Bounds in calculations

To bound a calculated quantity, ask which choice makes the result smallest or largest. For positive measurements, sums use lower with lower and upper with upper. A difference is smallest when its first quantity is smallest and the subtracted quantity is largest.

Example

A distance of \(120\text{ m}\) to the nearest metre has bounds \(119.5\) and \(120.5\). A time of \(8.0\text{ s}\) to the nearest tenth has bounds \(7.95\) and \(8.05\). The upper bound for speed is \(\dfrac{120.5}{7.95}=15.1572\ldots\text{ m/s}\); the lower bound is \(\dfrac{119.5}{8.05}=14.8447\ldots\text{ m/s}\).

The greatest distance and smallest time make the greatest speed. Do not divide two upper bounds. Keep the unrounded bound until deciding the final accuracy; a strict endpoint need not be attainable.