The length of a field is 92 m, correct to the nearest metre. Sam says that the length of the field could be 92.6 m. Explain why Sam is wrong.
Question 1 Report
The length of a field is 92 m, correct to the nearest metre. Sam says that the length of the field could be 92.6 m.
Explain why Sam is wrong.
Answer Details
This question tests whether you can turn a rounded measurement into an interval and then test a claimed value against it.
The length is 92 m correct to the nearest metre, so the half-unit is \( 0.5 \) m. The possible true lengths \( L \) satisfy \[ 91.5 \le L \lt 92.5 \] so the upper bound of the length is 92.5 m [B1].
Sam's value of 92.6 m is greater than 92.5 m, so it lies outside this interval and cannot be a possible length [B1]. To see why directly: a true length of 92.6 m is closer to 93 m than to 92 m, so it would have been recorded as 93 m, not 92 m.
The point to state in an explanation like this is not just "92.6 is too big" but the comparison with the actual bound. Quote the bound, then say the claimed value exceeds it.
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