GCSE Maths Number - How to Solve: Fractions, Decimals, and Percentages Conversions

How to Solve: Fractions, Decimals, and Percentages Conversions

GCSE / A-Level (Physics, Chemistry, Biology) – Complete Guide

Introduction

"Mastering fractions, decimals, and percentages isn’t just maths—it’s the key to acing 10-15% of your GCSE/A-Level science exams (e.g., calculating concentrations, error margins, or reaction yields). One wrong conversion, and your answer is worthless. Today, you’ll learn the exact steps to convert between them—fast, accurately, and under exam pressure."

WHAT YOU NEED TO KNOW FIRST

Before starting, you must understand: 1. Place value in decimals (tenths, hundredths, thousandths). 2. Basic fraction rules (e.g., simplifying, finding common denominators). 3. Percentage meaning (per 100).

If you’re shaky on any of these, pause and review them first.

KEY TERMS & FORMULAS

Key Terms

• Fraction: Part of a whole (e.g., ¾ = 3 parts out of 4).
• Decimal: A fraction written in base 10 (e.g., 0.75 = 75/100).
• Percentage: A fraction out of 100 (e.g., 75% = 75/100).

Formulas

1. Fraction → Decimal
   Method: Divide numerator by denominator.
   Example: ¾ → 3 ÷ 4 = 0.75

2. Decimal → Fraction
   Method: Write as a fraction over 10, 100, or 1000 (based on decimal places), then simplify.
   Example: 0.6 → 6/10 → 3/5

3. Decimal → Percentage
   Formula: Decimal × 100%
   Example: 0.45 → 0.45 × 100% = 45%

4. Percentage → Decimal
   Formula: Percentage ÷ 100%
   Example: 8% → 8 ÷ 100 = 0.08

5. Fraction → Percentage
   Method: Convert fraction → decimal → percentage.
   Example: 2/5 → 0.4 → 0.4 × 100% = 40%

6. Percentage → Fraction
   Method: Write as a fraction over 100, then simplify.
   Example: 60% → 60/100 → 3/5

MEMORISE THIS: The decimal ↔ percentage conversions (×100% or ÷100%) are the most critical for exams.

STEP-BY-STEP METHOD

How to Convert Between Fractions, Decimals, and Percentages

Follow these steps in order for any conversion:

1. Identify the starting format

• Is it a fraction, decimal, or percentage?

2. Choose the correct path

• Use the formulas above to pick the right conversion route.

3. Perform the conversion

• Fraction → Decimal: Divide numerator by denominator.
• Decimal → Fraction: Write over 10/100/1000, simplify.
• Decimal ↔ Percentage: ×100% or ÷100%.
• Fraction ↔ Percentage: Go via decimal.

4. Simplify (if needed)

• Fractions: Divide numerator/denominator by their highest common factor (HCF).
• Decimals: Round to 2-3 decimal places unless specified.

5. Check your answer

• Does it make sense? (e.g., 50% should be 0.5 or ½).

Worked Example (Using Steps)

Question: Convert 3/8 to a percentage.

Step 1: Starting format = fraction (3/8). Step 2: Path = Fraction → Decimal → Percentage. Step 3: - 3 ÷ 8 = 0.375 (decimal). - 0.375 × 100% = 37.5%. Step 4: Already simplified. Step 5: 3/8 is less than ½, so 37.5% makes sense.

Answer: 37.5%

WORKED EXAMPLES

Example 1 – Basic

Question: Convert 0.2 to a fraction. Working: 1. 0.2 = 2/10. 2. Simplify: 2 ÷ 2 = 1, 10 ÷ 2 = 5 → 1/5. What we did and why: Wrote the decimal as a fraction over 10, then simplified by dividing numerator/denominator by 2.

Example 2 – Medium

Question: Convert 12.5% to a decimal. Working: 1. 12.5% ÷ 100% = 0.125. What we did and why: Used the percentage → decimal formula (÷100%). No simplification needed.

Example 3 – Exam-Style

Question (GCSE Chemistry): A solution is 3/20 concentrated. What is this as a percentage? Working: 1. 3 ÷ 20 = 0.15 (decimal). 2. 0.15 × 100% = 15%. What we did and why: Converted fraction → decimal → percentage, then checked that 3/20 is less than ¼ (25%), so 15% is reasonable.

COMMON MISTAKES

EXAM TRAPS

1-MINUTE RECAP

"Night before the exam? Here’s the ultra-fast version: 1. Fraction → Decimal: Numerator ÷ denominator (e.g., ½ = 0.5). 2. Decimal → Percentage: ×100% (e.g., 0.5 = 50%). 3. Percentage → Decimal: ÷100% (e.g., 25% = 0.25). 4. Fraction → Percentage: Go via decimal (e.g., ¼ = 0.25 = 25%). 5. Always simplify fractions and check your answer—does it make sense? Pro tip: If stuck, convert to a decimal first. It’s the easiest middle step. You’ve got this—go smash those conversions!"