Error intervals
Objective. Write upper and lower bounds for rounded measurements.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
An error interval states the range of exact values that could have produced a rounded measurement. If a length is given as 8 cm to the nearest centimetre, the true value lies between 7.5 cm and 8.5 cm, written 7.5 ≤ l < 8.5. The lower bound is half a unit below the rounded value and the upper bound is half a unit above it; only the lower bound is included because anything reaching the upper bound would round up to the next value. The size of 'half a unit' depends on the degree of accuracy stated, such as nearest 10, nearest 0.1, or nearest significant figure. Error intervals are written using inequality notation with the rounded value sandwiched appropriately.
Worked example
A mass is recorded as 240 kg to the nearest 10 kg. Write the error interval for the true mass.
- 1The degree of accuracy is nearest 10, so half a unit is 5.
- 2Lower bound = 240 − 5 = 235.
- 3Upper bound = 240 + 5 = 245.
- 4Since 245 would round to 250, the interval must exclude it.
Answer: 235 ≤ m < 245
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. A common error is making both bounds inclusive, writing 7.5 ≤ l ≤ 8.5, which double-counts 8.5 as rounding to both 8 and 9. Use a strict inequality on the upper bound.
Your progress
Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.
0 of 5 steps complete
Your place saves automatically as you read.