Error intervals
- A measurement rounded to a given accuracy could be half a unit above or below the rounded value.
- If x = 7.4 to 1 decimal place, the error interval is 7.35 ≤ x < 7.45.
- The lower bound (7.35) is included; the upper bound (7.45) is not, because 7.45 would round to 7.5.
Finding bounds
- Halve the unit of rounding, then subtract for the lower bound and add for the upper bound.
- 50 cm to the nearest 10 cm: bounds 45 cm and 55 cm.
- 70 kg to the nearest 5 kg: bounds 67.5 kg and 72.5 kg.
Truncation
- Truncating means chopping off digits without rounding. If x = 5.8 truncated to 1 decimal place, then 5.8 ≤ x < 5.9.
Calculating with bounds (Higher)
- Maximum of a sum: upper + upper. Maximum of a difference: upper − lower.
- Maximum of a product: upper × upper. Maximum of a quotient: upper ÷ lower.
- Minimum of a quotient: lower ÷ upper.
- Give the final answer to a sensible accuracy, where the upper and lower bounds agree when rounded.
Key terms
- Error interval
- The range of possible values of a rounded number, such as 7.35 ≤ x < 7.45.
- Lower bound
- The smallest value that would round to the given value.
- Upper bound
- The value above which numbers would round up to the next value; the top of the error interval.
- Truncation
- Cutting off digits after a certain point without rounding.
- Degree of accuracy
- How precisely a number is given, such as to 1 decimal place.