--- title: "Upper and Lower Bounds" description: "Give the upper and lower bounds of a rounded measurement and write the error interval, using the half-unit rule for the accuracy stated." canonical: https://lightmysky.com/learn/mathematics/upper-and-lower-bounds-mt_HaoOqujpRU source: https://lightmysky.com/learn/mathematics/upper-and-lower-bounds-mt_HaoOqujpRU.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Upper and Lower Bounds Give the upper and lower bounds of a rounded measurement and write the error interval, using the half-unit rule for the accuracy stated. Subject: Mathematics · Area: Number Representation & Place Value · Ages 15 to 16 Page: https://lightmysky.com/learn/mathematics/upper-and-lower-bounds-mt_HaoOqujpRU ## Ready when they can - State the bounds of a length given as 12.4 cm to 1 decimal place - Write an error interval with the correct strict and inclusive signs - Say what a mass rounded to the nearest 10 g could really be ## Lesson: What a rounded number really means A rounded measurement hides a range, and half a unit each way finds it for you. 12.4 cm to 1 decimal place spans 12.35 cm up to 12.45 cm, since half of 0.1 is 0.05. Name the half step first, then add and subtract it. **Example.** A mass of 6.5 kg to 1 decimal place really means 6.45 kg <= mass < 6.55 kg. The lower bound joins in with <= and the upper bound stays out with <. Say the signs out loud as you write them. Whole-number rounding scales the same idea up. A mass shown as 40 g to the nearest 10 g spans 35 g up to 45 g, because the half step is 5 g. To 2 decimal places, 2.35 spans 2.345 <= x < 2.355. **Tip.** No calculation can promise more detail than its roughest input. Extra digits past the bounds are fiction, so keep the half step small and symmetric. **Recap.** Half a unit each way, lower bound in, upper bound out. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Bounds and error in rounded values](https://lightmysky.com/learn/mathematics/bounds-and-error-in-rounded-values-mt_VVn1IXjkzn) ## Opens up - [Calculating with Bounds in Compound Measures](https://lightmysky.com/learn/mathematics/calculating-with-bounds-in-compound-measures-mt_zfMz7x8dlf)