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MathidiaMathematics Academy
Number, accuracy and bounds
Lesson 5 of 75
Review

Accuracy reasoning

Objective. Judge whether stated numerical conclusions are justified.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Accuracy reasoning involves judging whether a numerical claim is actually supported by the level of precision in the data used. A conclusion is only as reliable as its least accurate measurement, so stating a result to more significant figures than the data justifies is misleading. For instance, if two lengths measured to the nearest centimetre are multiplied, claiming the area to the nearest square millimetre overstates the precision achieved. Good reasoning checks the error interval of each input and considers whether rounding could change the final decision, such as whether a part fits within a stated tolerance. This skill is tested by asking pupils to evaluate someone else's rounded statement.

Worked example

A rectangle has sides 6 cm and 9 cm, each measured to the nearest cm. Is the claim 'the area is exactly 54 cm²' justified?

Diagram of a rectangle
  1. 1Find bounds for each side: 5.5 ≤ l < 6.5 and 8.5 ≤ w < 9.5.
  2. 2Minimum possible area = 5.5 × 8.5 = 46.75 cm².
  3. 3Maximum possible area = 6.5 × 9.5 = 61.75 cm².
  4. 4Since the true area could be anywhere from 46.75 to 61.75, claiming exactly 54 is not justified.

Answer: No; the area could lie anywhere between 46.75 cm² and 61.75 cm², so 54 cm² is not guaranteed.

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Common mistake. Pupils often accept a calculator's full decimal display as 'the' accurate answer without considering the bounds of the original rounded data. Always test whether bounds could change the conclusion before trusting a precise-looking figure.

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