Conversion Hub
Fraction Converter
Type a mixed number once and see it instantly as an improper fraction, a decimal, and a percent — all three at the same time, all three exact, all three updating as you type.
Mixed Number
Improper
Decimal
Percent
View step-by-step working
Method
One Value, Three Notations
A mixed number, an improper fraction, a decimal, and a percent are four different outfits for the exact same number.
Worked Example — 2 3/4
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Combine into a numerator
2 × 4 + 3 = 11
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Improper fraction
11/4
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Divide for the decimal
11 ÷ 4 = 2.75
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Multiply by 100 for the percent
2.75 × 100 = 275%
2 3/4 = 11/4 = 2.75 = 275%
Worked Examples
The Same Value in Every Form
Quarters
1 1/4 = 5/4 = 1.25 = 125%
Halves
3 1/2 = 7/2 = 3.5 = 350%
Fifths
1 2/5 = 7/5 = 1.4 = 140%
Thirds — repeating
2 1/3 = 7/3 = 2.333… = 233.3…%
The improper fraction stays exact; the decimal and percent must be truncated.
A whole number
5 = 5/1 = 5.0 = 500%
A negative value
−1 1/2 = −3/2 = −1.5 = −150%
Why It Matters
Choosing the Right Form for the Job
Every one of these four notations is correct at all times — none of them is the "real" answer with the others being approximations. What changes is which one is easiest to work with for a given task. A recipe or a tape measure reads naturally as a mixed number. Hand arithmetic — adding, subtracting, multiplying, or dividing — is genuinely simpler once everything is an improper fraction, since there is only one numerator and one denominator to track instead of a whole number plus a fraction.
A decimal is the form to reach for when comparing sizes quickly or typing a value into a calculator or spreadsheet, since decimals sort and compare the way ordinary numbers do. A percent is the form for communicating a rate or proportion to another person — "275% of the recipe" reads more naturally in conversation than "2.75 times" or "11/4 of."
The one place the choice genuinely matters for correctness, not just convenience, is exactness. Whenever a denominator has a prime factor other than 2 or 5 — thirds, sixths, sevenths, ninths, and so on — its decimal and percent forms repeat forever and have to be cut off somewhere. The improper fraction never has this problem; 7/3 is exactly 7/3 no matter how it's written, while 2.333… is always an approximation once it's been truncated to fit on a screen.
For that reason, any calculation that will be converted back into a fraction later — a recipe scaled up, a measurement split evenly — is safer done in fraction form throughout, saving the decimal or percent conversion for the very last step, purely for display.
Quick Reference
Common Fraction, Decimal, and Percent Equivalents
The fractions that show up most often in daily life — halves, thirds, quarters, fifths, sixths, eighths, tenths, and sixteenths — laid out with their decimal and percent equivalents side by side. Values with a trailing ellipsis repeat forever and have been truncated for display; every fraction to the left of it stays exact.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33…% |
| 2/3 | 0.667… | 66.67…% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/6 | 0.167… | 16.67…% |
| 5/6 | 0.833… | 83.33…% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
| 1/16 | 0.0625 | 6.25% |
Notice the pattern: any denominator built only from 2s and 5s — halves, quarters, fifths, eighths, tenths, sixteenths — lands on a decimal that stops cleanly. Anything with a 3 in its denominator, like thirds and sixths, repeats forever no matter how far it's carried out.
Common Mistakes
Where Conversions Between Forms Go Wrong
Questions
Frequently Asked Questions
Questions about moving between mixed numbers, fractions, decimals, and percents.