Convert fractions, decimals, percentages and ratios
Express one quantity in equivalent forms · Distinguish a ratio from a share of the whole · Order mixed forms after conversion
Section Paper 3 · Historical Core · calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Fraction simplification
- Division
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Express one quantity in equivalent forms
- Distinguish a ratio from a share of the whole
- Order mixed forms after conversion
Equivalent forms
A fraction is numerator divided by denominator; a percentage is a fraction of 100. Thus 3/8 = 0.375 = 37.5%. To convert a terminating decimal to a fraction, use its place value and simplify: 0.24 = 24/100 = 6/25.
A ratio a:b between two categories gives first-category fraction a/(a+b) of their combined total. If instead the notation compares a part directly with its whole, a:b means a/b; identify the meaning before converting.
Comparison
Convert all quantities into one form, then compare values. A percent sign changes the scale: 0.5% = 0.005, not 0.5. Keep enough precision when ordering close quantities; an early rounded tie may hide their true order.
Sources for this lesson
Pause and explain
What decimal is 0.5%?
Worked example
Order 2/5, 0.38 and 41%.
Show the worked solution
- 2/5 = 0.4 and 41% = 0.41.
- Compare 0.38, 0.4 and 0.41.
Answer 0.38 < 2/5 < 41%.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Write 7/20 as a decimal and percentage.
Give me a hint
Make a denominator of 100.
Compare my reasoning
- 7/20 = 35/100.
- This is 0.35 and 35%.
0.35; 35%.
Look for these in your work
- Keep equivalent values
- Use the percent sign correctly
Order 0.62, 5/8 and 63%.
Give me a hint
Convert without premature rounding.
Compare my reasoning
- 5/8 = 0.625; 63% = 0.63.
- 0.62 < 0.625 < 0.63.
0.62 < 5/8 < 63%.
Look for these in your work
- Use one common form
- Retain enough decimal places
A group has returning:new students in ratio 3:2. What fraction and percentage are new?
Give me a hint
The whole has five parts.
Compare my reasoning
- New share = 2/(3 + 2) = 2/5.
- 2/5 = 40%.
2/5 or 40% are new.
Look for these in your work
- Identify a part-to-part ratio
- Convert its share of the whole
Common mistakes
- 0.5% and 50% are different.
- State whether a ratio is part:part or part:whole.
What can you explain now?
What decimal is 0.5%?
Compare with the explanation
0.005.
Percent means divide by 100.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
What decimal is 0.5%?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.