Calculating With Bounds: Multiplication and Division

A rectangle's sides are given as $4.5$ cm and $3.2$ cm, both to $1$ decimal place. Find the maximum and minimum possible area.

• 1Bounds of $4.5$: $4.45$ to $4.55$. Bounds of $3.2$: $3.15$ to $3.25$
• 2Maximum area = max × max = $4.55\times 3.25=14.7875$
• 3Minimum area = min × min = $4.45\times 3.15=14.0175$

Answer: Maximum ≈ $14.79$ cm², Minimum ≈ $14.02$ cm²

A distance is measured as $100$ $m$ (to the nearest $1$ $m$) and a time as $10$ s (to the nearest $1$ s). Speed = distance ÷ time. Find the maximum and minimum possible speed.

• 1Bounds of $100$: $99.5$ to $100.5$. Bounds of $10$: $9.5$ to $10.5$
• 2Maximum speed = max(distance) ÷ min(time) = $100.5÷9.5$ ≈ $10.58$
• 3Minimum speed = min(distance) ÷ max(time) = $99.5÷10.5$ ≈ $9.48$

Answer: Maximum ≈ $10.58$ $m$/s, Minimum ≈ $9.48$ $m$/s