The length of a wall is 9 metres to the nearest metre.
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Complete the error interval for the length of the wall.
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__________ m ≤ length < __________ m
How to approach this question
1. Identify the degree of accuracy. "To the nearest metre" means the accuracy is 1 m.
2. Halve the degree of accuracy.
3. To find the lower bound, subtract this value from the measurement.
4. To find the upper bound, add this value to the measurement.
5. Write the final answer in the form: lower bound ≤ value < upper bound.
Full Answer
When a measurement is given to a certain degree of accuracy, there is a range of possible actual values. This range is called the error interval.
The length is 9 metres to the nearest metre.
The unit of rounding is 1 metre.
We find half of this unit: 1 / 2 = 0.5 metres.
The lower bound is the measured value minus 0.5:
9 - 0.5 = 8.5 m.
The upper bound is the measured value plus 0.5:
9 + 0.5 = 9.5 m.
Any value from 8.5 up to (but not including) 9.5 would round to 9 to the nearest metre. For example, 8.5 rounds up to 9, and 9.499... rounds down to 9. 9.5 would round up to 10.
So the error interval is 8.5 ≤ length < 9.5.
Common mistakes
✗ Using the wrong inequality signs, for example, using ≤ for the upper bound. The length must be strictly less than the upper bound.
✗ Calculating the bounds incorrectly, for example, using 8 and 10, or 8.9 and 9.1.
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