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Bounds and effects of measurement error
Bounds and effects of measurement error
Example 1
A rectangle is measured as 7cm by 10cm, each to the nearest centimetre. Find the upper bound for its area, in cm2.
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Answer: 78.75
- The side lengths are less than 7.5 and 10.5. Multiplying the upper bounds gives an area upper bound of 78.75cm2; the area is strictly below it.
Example 2
A cube's edge is recorded as 2cm to the nearest centimetre. Find the lower bound for its volume, in cm3.
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Answer: 3.375
- The smallest possible edge is 1.5cm. Cube this lower bound: 3.375cm3.
Example 3
A length is recorded as 20mm to the nearest 10mm. What is the maximum possible absolute rounding error, in mm?
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Answer: 5
- The greatest distance from the rounded value is half the rounding unit: 210=5mm.
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