Upper and lower bounds · Year 11
In Year 11 you learn: bounds in calculations.
A rounded measurement could be a little bigger or smaller than it says. The bounds are the smallest and largest values it could really be. Working with bounds tells us how accurate a calculation from rounded measurements can be, which matters in engineering, science and safety checks.
Key facts
- The bounds are half the rounding unit either side: 7 cm to the nearest cm is between 6.5 cm and 7.5 cm.
- Error interval: 6.5 ≤ x < 7.5 (the upper bound itself would round up).
- Truncated values only go up: 3.7 truncated to 1 d.p. means 3.7 ≤ x < 3.8.
- Biggest sum or product: add or multiply the upper bounds.
- Biggest difference: upper bound − lower bound.
- Biggest quotient: upper bound ÷ lower bound (biggest top, smallest bottom).
Worked examples
Example 1
A car travels 200 km (nearest 10 km) in 2.5 hours (nearest 0.1 hour). Find the greatest possible average speed.
Answer: 83.7 km/h (3 s.f.)