Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Limits of Accuracy — upper and lower bounds, error intervals and bounds of calculations — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise Limits of Accuracy in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Limits of Accuracy revision-guide angle, while Tutopiya’s Limits of Accuracy subtopic page owns the learning resource and the free Limits of Accuracy quiz owns the practice.

Limits of Accuracy appear throughout the Number unit of Cambridge IGCSE Mathematics (0580/0607) and test whether you understand that rounded measurements have a range, not a single exact value. This guide explains what Limits of Accuracy covers, how to find upper and lower bounds, and where to practise each skill.

Key takeaways

• A value rounded to n decimal places has an error interval of half a unit in the last place.
• The lower bound is the smallest value that would round to the given figure; the upper bound is the largest.
• For calculations, use the worst-case combination — LB÷UB for minimum quotient, UB÷LB for maximum.
• Limits of Accuracy builds on Estimation and Rounding Numbers.

What are Limits of Accuracy in Cambridge IGCSE Maths?

Limits of Accuracy is the study of how rounding affects measurements and calculations. When a length is given as 4.2 cm correct to 1 decimal place, the true value lies in an interval around 4.2. In Cambridge IGCSE Mathematics, you find upper and lower bounds, write error intervals, and calculate bounds of expressions involving rounded values.

Read the full explanation, worked examples and notes on Tutopiya’s Limits of Accuracy subtopic page before you attempt questions.

The core ideas you must master

These four ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
Degree of accuracy	How a value was rounded (1 d.p., 2 s.f., nearest 10)	“correct to 1 decimal place”
Lower bound (LB)	Smallest value that rounds to the stated figure	”Write down the lower bound of 6.3”
Upper bound (UB)	Largest value that rounds to the stated figure	”Write down the upper bound of 6.3”
Error interval	LB ≤ x < UB (strict inequality on the top)	“Write the error interval for 350 (2 s.f.)“

How to find upper and lower bounds — step by step

The method depends on how the value was rounded. Always identify the place value of the final digit first.

1. Find half a unit in the place the value was rounded to. For 4.2 (1 d.p.), half a unit = 0.05.
2. Subtract half a unit for the lower bound: LB = 4.2 − 0.05 = 4.15.
3. Add half a unit for the upper bound, but use strict inequality on top: UB = 4.2 + 0.05 = 4.25, so 4.15 ≤ x < 4.25.
4. For significant figures, apply the same logic to the relevant place value. 350 (2 s.f.) → LB = 345, UB = 355.

Once you have worked through a few, test yourself with the free Limits of Accuracy quiz — it tells you fast whether the method has actually stuck.

Bounds of calculations: which combination to use

When a formula uses rounded measurements, the extreme results come from combining bounds strategically.

Operation	Maximum result	Minimum result
a + b	UB(a) + UB(b)	LB(a) + LB(b)
a − b	UB(a) − LB(b)	LB(a) − UB(b)
a × b	UB(a) × UB(b)	LB(a) × LB(b)
a ÷ b	UB(a) ÷ LB(b)	LB(a) ÷ UB(b)

Limits of Accuracy in past-paper wording: command words that matter

Most lost marks come from using ≤ on both ends of an interval or picking the wrong bound combination in a calculation.

Command word / phrase	What the question wants	Typical stem
Write down the lower bound	State LB only, to required accuracy	”Write down the lower bound of 8.4 cm.”
Write down the upper bound	State UB only	”Write down the upper bound of 8.4 cm.”
Write the error interval	LB ≤ x < UB in correct notation	”Write the error interval for 1200 (2 s.f.).”
Calculate the upper bound of …	Apply worst-case bounds to a formula	”Calculate the upper bound of the perimeter.”
Work out the maximum possible value	Same as upper bound of a result	”Work out the maximum possible value of V.”
Show that	Prove a bound statement with working	”Show that the area is less than 50 cm².”

Worked exam-style stems (how to answer the wording)

1. “A rectangle has length 6.8 cm and width 4.3 cm, each correct to 1 decimal place. Calculate the upper bound of the area.” LB length = 6.75, UB length = 6.85; LB width = 4.25, UB width = 4.35. Maximum area = 6.85 × 4.35 = 29.7975 cm². Reward: correct bounds for each measurement, then correct multiplication.
2. “Write the error interval for 0.045 correct to 2 decimal places.” Half unit = 0.005. Interval: 0.0445 ≤ x < 0.0455. Reward: correct half-unit; strict inequality on the upper end.
3. “The speed of a car is 80 km/h correct to the nearest 10 km/h. Work out the lower bound of the speed.” Nearest 10 → half unit = 5. LB = 80 − 5 = 75 km/h. Reward: identifying the rounding level before calculating.

When you can recognise the wording instantly, work the full set on the Number topical past-paper questions and the Limits of Accuracy quiz to lock the method in.

How Limits of Accuracy connects to the rest of Number

Rounding rules from Estimation and Rounding Numbers are the foundation — if you cannot identify the rounding place, bounds will go wrong. Bounds also appear in measurement and mensuration questions across the syllabus. Use the Cambridge IGCSE Maths resource hub to move from a weak subtopic into the next.

Common mistakes students make

• Writing 4.15 ≤ x ≤ 4.25 instead of 4.15 ≤ x < 4.25 — the upper bound is not included.
• Using the same bound combination for every operation instead of the worst-case pairing from the table above.
• Confusing 2 significant figures with 2 decimal places when finding half a unit.

When you need more support

If bounds-of-calculations questions keep tripping you up, work through the Estimation and Rounding Numbers quiz and the Number topical past-paper questions, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Is Limits of Accuracy hard in Cambridge IGCSE Maths? The concepts are straightforward once you know the half-unit rule. The difficulty is staying systematic on multi-step bounds-of-calculations questions — write out each LB and UB before combining.

Why is the upper bound not included in the error interval? Because a value exactly at the upper bound would round up to the next number. The true value is always strictly below the upper bound.

What is the difference between bounds and estimation? Estimation gives a rough approximate value. Bounds give the exact range within which the true value must lie, based on how a measurement was rounded.

How do I revise Limits of Accuracy effectively? Read the subtopic notes, practise writing error intervals until the strict inequality is automatic, then take the Limits of Accuracy quiz. Revisit any calculation-bound questions you got wrong.

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