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.
What a learner can do afterwards
- 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
1 · Read
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.
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.
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.
Half a unit each way, lower bound in, upper bound out.
2 · Watch
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Where it sits
Learn first
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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.