Practice Maths

L35 — Converting Between Fractions, Decimals & Percentages

Key Terms

fraction
A number written as numeratordenominator — the top shows how many parts, the bottom shows how many parts the whole is divided into.
decimal
A number written using a decimal point to show values less than one. E.g. 0.75.
percentage
A fraction out of 100, written with a % symbol. E.g. 75%.

Conversion Rules

  • Fraction → Decimal: divide numerator ÷ denominator
  • Decimal → Percentage: multiply × 100
  • Percentage → Decimal: divide ÷ 100
  • Percentage → Fraction: write over 100, then simplify
Quick shortcuts to memorise:
12 = 0.5 = 50%    14 = 0.25 = 25%    34 = 0.75 = 75%    15 = 0.2 = 20%    110 = 0.1 = 10%    18 = 0.125 = 12.5%

Worked Examples

Convert 34 to decimal and percentage:

3 ÷ 4 = 0.75  →  0.75 × 100 = 75%

Convert 0.6 to fraction and percentage:

0.6 = 610 = 35  →  0.6 × 100 = 60%

Convert 45% to decimal and fraction:

45 ÷ 100 = 0.45  →  45100 = 920

Three Languages for the Same Number

Fractions, decimals, and percentages are three different ways of writing the same thing. 12 = 0.5 = 50%. Being able to move between these three forms is like being trilingual — you can communicate in whatever language the situation requires.

  • A sale tag shows “25% off.”
  • A nutritionist talks about “0.3 g of fat per gram.”
  • A recipe says “13 cup of milk.”

The Conversion Map

Think of three cities (Fraction, Decimal, Percentage) connected by roads:

  • Fraction → Decimal: divide the top by the bottom. 34 = 3 ÷ 4 = 0.75.
  • Decimal → Percentage: multiply by 100. 0.75 × 100 = 75%.
  • Percentage → Decimal: divide by 100. 75% ÷ 100 = 0.75.
  • Percentage → Fraction: write over 100 and simplify. 75% = 75100 = 34.

So to go from fraction to percentage: divide first, then multiply by 100. 58 = 5 ÷ 8 = 0.625 → 0.625 × 100 = 62.5%.

Learn the most common ones by heart: 12 = 0.5 = 50%, 14 = 0.25 = 25%, 34 = 0.75 = 75%, 15 = 0.2 = 20%, 18 = 0.125 = 12.5%. These come up constantly in shopping, test results, and everyday conversation.

Comparing Mixed Forms

To arrange 0.7, 65%, 34, and 0.68 in order, convert everything to decimals first:

  • 0.7 → 0.7
  • 65% → 0.65
  • 34 → 0.75
  • 0.68 → 0.68
  • Order: 0.65, 0.68, 0.7, 0.75  →  so: 65%, 0.68, 0.7, 34

Finding a Percentage of a Quantity

Converting to decimals makes percentage calculations easy:

  • 30% of 90 = 0.30 × 90 = 27
  • 15% of $60 = 0.15 × 60 = $9
  • 20% off → pay 80% → multiply by 0.8
Common mistake: Confusing 0.4 with 0.4% — they are completely different! 0.4 = 40%, while 0.4% = 0.004 as a decimal. The percent sign fundamentally changes the value.

  1. Fractions to Decimals

    1. 12
    2. 34
    3. 15
    4. 25
    5. 710
    6. 38
    7. 58
    8. 14

  2. Fractions to Percentages

    1. 14
    2. 35
    3. 710
    4. 18
    5. 320
    6. 925
    7. 1350
    8. 58

  3. Decimals to Fractions (simplified)

    1. 0.5
    2. 0.25
    3. 0.8
    4. 0.6
    5. 0.75
    6. 0.4
    7. 0.35
    8. 0.125

  4. Decimals to Percentages

    1. 0.3
    2. 0.75
    3. 0.07
    4. 0.9
    5. 0.45
    6. 0.125
    7. 0.02
    8. 1.5

  5. Percentages to Decimals and Fractions

    1. 50%
    2. 25%
    3. 80%
    4. 15%
    5. 4%
    6. 37.5%
    7. 110%
    8. 2.5%

  6. Complete the Conversion Table

    Convert each starting value to all three forms:

    1. Start: 25 → decimal = ?, percentage = ?
    2. Start: 0.35 → fraction = ?, percentage = ?
    3. Start: 60% → decimal = ?, fraction = ?
    4. Start: 78 → decimal = ?, percentage = ?
    5. Start: 0.04 → fraction = ?, percentage = ?
    6. Start: 12.5% → decimal = ?, fraction = ?

  7. Order from Smallest to Largest

    1. 0.7,  65%,  34,  0.68
    2. 30%,  0.32,  13,  0.29
    3. 58,  60%,  0.65,  0.63
    4. 0.92,  85%,  910,  89%

  8. Real-World Conversions

    1. A jacket is on sale for 25% off. Write the discount as a decimal multiplier.
    2. A student scored 1720 on a test. What is their percentage score?
    3. A tank is 0.6 full. What percentage is full? What fraction is empty?
    4. A recipe uses 750 mL of milk out of 1 L total liquid. Express this as a fraction, decimal, and percentage.
    5. Three friends each save a different fraction of their pocket money: Alex saves 14, Blake saves 30%, Casey saves 0.28. Who saves the most?

  9. Percentage of Quantities

    Calculate:

    1. 50% of 80
    2. 25% of 120
    3. 10% of 350
    4. 75% of 200
    5. 30% of 90
    6. 15% of 60
    7. 40% of 250
    8. 5% of 140

  10. Exam Challenge

    1. A store offers 20% off a $85 item. What is the sale price?
    2. If 35% of a class are boys and there are 14 boys, how many students are in the class?
    3. A bottle is 0.375 full. Express this as a percentage and as a fraction in simplest form.
    4. Which is greater: 0.4% or 0.4? Explain how you know.
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