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.
What a learner can do afterwards
- 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
1 · Read
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.
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.
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.
Max divides upper by lower, max multiplies upper by upper, then round to what the inputs support.
2 · Watch
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Where it sits
Learn first
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.