The length of a fence panel on Gorton Farm is given as 2.7 metres, correct to the nearest 0.1 metres. Write down the lower bound and the upper bound of this...
Question 1 Report
The length of a fence panel on Gorton Farm is given as 2.7 metres, correct to the nearest 0.1 metres.
Write down the lower bound and the upper bound of this length. (2)
Answer Details
A measurement given to the nearest \(0.1\) m has been rounded, so the true length lies within half a division either side of the stated value. Half of \(0.1\) m is \(0.05\) m, and that is the margin in each direction.
\[\text{Lower bound} = 2.7 - 0.05 = 2.65 \text{ metres}\][1]
\[\text{Upper bound} = 2.7 + 0.05 = 2.75 \text{ metres}\][1]
Any true length from \(2.65\) m up to \(2.75\) m rounds to \(2.7\) m to the nearest \(0.1\) m, which is exactly why these are the bounds. A length of \(2.649\) m would round to \(2.6\) m, and \(2.751\) m would round to \(2.8\) m.
The usual error is halving the stated value or using \(0.1\) as the margin instead of \(0.05\). The rule is always half of the unit of rounding, whatever that unit happens to be.
Note the slight asymmetry in what actually rounds where: a length of exactly \(2.65\) m rounds up to \(2.7\) m by the usual convention and is included, while exactly \(2.75\) m would round up to \(2.8\) m. The upper bound is therefore the limit the length must stay below, though at this level both values are quoted as the bounds.
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