Question 1Warm-upFoundation
, correct to 1 decimal place. Write down the error interval for .
Half of 0.1 is 0.05.
Worked solution
- Rounded to the nearest 0.1, so take off and add half of 0.1, which is 0.05.
Answer:
GCSE & IGCSE maths practice
Bounds and error intervals questions and answers
A measurement rounded to some accuracy could have been anywhere in a small range. The lower and upper bounds are the ends of that range, and an error interval writes it as an inequality like . The questions start with error intervals (Foundation), then move on to the Higher skill of finding the bounds of a calculation by choosing the right bound for each value.
10 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated .
Where bounds and error intervals comes up
| GCSE (AQA, Edexcel, OCR) | Error intervals from rounding or truncation: Foundation and Higher. Upper and lower bounds of calculations: Higher only. |
|---|---|
| Cambridge IGCSE (0580) | Core: upper and lower bounds for data rounded to a given accuracy. Extended: bounds of the results of calculations. |
| Edexcel International GCSE (4MA1) | Foundation: identifying upper and lower bounds. Higher: solving problems with upper and lower bounds. |
The method
- Rounded: halve the unit you rounded to. Subtract it for the lower bound and add it for the upper bound.
- Truncated: the lower bound is the value itself, and the upper bound is one whole unit more.
- Write the error interval as lower ≤ x < upper.
- Adding or multiplying: upper with upper gives the upper bound; lower with lower gives the lower bound.
- Subtracting or dividing: for the upper bound use upper − lower (or upper ÷ lower); for the lower bound use lower − upper (or lower ÷ upper).
Bounds and error intervals questions
Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.
Warm-up
Question 2Warm-upFoundation
A number is 340, rounded to the nearest 10. Write down the error interval for .
Half of 10 is 5.
Worked solution
- Half of 10 is 5.
Answer:
Question 3Warm-upFoundation
, truncated to 1 decimal place. Write down the error interval for .
Truncating chops off digits, so the number could be anything from 2.6 up to (not including) 2.7.
Worked solution
- Truncation removes the digits after the first decimal place, so could be 2.6, 2.61, ..., 2.6999...
Answer:
Exam-style
Question 4Exam-styleFoundation
A crowd is 5000 people, correct to 1 significant figure. Write down the error interval for the number of people, .
1 significant figure here means the nearest 1000.
Worked solution
- To 1 s.f., 5000 is rounded to the nearest 1000. Half of 1000 is 500.
Answer:
Question 5Exam-styleHigher
A rectangle measures 8 cm by 5 cm, each correct to the nearest centimetre. Find the upper bound of its area.
Multiply the two upper bounds.
Worked solution
- Upper bounds: 8.5 cm and 5.5 cm.
Answer:
Question 6Exam-styleHigher
and , both correct to the nearest whole number. Find the upper bound of .
To make a fraction as big as possible, use the biggest top and the smallest bottom.
Worked solution
- Upper bound of = 12.5, lower bound of = 2.5.
Answer:
Question 7Exam-styleHigher
correct to the nearest whole number, and correct to 1 decimal place. Find the lower bound of .
Smallest a minus biggest b.
Worked solution
- Lower bound of = 19.5, upper bound of = 7.25.
Answer:
Question 8Exam-styleHigher
, correct to 1 decimal place. Find the upper bound of .
The upper bound of x is 4.05.
Worked solution
- Upper bound of = 4.05
Answer:
Challenge
Question 9ChallengeHigher
A runner covers 100 m, correct to the nearest metre, in 12.3 seconds, correct to 1 decimal place. Find the lower bound of the runner's average speed, in m/s, to 3 significant figures.
Speed = distance ÷ time. For the smallest speed: smallest distance ÷ largest time.
Worked solution
- Lower bound of distance = 99.5 m, upper bound of time = 12.35 s.
- To 3 s.f.: m/s
Answer: m/s
Question 10ChallengeHigher
A coach travels 240 km, correct to the nearest 10 km, in 3.5 hours, correct to the nearest half hour. Find the upper bound of its average speed, in km/h, to 1 decimal place.
Nearest half hour means the time is between 3.25 and 3.75 hours.
Worked solution
- Upper bound of distance = 245 km. Lower bound of time = 3.25 h (half of 0.5 h is 0.25 h).
- To 1 d.p.: km/h
Answer: km/h
Common mistakes
- Using the whole unit instead of half: 340 to the nearest 10 is 335 to 345, not 330 to 350.
- Writing ≤ for the upper bound of an error interval: it's x < 345.
- Dividing upper by upper to get the upper bound of a quotient.
- Rounding bounds before the end of a calculation.
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Sources
The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:
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