Estimating by rounding
Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b; understand upper and lower bounds of rounded values
What a learner can do afterwards
- Estimate the answer to a calculation by rounding all values appropriately
- Calculate upper and lower bounds of a rounded measurement
- Express error intervals using inequality notation
The lesson
Before you work out an exact answer, it helps to guess a rough one first. Round each number in the calculation to a nearby value that's easy to work with, then do the easier calculation. That rough answer is your estimate, and it tells you whether your exact answer is reasonable.
Estimate 39 × 21. Round 39 up to 40, and round 21 down to 20. Now multiply the easier numbers: 40 × 20 = 800. The exact answer is 819, so 800 is a quick check that you're in the right area.
Rounding a measurement works a bit differently. If a length is 7 cm to the nearest cm, it wasn't measured exactly — it just rounded to 7. The real length could be a little more or a little less than 7 cm, somewhere within half a centimetre either side.
The two ends aren't treated the same. The lower bound, 6.5 cm, is included, because 6.5 cm itself would round up to 7 cm. The upper bound, 7.5 cm, is not included, because 7.5 cm would round up to 8 cm instead. We write this as 6.5 ≤ x < 7.5.
Round first to estimate fast, and remember every rounded value hides a range: half a unit below up to, but not including, half a unit above.
Watch it
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.