1.7

Limits of accuracy

Cambridge IGCSE Mathematics (0580)  · Unit 1: Number  · 9 flashcards

Limits of accuracy is topic 1.7 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 1 — Number , alongside Types of number, Fractions, decimals and percentages and Operations and order of operations.  In one line: The upper bound is the smallest value that would round *down* to the given number. The lower bound is the largest value that would round *up* to the given number.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.  It is a Supplement (Extended-tier) topic, so it appears only on the Extended-tier papers.

The deck below contains 9 flashcards — 2 definitions, 2 key concepts and 2 application cards — covering the precise wording mark schemes reward.  Use the 2 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

'upper bound' and 'lower bound' in the context of rounded numbers

The upper bound is the smallest value that would round *down* to the given number. The lower bound is the largest value that would round *up* to the given number.

Example: if a length is measured as 8 cm to the nearest cm, the upper bound is 8.5 cm and the lower bound is 7.5 cm.

Questions this Limits of accuracy deck will help you answer

Definition Flip

Define 'upper bound' and 'lower bound' in the context of rounded numbers.

Answer Flip

The upper bound is the smallest value that would round *down* to the given number. The lower bound is the largest value that would round *up* to the given number.

Example: if a length is measured as 8 cm to the nearest cm, the upper bound is 8.5 cm and the lower bound is 7.5 cm.
Key Concept Flip

A length is measured as 8.3 cm to the nearest 0.1 cm. State the error interval for this measurement.

Answer Flip

The error interval is the range of possible values for the actual length. In this case, the error interval is 8.25 cm ≤ length < 8.35 cm.

Key Concept Flip

The weight of a bag of sugar is given as 500g, correct to the nearest 10g. Calculate the maximum possible weight of 6 bags of sugar.

Answer Flip

First, find the upper bound of a single bag: 505g. Then, multiply by 6: 505g * 6 = 3030g. Therefore, the maximum possible weight is 3030g.

Key Concept Flip

A rectangle has a length of 12 cm and a width of 5 cm, both measured to the nearest cm. Calculate the minimum possible area of the rectangle.

Answer Flip

To find the minimum area, use the lower bounds of both measurements. Lower bound of length = 11.5 cm, Lower bound of width = 4.5 cm. Minimum area = 11.5 cm * 4.5 cm = 51.75 cm².

Definition Flip

Explain the difference between a 'continuous' and a 'discrete' variable in the context of limits of accuracy.

Answer Flip

A continuous variable can take any value within a range (

Example: height). A discrete variable can only take specific, separate values (. number of students). This distinction affects how we determine the bounds.
Key Concept Flip

The time taken for a journey is recorded as 2 hours, correct to the nearest half hour. What is the lower bound for the journey time in minutes?

Answer Flip

The measurement is to the nearest 30 minutes. The lower bound is found by subtracting half of the degree of accuracy (30/2 = 15 minutes) from the recorded time. Therefore 2 hours - 15 minutes = 1 hour 45 minutes = 105 minutes.

Example: if the length of a rectangle is given as 8cm correct to the nearest cm, the lower bound is 7.5cm.
Key Concept Flip

The height of a tower is 50m, correct to the nearest meter. A student calculates the volume of a cylinder with this height. What is the implication for the accuracy of the volume calculation?

Answer Flip

The volume calculation will also have a limit of accuracy. The calculated volume will be between a lower and upper bound depending on whether the lower or upper bound of the height measurement is used.

Key Concept Flip

- Topic: 1.7 Limits of accuracy - Question: A student measures the side of a square as 6 cm. What further information is needed to determine the limits of accuracy of the area?

Answer Flip

You need to know the degree of accuracy to which the side length was measured (e.g., to the nearest cm, to the nearest mm). This determines the upper and lower bounds for the side length, and subsequently the area.

Example: If the side is 6 cm to the nearest cm, the side could be between 5.5 cm and 6.5 cm.
Key Concept Flip

Topic: 1.7 Limits of Accuracy. Question: A machine produces bolts with a stated length of 5cm, correct to the nearest millimetre. What are the upper and lower bounds for the actual length of a bolt produced by this machine? Why is understanding these limits important?

Answer Flip

The upper bound is 5.05cm and the lower bound is 4.95cm. These limits are critical because if bolts are consistently too long or too short, they could cause assembly problems, weaken structures, or lead to malfunctions.

Example: if bolts consistently exceeded 5.05cm in a bridge construction, they might not fit properly and compromise the integrity of the structure.

Review the material

Read revision notes with definitions, equations, and exam tips.

Read Notes

Test yourself

Practice with MCQ questions to check your understanding.

Take Mathematics Quiz
1.6 Approximation and estimation 1.8 Surds

Key Questions: Limits of accuracy

Define 'upper bound' and 'lower bound' in the context of rounded numbers.

The upper bound is the smallest value that would round *down* to the given number. The lower bound is the largest value that would round *up* to the given number.

Example: if a length is measured as 8 cm to the nearest cm, the upper bound is 8.5 cm and the lower bound is 7.5 cm.
Explain the difference between a 'continuous' and a 'discrete' variable in the context of limits of accuracy.

A continuous variable can take any value within a range (

Example: height). A discrete variable can only take specific, separate values (. number of students). This distinction affects how we determine the bounds.

More topics in Unit 1 — Number

Limits of accuracy sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

1.1 Types of number

10 flashcards
1.2 Fractions, decimals and percentages

10 flashcards
1.3 Operations and order of operations

9 flashcards
1.4 Powers and roots

9 flashcards
1.5 Ratio, proportion and rate

18 flashcards
1.6 Approximation and estimation

10 flashcards
1.8 Surds

9 flashcards

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

upper bound lower bound error interval maximum minimum limits of accuracy bounds continuous discrete

Key terms covered in this Limits of accuracy deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

'upper bound' and 'lower bound' in the context of rounded numbers
Explain the difference between a 'continuous' and a 'discrete' variable in the context of limits of accuracy

Related Mathematics guides

Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.

IGCSE Maths vs Additional Maths

Choosing between 0580 and 0606, and what each paper expects

Cambridge maths notation guide

Notation conventions Cambridge expects in your answers

How to study this Limits of accuracy deck

Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.