The length of a wall is 9 metres to the nearest metre. Complete the error interval for the length of the wall.
How to approach this question
1. The measurement is given to the nearest metre.
2. Find the degree of accuracy, which is 1 metre.
3. Halve the degree of accuracy: 1 / 2 = 0.5 metres.
4. To find the lower bound, subtract this value from the measurement: 9 - 0.5 = 8.5 m.
5. To find the upper bound, add this value to the measurement: 9 + 0.5 = 9.5 m.
6. The error interval is written as: lower bound ≤ value < upper bound.
7. So, the interval is 8.5 ≤ length < 9.5.
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.
1. Find the degree of accuracy: It is 1 metre.
2. Halve this value: 1 ÷ 2 = 0.5 metres.
3. The lower bound is the smallest value that would round up to 9. We find this by subtracting 0.5 from the measurement:
Lower bound = 9 - 0.5 = 8.5 m.
4. The upper bound is the smallest value that would round up to the *next* measurement (10). We find this by adding 0.5 to the measurement:
Upper bound = 9 + 0.5 = 9.5 m.
The error interval is written as: Lower Bound ≤ actual length < Upper Bound.
The actual length can be equal to the lower bound (8.5 would round up to 9), but it must be strictly less than the upper bound (9.5 would round up to 10).
So, the error interval is: 8.5 ≤ length < 9.5.
Common mistakes
✗ Using the wrong inequality signs (e.g., < instead of ≤ for the lower bound, or ≤ instead of < for the upper bound).
✗ Calculating the bounds incorrectly (e.g., 8 and 10, or 8.9 and 9.1).
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