Pre-O Level Mathematics
Limit of Accuracy
Learning Objectives
• Understand the meaning of limit of accuracy.
• Identify upper and lower bounds.
• Calculate maximum possible error.
• Apply accuracy concepts in real-life measurements.
Introduction
When we measure or round a number, we do not get the exact value. There is always a small range
within which the true value lies. This range is called the limit of accuracy.
Definition
The limit of accuracy is the smallest range within which the true value of a measured or rounded
quantity lies.
Rounding and Accuracy
Whenever a number is rounded, its accuracy depends on the place value used.
Nearest whole number → ±0.5
Nearest 0.1 → ±0.05
Nearest 0.01 → ±0.005
Nearest 10 → ±5
Upper and Lower Bounds
Lower bound = rounded value − half of rounding unit
Upper bound = rounded value + half of rounding unit
Worked Example
A length is given as 12 cm correct to the nearest cm.
Lower bound = 11.5 cm
Upper bound = 12.5 cm
11.5 ≤ length < 12.5
Maximum Possible Error
Maximum possible error is equal to half of the rounding unit.
Exam Tips
• Always use half of the rounding unit.
• Upper bound is not inclusive.
• Use correct inequality symbols.
Summary
Limit of accuracy gives a range for the true value. It is important for understanding real-life
measurements and examination questions.