Percentages • Topic 2 of 3

Converting Between Fractions, Decimals, Percents

The Conversion Triangle:

        PERCENT
           %
        ↗     ↖
       /       \
    FRACTION   DECIMAL

Conversion Rules:

From	To	Method
Percent	Fraction	Put over 100, simplify
Percent	Decimal	Divide by 100
Fraction	Decimal	Divide numerator by denominator
Decimal	Percent	Multiply by 100
Decimal	Fraction	Write decimal as fraction, simplify
Fraction	Percent	Convert to decimal first, then ×100

CONVERSION FLOWCHART:

    FRACTION ──────divide───→ DECIMAL
         ↑                        │
         │                        │
      simplify                multiply
         │                        │
         │                        ↓
    ┌───┴───────────────────    PERCENT
    │   put over 100              │
    │                        divide by 100
    │                        multiply by 100
    ↓                              │
    DECIMAL ←─────write as fraction──┘


COMMON EQUIVALENTS (MEMORIZE!):

    Fraction    Decimal    Percent
    ───────────────────────────────
    ½          0.5        50%
    ¼          0.25       25%
    ¾          0.75       75%
    ⅕          0.2        20%
    ⅖          0.4        40%
    ⅗          0.6        60%
    ⅘          0.8        80%
    ⅓          0.333...   33⅓%
    ⅔          0.666...   66⅔%
    ⅛          0.125      12.5%
    ⅜          0.375      37.5%
    ⅝          0.625      62.5%
    ⅞          0.875      87.5%

Solved Examples

Worked Example

Convert (3)/(5) to percent

Solution

Method A: (3)/(5) = 0.6, 0.6 × 100 = 60%
Method B: (3)/(5) = 60/100 = 60%
Answer: 60%

Worked Example

Convert 0.375 to fraction and percent

Solution

Fraction: 0.375 = 375/1000 = simplify divide 125 → (3)/(8)
Percent: 0.375 × 100 = 37.5%
Answer: (3)/(8) and 37.5%

Worked Example

Convert 120% to decimal and fraction

Solution

Decimal: 120% ÷ 100 = 1.2
Fraction: 120/100 = 12/10 = 6/5 = 1⅕
Answer: 1.2 and 6/5

Key Points

Decimal → Percent: multiply by 100 (move decimal 2 places right)
Percent → Decimal: divide by 100 (move decimal 2 places left)
Fraction → Decimal: numerator ÷ denominator
Fraction → Percent: numerator ÷ denominator × 100
Memorize common conversions (½=50%, ¼=25%, etc.)

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.To change a decimal to a percent, multiply by:

Explanation: $\times100$.

Q2.To change a percent to a decimal, divide by:

Explanation: $\div100$.

Q3.$\tfrac12=0.5=$

Explanation: $50\%$.

Q4.$0.25=$

Explanation: $25\%$.

Practice more MCQs → 📝 Assignment · 35 marks