--- title: "Calculating with Bounds in Compound Measures" description: "Combine bounds in a calculation by picking the values that give the greatest and least results, including for speed, density and other compound measures." canonical: https://lightmysky.com/learn/mathematics/calculating-with-bounds-in-compound-measures-mt_zfMz7x8dlf source: https://lightmysky.com/learn/mathematics/calculating-with-bounds-in-compound-measures-mt_zfMz7x8dlf.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`. # Calculating with Bounds in Compound Measures Combine bounds in a calculation by picking the values that give the greatest and least results, including for speed, density and other compound measures. Subject: Mathematics · Area: Number Representation & Place Value · Ages 15 to 16 Page: https://lightmysky.com/learn/mathematics/calculating-with-bounds-in-compound-measures-mt_zfMz7x8dlf ## Ready when they can - Pick which bounds give the greatest result of a division - Find the range of possible speeds from a bounded distance and time - Give a final answer to an accuracy the bounds actually support ## Lesson: Best and worst your measurements allow Speed divides distance by time, and rounded inputs make the answer a range for you. For the greatest speed, pair the longest distance with the shortest time: upper over lower. The smallest speed flips the pair: lower over upper. With 100 m (95 to 105) and 8 s (7.5 to 8.5), the greatest speed is 105 divided by 7.5 = 14. **Example.** Distance 250 m to the nearest 10 m spans 245 to 255 m, and time 12 s to the nearest second spans 11.5 to 12.5 s. The greatest speed is 255 divided by 11.5: longest distance, shortest time. State which bounds you used every time. Products maximise differently: for a maximum, take upper times upper. Length 6 cm (5.5 to 6.5) by width 4 cm (3.5 to 4.5) gives at most 6.5 times 4.5 = 29.25. Density is mass over volume, so maximum density needs the heaviest mass in the smallest volume: 405 divided by 45 = 9 g per cm cubed. Pressure works the same way: maximum pressure is upper force over lower area. **Tip.** Quote only the accuracy the bounds allow. Inputs to 2 figures earn about 2 figures back, never a five-decimal sprawl. Overlong decimals pretend knowledge the measurements never had. **Recap.** Max divides upper by lower, max multiplies upper by upper, then round to what the inputs support. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Upper and Lower Bounds](https://lightmysky.com/learn/mathematics/upper-and-lower-bounds-mt_HaoOqujpRU) - [Compound Units](https://lightmysky.com/learn/mathematics/compound-units-mt_kLQOzZYrd5) ## Opens up - [Modelling Motion in a Straight Line](https://lightmysky.com/learn/mathematics/modelling-motion-in-a-straight-line-mt_no78_6w1rS)