Number
Rounding and bounds
Explore accuracy and included or excluded endpoints.
Predict, test and explain
Step 1 of 3
Predict
What does 3.75 round to, to 1 decimal place, using halfway rounds up?
Scroll the diagram sideways to see every label.
The filled lower endpoint is included. The open upper endpoint is excluded: that value rounds to the next step. Halfway rounds up for these positive values.
Check the working
| Quantity | Value |
|---|---|
| Rounded | 7.4 |
| Lower bound, included | 7.35 |
| Upper bound, excluded | 7.45 |
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Hints, self-check and connections
Try a self-check
Fixed values, separate from the diagram controls.
A positive length is recorded as 3.7 cm to the nearest 0.1 cm. Give its error interval, using halfway rounds up.
Hint
Find half the rounding step on either side of 3.7.
Reveal answer
The lower bound is included; the upper bound is excluded because 3.75 rounds to 3.8.
Build an explanation
Hint 1
Identify the rounding unit. To the nearest 0.1, the unit is 0.1 and half the unit is 0.05.
Hint 2
Subtract half the unit for the lower bound and add half the unit for the upper bound.
Hint 3
Include the lower bound and exclude the upper bound: lower bound ≤ actual value < upper bound.
Worked example
This example uses fixed values, separate from the diagram controls.
A length L is recorded as 7.4 cm to the nearest 0.1 cm. Write its error interval.
- Half the rounding unit is 0.1 ÷ 2 = 0.05 cm.
- The lower bound is 7.4 − 0.05 = 7.35 cm.
- The upper bound is 7.4 + 0.05 = 7.45 cm. This endpoint rounds to 7.5 cm, so it is excluded.
Answer: 7.35 cm ≤ L < 7.45 cm
Connect this idea
Watch out: The upper bound is excluded. L = 7.45 cm does not round to 7.4 cm under the usual school rounding rule.