Error intervals and bounds
Error intervals
A length of 6.4 cm, rounded to 1 decimal place, could have been anything from 6.35 cm up to (but not including) 6.45 cm.
Go half a unit of rounding either way.
6.35 ≤ L < 6.45
The lower bound is included (6.35 rounds up to 6.4). The upper bound is not (6.45 rounds up to 6.5), but it is still called the upper bound.
If 3.7 came from truncating to 1 decimal place, the number was 3.7 or more and less than 3.8: 3.7 ≤ x < 3.8.
Counting whole things
48,000 people, to 2 significant figures, means between 47,500 and 48,500.
People are whole, so the least is 47,500 and the greatest is 48,499.
Bounds in calculations (Higher)
To make an answer as big as possible, choose each bound to push it up.
- Sum or product: biggest = upper + upper, or upper × upper.
- Difference: biggest = upper − lower. Least = lower − upper.
- Quotient: biggest = upper ÷ lower. Least = lower ÷ upper.
- speed = distance ÷ time, distance 340 m (nearest 10 m), time 42.6 s (1 d.p.)
- greatest distance 345 m, least time 42.55 s
- upper bound of speed = 345 ÷ 42.55 = 8.108... m/s
A suitable degree of accuracy: round the upper and lower bounds. Use the most figures for which they agree.
Bounds on the calculator
A drone flies 340 m (to the nearest 10 m) in 42.6 s (to 1 decimal place). Work out 345 ÷ 42.55 and 335 ÷ 42.65. Round both to 3 significant figures, then to 2. At which accuracy do they agree?
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