Fiducia TogetherBounds and error intervals
The range a rounded measurement could actually be.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
If a value is rounded, the upper and lower bounds are the limits of what it could have been. A length of 4.5 cm to 1 decimal place lies between 4.45 and 4.55.
Where it applies
Higher tier maths, and it connects to precision in science.
How it works
Calculating with bounds needs care about which combination gives the maximum or minimum. For a division, the maximum comes from the largest numerator and the smallest denominator.
Truncation is different from rounding and produces different bounds.
How to use it in your work
Write the lower and upper bound of every quantity before calculating.
Think about which combination gives the extreme you want. For subtraction, the maximum uses the largest first value and the smallest second.
The upper bound is conventionally written as the value it goes up to, not that value minus a bit.
Where to get help
Your teacher and your board's specification. Bitesize for worked examples, and the subject song for the topic list.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.