Rounding, Bounds and Error Intervals
Round to specified accuracy and reason with intervals, limits of accuracy and bounds.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Decimal places and significant figures
Exam cue: Identify half of the rounding unit, write the lower endpoint inclusive and upper endpoint exclusive, then choose bounds according to the operation.
Concept 2
Error intervals
Exam cue: Confirm that every value in the interval rounds to the stated measurement and test the extremal combination.
Concept 3
Upper and lower bounds
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation core with Higher-tier extensions
Both tiers round and estimate. Higher develops formal error intervals and upper/lower-bound calculations in compound and multi-step contexts.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Treating a rounded value as exact or including the upper endpoint of its error interval.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Rounded to nearest u
The error is less than half of u.
Error interval
Lower bound ≤ actual value < upper bound.
Maximum quotient
Use the largest possible numerator and smallest positive denominator.
Rounding, Bounds and Error Intervals: method
Identify half of the rounding unit, write the lower endpoint inclusive and upper endpoint exclusive, then choose bounds according to the operation.
Rounding, Bounds and Error Intervals: check
Confirm that every value in the interval rounds to the stated measurement and test the extremal combination.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Foundation · AO1 technique · Non-calculator — Round 48.367 to two decimal places.
Foundation · AO1 technique · Non-calculator — A laboratory mass is recorded as 0.006784 g. Round this measurement to two significant figures.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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