm to the nearest centimetre.
Complete the error interval.

Answer cm

Worked Solution & Answer

Half of 1 cm is 0.5 cm, so 7.5 cm ⩽ length < 8.5 cm. M1 A1

Answer: Answer 7.5, 8.5 cm

Question Paper (PDF) • Mark Scheme (PDF)

Question 4 AQA Nov 2023 3F Q19

[2 marks]

The length of a line is 8 cm to the nearest centimetre.

Complete the error interval.
cm ≤ length < cm

Answer cm

Worked Solution & Answer

Half a unit is 1 ÷ 2 = 0.5 cm M1
Lower bound = 8 - 0.5 = 7.5 cm
Upper bound = 8 + 0.5 = 8.5 cm
Error interval: 7.5 ≤ length < 8.5. A1

Answer: Answer 7.5, 8.5 cm

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Question 5

[2 marks]

Work out
A number x is written correct to 2 significant figures.
The result is 1.9
Complete the error interval for x.

Worked Solution & Answer

1.85 ≤ x < 1.95 M1 A1

Answer: 1.85, 1.95

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Question 6 AQA Nov 2018 3F Q21 / 3H Q5

[2 marks]

The length of a table is 110 cm to the nearest cm

Complete the error interval.

Worked Solution & Answer

For rounding to the nearest 1 cm, the maximum error is ± 0.5 cm: M1
• Lower bound: 110 - 0.5 = 109.5 cm
• Upper bound: 110 + 0.5 = 110.5 cm
Interval: 109.5 cm ≤ length < 110.5 cm A1

Answer: 109.5, 110.5 cm

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Question 7

[2 marks]

Martin used his calculator to work out the value of a number P.
He wrote down the first two digits of the answer on his calculator.
He wrote down 1.2
Complete the error interval for P.

Worked Solution & Answer

Truncated to 1.2 M1
⇒ 1.2 ⩽ P < 1.3 A1

Answer: 1.2, 1.3

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Question 8

[2 marks]

Martin truncates the number N to 1 digit.
The result is 7
Write down the error interval for N.

Worked Solution & Answer

Truncating to 1 digit gives 7 for any number from 7 up to (but not including) 8: 7 ⩽ N < 8. M1 A1

Answer: 7 ≤ N < 8

Question Paper (PDF) • Mark Scheme (PDF)

Question 9

[2 marks]

Freya writes down the value of x, correct to 1 decimal place.
She writes x = 6.4
Complete the error interval for x.

Worked Solution & Answer

Half a unit of accuracy = 0.05 M1
⇒ lower bound = 6.35, upper bound = 6.45 A1

Answer: 6.35, 6.45

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Question 10 AQA Jun 2025 2F Q23 / 2H Q5

[4 marks]

(a) Error interval for 160 cm to nearest 10 cm. [2 marks]
5 (b) Panel is 2 m to nearest 10 cm. Show total of 3 panels < 6.2 m. [2 marks]

(a) The length of a fence panel is 160 cm to the nearest 10 cm
Complete the error interval. [2 marks]

Answer cm

(b) A different fence panel measures 2 metres to the nearest 10 cm
Kim says that the total length of **three** of these fence panels must be less than 6.2 m
Show that Kim is correct. [2 marks]

Worked Solution & Answer

(a)

155 ≤ length < 165 M1 A1

Answer (a): Answer 155, 165 cm

(b)

Maximum single length = 2.05 m. 3 × 2.05 = 6.15 m M1
Since 6.15 < 6.2, Kim is correct C1

Answer (b): Upper bound = 3 × 2.05 m = 6.15 m < 6.2 m

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Score: 0 / 10 (0 / 22 marks)

Error intervals Worksheets Next: Operations with fractions →

Grade 3 Quizzes

24 Topics

3A - Error intervals	3B - Operations with fractions
3C - Estimation	3D - Writing and simplifying ratio
3E - Ratio	3F - Proportion recipes
3G - Percentages	3H - Percentage change
3J - Exchange rates	3K - Conversions and units
3L - Scale drawings	3M - Best buy questions
3N - Substitution	3P - Solving linear equations
3Q - Straight line graphs	3R - Area and circumference
3S - Rotations	3T - Reflections
3U - Enlargements	3V - Translations
3W - Mixed transformations	3X - Area of compound shapes
3Y - Frequency trees	3Z - Two way tables