A car park's height barrier is set to a value that rounds to \(2.1\) m to the nearest \(0.1\) m. Write down the error interval for the exact height, \(h\) m...
Question 1 Report
A car park's height barrier is set to a value that rounds to \(2.1\) m to the nearest \(0.1\) m.
- Write down the error interval for the exact height, \(h\) metres, of the barrier. (2)
- A van has height exactly \(2.14\) m. Use your error interval to explain whether the van is certain to pass under the barrier. (1)
Answer Details
Rounding to the nearest \(0.1\) m means the exact height lies within half of \(0.1\) m either side of the rounded value; this range of possible exact values, the error interval, can then be used to judge whether a specific van is guaranteed to fit under the barrier in every possible case.
- Since \(2.1\) is the value to the nearest \(0.1\), the exact height satisfies: \[ 2.05 \leq h \lt 2.15 \] [2 marks]
- Since \(h\) could be as low as \(2.05\) m, which is less than the van's height of \(2.14\) m, the van is not certain to pass under the barrier. [1 mark]
Even though \(2.1\) m, the rounded barrier height, is taller than the \(2.14\) m van by rounding alone, the true barrier height could genuinely be as low as \(2.05\) m within the error interval, which is shorter than the van; this is exactly why rounded measurements cannot be relied on for a safety-critical check like clearance under a barrier.
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