Equivalent Fractions, Decimals and Percentages Table

Why a reference table helps

When you are working through maths problems, estimating, or checking answers, knowing the common equivalents by heart saves time. This table collects the most useful fractions in one place, alongside their decimal and percentage forms.

You can also use it as a study aid. Cover one column and try to recall the other values from memory.

Halves, thirds, and quarters

| Fraction | Decimal | Percentage | |----------|---------|------------| | 1/2 | 0.5 | 50% | | 1/3 | 0.333... | 33.33% | | 2/3 | 0.666... | 66.67% | | 1/4 | 0.25 | 25% | | 2/4 (= 1/2) | 0.5 | 50% | | 3/4 | 0.75 | 75% |

These are the most commonly used equivalents. If you memorise nothing else, memorise these.

Fifths

| Fraction | Decimal | Percentage | |----------|---------|------------| | 1/5 | 0.2 | 20% | | 2/5 | 0.4 | 40% | | 3/5 | 0.6 | 60% | | 4/5 | 0.8 | 80% |

Fifths produce clean terminating decimals because 5 is a factor of 10.

Sixths

| Fraction | Decimal | Percentage | |----------|---------|------------| | 1/6 | 0.1666... | 16.67% | | 2/6 (= 1/3) | 0.333... | 33.33% | | 3/6 (= 1/2) | 0.5 | 50% | | 4/6 (= 2/3) | 0.666... | 66.67% | | 5/6 | 0.8333... | 83.33% |

Notice that 1/6 and 5/6 produce repeating decimals because 6 has a factor of 3.

Eighths

| Fraction | Decimal | Percentage | |----------|---------|------------| | 1/8 | 0.125 | 12.5% | | 2/8 (= 1/4) | 0.25 | 25% | | 3/8 | 0.375 | 37.5% | | 4/8 (= 1/2) | 0.5 | 50% | | 5/8 | 0.625 | 62.5% | | 6/8 (= 3/4) | 0.75 | 75% | | 7/8 | 0.875 | 87.5% |

All eighths terminate because 8 = 2³ and the only prime factor is 2.

Tenths

| Fraction | Decimal | Percentage | |----------|---------|------------| | 1/10 | 0.1 | 10% | | 3/10 | 0.3 | 30% | | 7/10 | 0.7 | 70% | | 9/10 | 0.9 | 90% |

Tenths are the simplest conversions since our number system is base 10.

Twelfths

| Fraction | Decimal | Percentage | |----------|---------|------------| | 1/12 | 0.0833... | 8.33% | | 5/12 | 0.4166... | 41.67% | | 7/12 | 0.5833... | 58.33% | | 11/12 | 0.9166... | 91.67% |

Twelfths are common in clock arithmetic (1 hour = 1/12 of a half-day) and measurement.

Twentieths and twenty-fifths

| Fraction | Decimal | Percentage | |----------|---------|------------| | 1/20 | 0.05 | 5% | | 3/20 | 0.15 | 15% | | 7/20 | 0.35 | 35% | | 9/20 | 0.45 | 45% | | 1/25 | 0.04 | 4% | | 3/25 | 0.12 | 12% |

These appear frequently in test questions about discounts and data.

How the conversions work

All three forms represent the same value:

• Fraction to decimal: Divide numerator by denominator.
• Decimal to percentage: Multiply by 100.
• Percentage to fraction: Divide by 100 and simplify.

For a full walkthrough of the methods, see the Fractions to Decimals and Percent guide.

Using the table for estimation

When you see a fraction in a problem, match it to the nearest value in this table to estimate the answer quickly. For instance, 5/9 is close to 5/10 = 0.5, but also close to 4/8 = 0.5. The exact value (0.555...) is slightly above half. That kind of quick estimation helps you catch calculation errors.

The Fractions Estimating Calculator can help you practise this skill.

Patterns to notice

1. Fractions with denominators that are powers of 2 or 5 always terminate. That includes halves, quarters, fifths, eighths, tenths, twentieths, twenty-fifths, and fiftieths.

2. Fractions with 3, 7, 11, or 13 in the denominator always repeat (when in lowest terms).

3. Equivalent fractions give the same decimal and percentage. 2/4, 3/6, and 1/2 are all 0.5 = 50%.

4. Complementary fractions add up to 1. 3/8 + 5/8 = 1, and their percentages add to 100% (37.5% + 62.5% = 100%).

Tips for memorisation

• Start with benchmarks: 1/2, 1/4, 3/4, 1/3, 2/3. These appear most often.
• Build from what you know: If you know 1/8 = 12.5%, then 3/8 = 3 × 12.5% = 37.5%.
• Use the complement: If 3/5 = 60%, then 2/5 = 100% - 60% = 40%.
• Practise with flashcards: Cover one column and test yourself.

FAQ

Do I need to memorise all of these? For most purposes, knowing halves, thirds, quarters, fifths, and eighths is sufficient. The others can be worked out from these.

What about sevenths? Sevenths produce a repeating block of six digits: 1/7 = 0.142857..., 2/7 = 0.285714..., etc. They are rarely required from memory.

How do I handle fractions not on this table? Use the division method: divide numerator by denominator, then multiply by 100 for the percentage. The table just saves time for common values.

Are these the same in all countries? Yes. Fractions, decimals, and percentages are universal mathematical concepts. Notation may vary slightly (comma vs point for decimals in some countries), but the values are the same everywhere.