Decimal to Fraction Calculator
Enter a decimal number and instantly see it as a simplified fraction, a mixed number, and a percentage — built for homework, measurements, and everyday conversions. Works in reverse too: enter a fraction to see its decimal.
Convert Decimals to Fractions
Enter a decimal, or enter the fraction fields directly — everything updates instantly.
3/4
Why Convert Decimals to Fractions?
A decimal like 0.75 and a fraction like 3/4 represent exactly the same value, just written differently. Decimals are convenient for calculators and digital displays, while fractions are often easier to work with for measurements, recipes, and situations where a value needs to be split into equal parts. Converting between the two lets you move fluidly between whichever form is more useful for the task at hand.
Every terminating decimal (one that doesn't go on forever) can be converted to an exact fraction, because it's really just a whole number divided by a power of ten. Once that fraction is written down, it's simplified to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD).
The Decimal to Fraction Method
Converting a terminating decimal to a fraction follows the same three steps every time.
Terminating Decimals
0.d₁d₂...dₙ = (d₁d₂...dₙ) / 10ⁿ
Write the decimal digits as the numerator over 1 followed by as many zeros as there are decimal places, then simplify.
Example: 0.375 = 375/1000 = 3/8
Repeating Decimals
0.ṙ = r / (10ᵏ − 1)
For a purely repeating decimal with k repeating digits, place those digits over k nines, then simplify.
Example: 0.666... = 6/9 = 2/3
Decimal to Fraction Conversion Table
A ready reference for decimals that come up often in measurements, grades, and recipes.
| Decimal | Fraction | Percentage |
|---|---|---|
| 0.1 | 1/10 | 10% |
| 0.2 | 1/5 | 20% |
| 0.25 | 1/4 | 25% |
| 0.333... | 1/3 | 33.33% |
| 0.5 | 1/2 | 50% |
| 0.625 | 5/8 | 62.5% |
| 0.666... | 2/3 | 66.67% |
| 0.75 | 3/4 | 75% |
For a decimal not listed here, the calculator at the top of this page computes the exact simplified fraction instantly.
Worked Examples: Step by Step
Example 1: Convert 0.6 to a fraction
- Write over a power of 10: 0.6 = 6/10
- Find the GCD of 6 and 10: GCD = 2
- Simplify: 6/10 = 3/5
- Answer: 0.6 = 3/5
Example 2: Convert 0.125 to a fraction
- Write over a power of 10: 0.125 = 125/1000
- Find the GCD of 125 and 1000: GCD = 125
- Simplify: 125/1000 = 1/8
- Answer: 0.125 = 1/8
Example 3: Convert 2.4 to a mixed number and improper fraction
- Separate the whole number: 2.4 = 2 + 0.4
- Convert the decimal part: 0.4 = 4/10 = 2/5
- Mixed number: 2 2/5
- Improper fraction: (2×5 + 2)/5 = 12/5
- Answer: 2.4 = 2 2/5 = 12/5
Where This Conversion Comes Up
Cooking and Baking
Digital kitchen scales often display weights as decimals, while measuring cups and spoons are marked in fractions, so converting between the two keeps a recipe accurate.
Construction and Woodworking
A laser measure or digital caliper reads in decimal inches, but a tape measure is marked in fractions, making this conversion a daily task on a job site.
Homework and Test Prep
Decimal-to-fraction conversion is a core topic in elementary and middle school math, and checking answers helps confirm the simplification step was done correctly.
Grading and Statistics
A grade or score reported as a decimal (like 0.85) is sometimes more intuitive expressed as a fraction or percentage (17/20 or 85%) when communicating results.
Sewing and Pattern Making
Pattern software often exports measurements as decimals, while sewing rulers and seam guides are marked in fractional inches, requiring a quick conversion before cutting.
Common Mistakes When Converting
- Using the wrong power of ten. 0.75 has two decimal places, so it goes over 100 (75/100), not 10 or 1000 — miscounting the decimal places gives a fraction ten times too large or too small.
- Forgetting to simplify the result. A fraction like 50/100 is correct but should be reduced to 1/2 by dividing both terms by their GCD for a clear, standard answer.
- Treating a repeating decimal as if it terminates. Rounding 0.333... to 0.33 before converting gives 33/100, which is close but not exactly equal to the true value of 1/3.
- Dropping the whole number when converting a decimal greater than 1. 1.25 should become the mixed number 1 1/4 (or improper fraction 5/4), not just 1/4 — the whole-number part must be carried through.
Cheat Sheet: Common Decimal Places
| Decimal Places | Denominator | Example |
|---|---|---|
| 1 place | 10 | 0.4 = 4/10 = 2/5 |
| 2 places | 100 | 0.36 = 36/100 = 9/25 |
| 3 places | 1,000 | 0.125 = 125/1000 = 1/8 |
| 4 places | 10,000 | 0.0625 = 625/10000 = 1/16 |
Frequently Asked Questions
How do I convert a decimal to a fraction?
Write the decimal digits over a power of 10 matching the number of decimal places, then simplify using the greatest common divisor. For example, 0.8 = 8/10 = 4/5.
What is 0.35 as a fraction?
0.35 equals 35/100, which simplifies to 7/20.
How do I convert a repeating decimal to a fraction?
Place the repeating digits over a denominator made of the same number of nines, then simplify. For example, 0.181818... = 18/99 = 2/11.
How do I convert a fraction back to a decimal?
Divide the numerator by the denominator. For example, 9/16 = 9 ÷ 16 = 0.5625.
How do I convert a decimal greater than 1 to a fraction?
Separate the whole number part first, convert the decimal part to a fraction, then either keep it as a mixed number or combine into an improper fraction. For example, 3.2 = 3 1/5 = 16/5.
Is every decimal convertible to an exact fraction?
Every terminating or repeating decimal can be written as an exact fraction. Non-repeating, non-terminating decimals (like π) are irrational and cannot be expressed as an exact fraction, only approximated by one.
Does this calculator work in reverse, from fraction to decimal?
Yes. Enter values into the numerator and denominator fields and the decimal field updates automatically — the button lets you jump straight to entering a fraction instead.