How to Solve: Fractions, Decimals, and Percentages Conversions

How to Solve: Fractions, Decimals, and Percentages Conversions

GCSE & A-Level Maths

Introduction

"Mastering fractions, decimals, and percentages conversions unlocks 5–10% of your GCSE Maths exam marks—whether it’s calculating discounts, interpreting data, or solving ratio problems. One wrong conversion, and your answer is worth zero. Let’s make sure that never happens."

What You Need To Know First

Before diving in, ensure you understand: 1. Place value in decimals (tenths, hundredths, thousandths). 2. Simplifying fractions (dividing numerator and denominator by their highest common factor). 3. Basic percentage meaning (per 100).

If any of these feel shaky, pause and review them first.

Key Vocabulary

Formulas To Know

1. Fraction → Decimal
2. Method: Divide numerator by denominator.
3. Example: 3/4 = 3 ÷ 4 = 0.75

4. MEMORISE THIS

5. Decimal → Fraction

6. Method: Write as a fraction over 10, 100, 1000, etc., then simplify.
7. Example: 0.6 = 6/10 = 3/5

8. MEMORISE THIS

9. Percentage → Fraction

10. Method: Write as a fraction over 100, then simplify.
11. Example: 40% = 40/100 = 2/5

12. MEMORISE THIS

13. Fraction → Percentage

14. Method: Convert to decimal first, then multiply by 100.
15. Example: 3/5 = 0.6 → 0.6 × 100 = 60%

16. MEMORISE THIS

17. Decimal → Percentage

18. Method: Multiply by 100 and add %.
19. Example: 0.25 → 0.25 × 100 = 25%

20. MEMORISE THIS

21. Percentage → Decimal

22. Method: Divide by 100.
23. Example: 85% → 85 ÷ 100 = 0.85
24. MEMORISE THIS

Step-by-Step Method

How to Convert Between Fractions, Decimals, and Percentages

1. Fraction → Decimal

Step 1: Divide the numerator by the denominator. Step 2: Write the answer as a decimal. Example: 7/8 → 7 ÷ 8 = 0.875

2. Decimal → Fraction

Step 1: Count the decimal places (e.g., 0.35 has 2 places). Step 2: Write as a fraction over 10, 100, or 1000 (e.g., 35/100). Step 3: Simplify the fraction (e.g., 35/100 = 7/20).

3. Percentage → Fraction

Step 1: Write the percentage as a fraction over 100. Step 2: Simplify the fraction. Example: 60% → 60/100 = 3/5

4. Fraction → Percentage

Step 1: Convert the fraction to a decimal (divide numerator by denominator). Step 2: Multiply by 100 and add %. Example: 2/5 → 2 ÷ 5 = 0.4 → 0.4 × 100 = 40%

5. Decimal → Percentage

Step 1: Multiply by 100. Step 2: Add the % sign. Example: 0.125 → 0.125 × 100 = 12.5%

6. Percentage → Decimal

Step 1: Divide by 100. Step 2: Remove the % sign. Example: 37.5% → 37.5 ÷ 100 = 0.375

Worked Examples

Example 1 – Basic: Convert 3/8 to a decimal and percentage

Step 1: Fraction → Decimal 3 ÷ 8 = 0.375

Step 2: Decimal → Percentage 0.375 × 100 = 37.5%

What we did and why: - We divided the numerator by the denominator to get the decimal. - Then, we multiplied by 100 to convert to a percentage.

Example 2 – Medium: Convert 0.15 to a fraction and percentage

Step 1: Decimal → Fraction 0.15 = 15/100 → Simplify: 3/20

Step 2: Decimal → Percentage 0.15 × 100 = 15%

What we did and why: - We wrote 0.15 as 15/100 and simplified. - Multiplying by 100 gave us the percentage.

Example 3 – Exam-Style: Which is larger, 45% or 7/16?

Step 1: Convert both to decimals for easy comparison. - 45% → 45 ÷ 100 = 0.45 - 7/16 → 7 ÷ 16 = 0.4375

Step 2: Compare the decimals. 0.45 > 0.4375 → 45% is larger.

What we did and why: - We converted both to decimals to compare them directly. - This avoids mistakes from comparing fractions and percentages directly.

Common Mistakes

Exam Traps

1-Minute Recap

"Here’s the night-before cheat sheet: 1. Fraction → Decimal: Divide numerator by denominator. 2. Decimal → Fraction: Write over 10/100/1000, then simplify. 3. Percentage → Fraction: Write over 100, simplify. 4. Fraction → Percentage: Convert to decimal first, then ×100. 5. Decimal → Percentage: ×100. 6. Percentage → Decimal: ÷100.

Common traps? - Always simplify fractions. - Watch for recurring decimals. - Don’t mix up numerator and denominator.

You’ve got this—go ace that exam!