Decimals, Conversion and Ordering
Convert among fractions, decimals and percentages and order values in a common representation.
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
Terminating decimals
Exam cue: Convert all values to one exact or sufficiently precise representation before comparing.
Concept 2
Fraction-decimal-percentage conversion
Exam cue: Place each value approximately on a 0-to-1 or percentage scale and verify the order.
Concept 3
Ordering mixed number forms
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 and Higher
The core techniques are assessed at both tiers. Higher questions can combine them with less scaffolding, algebraic generalisation and unfamiliar 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
Comparing the number of written decimal places instead of place value.
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
Decimal to percentage
Multiply by 100 and attach the percent sign.
Percentage to decimal
Divide by 100.
Terminating decimal condition
In lowest terms, the denominator has only prime factors 2 and 5.
Decimals, Conversion and Ordering: method
Convert all values to one exact or sufficiently precise representation before comparing.
Decimals, Conversion and Ordering: check
Place each value approximately on a 0-to-1 or percentage scale and verify the order.
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 — Convert the terminating decimal 0.375 to its simplest fractional form.
Foundation · AO1 technique · Non-calculator — Write 7/16 as a terminating decimal.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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