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GCSE Maths / Edexcel

Bounds and error intervals

Find lower and upper bounds from rounded values, write error intervals, and use bounds in calculations.

Number and Place ValueFoundation and HigherGrades 5 to 7Focused skill

Curriculum path: GCSE Maths > Edexcel > Number > Bounds and error intervals

Pearson Edexcel GCSE Maths number: use limits of accuracy and error intervals.

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Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Bounds are about possible original values before rounding.

The lower bound is the smallest value that would round to the given number.

The upper bound is the next value that would round up to a different number, so it is not included in the interval.

First identify the rounding step. Nearest 10 has step 10, nearest 1 has step 1, 1 decimal place has step 0.1, and nearest 10p has step 0.10 pounds.

Half the step tells you how far to go below and above the rounded value.

Use lower bound <= x < upper bound. The lower bound is included; the upper bound is not included.

Key ruleHalf-step below gives the lower bound; half-step above gives the upper bound.

Worked examples

Nearest 10

A number is 350 to the nearest 10. Write the error interval.

  1. The rounding step is 10.
  2. Half the step is 5.
  3. Lower bound = 350 - 5 = 345.
  4. Upper bound = 350 + 5 = 355.

Answer: 345 <= x < 355

One decimal place

A length is 12.4 cm to 1 decimal place. Write the error interval.

  1. 1 decimal place has a step of 0.1.
  2. Half the step is 0.05.
  3. Lower bound = 12.4 - 0.05 = 12.35.
  4. Upper bound = 12.4 + 0.05 = 12.45.

Answer: 12.35 <= x < 12.45

Money to nearest 10p

A price is £3.40 to the nearest 10p. Give the upper bound.

  1. Nearest 10p means a step of £0.10.
  2. Half the step is £0.05.
  3. Upper bound = £3.40 + £0.05.

Answer: £3.45

Common mistakes

  • Using 0.5 for every bounds question.
  • Including the upper bound in the error interval.
  • Using the rounded value itself as the lower bound.
  • Adding the full rounding step instead of half the step.
  • Using lower bounds when the question asks for a maximum calculation.

Quick exercise

Try these before moving to the exam-style questions.

  1. A number is 70 to the nearest 10. Give the lower bound.
  2. A number is 70 to the nearest 10. Give the upper bound.
  3. A length is 8.2 cm to 1 decimal place. Give the lower bound.
  4. A mass is 7 kg to the nearest kg. Give the error interval.
  5. A price is £3.40 to the nearest 10p. Give the upper bound.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundation and HigherNon-calculator2 marks

A number, x, is 80 to the nearest 10. Write the error interval.

boundserror intervalnearest 10
Standard exam styleFoundation and HigherCalculator3 marks

A length is 6.8 cm to 1 decimal place. Find the lower and upper bounds.

decimal boundsone decimal placelimits of accuracy
ChallengeHigherCalculator4 marks

A rectangle has length 12.4 cm to the nearest 0.1 cm and width 5.8 cm to the nearest 0.1 cm. Find the upper bound for its area.

upper boundareahigher reasoning