Upper and lower bounds (error intervals)
A measurement of 12 cm to nearest cm has bounds 11.5 ≤ x < 12.5.
Higher tier topic. A rounded value carries an error interval: half the rounding interval either side. Calculations propagate the bounds: max sum uses both upper bounds; max difference uses upper minus lower.
Worked examples
15 cm to nearest cm: bounds 14.5 ≤ x < 15.5.
(15 cm + 8 cm) max = 15.5 + 8.5 = 24 cm. Both upper.
(15 cm − 8 cm) max = 15.5 − 7.5 = 8 cm. Upper minus lower.
Frequently asked questions
Why 14.5 not 14.49999?
Convention: bounds use exact half values. 14.5 rounds up to 15, but the lower bound is the smallest value that rounds to 15.
Strictly less than the upper bound?
Yes by convention — 15.5 rounds up to 16. So bounds use 14.5 ≤ x < 15.5.