Fraction Conversion Tool
Use decimal, percentage, mixed number, fraction, or repeating decimal input.
Example Data Table
These examples show common input styles and their reduced results.
| Input | Input type | Simplified fraction | Mixed form |
|---|---|---|---|
| 0.625 | Decimal | 5/8 | 5/8 |
| 37.5% | Percentage | 3/8 | 3/8 |
| 3 1/4 | Mixed number | 13/4 | 3 1/4 |
| 1.2(45) | Repeating decimal | 137/110 | 1 27/110 |
| -2.75 | Decimal | -11/4 | -2 3/4 |
Formula Used
The method depends on the value you enter. Every final fraction is reduced by the greatest common divisor.
For a mixed number, multiply the whole number by the denominator. Add the fractional numerator. Keep the original sign. The calculator then reduces the result.
How to Use This Calculator
- Enter one number in the value field.
- Select the input type that matches your number.
- Choose automatic, fraction, mixed, or both result forms.
- Select exact mode for a complete value.
- Select denominator-limit mode for a simpler approximation.
- Choose a maximum denominator when using the limited mode.
- Press the conversion button to show the answer above the form.
- Download the result as CSV or PDF when you need a record.
Understand Fraction Notation
Why Fraction Notation Matters
Fractions show exact parts of a whole. They are useful when decimals feel long or unclear. A value such as 0.375 becomes 3/8. That form is easier to compare, measure, and reuse. It supports decisions.
From Decimals to Fractions
A terminating decimal can become a fraction by using place value. One decimal digit uses ten as the denominator. Two digits use one hundred. Three digits use one thousand. For example, 0.64 becomes 64/100. Both divide by four. The reduced answer is 16/25.
Trailing zeros do not change a value. The numbers 0.5, 0.50, and 0.500 represent the same amount. Their starting denominators differ, but reduction produces 1/2 in every case. Keeping a fraction reduced makes it shorter.
Working With Percentages
A percentage means parts per hundred. Convert 37.5% by first writing 37.5/100. Move the decimal one place or build an exact decimal fraction. The final reduced form is 3/8. Percent conversion is helpful for discounts, rates, test scores, and probability.
Mixed Numbers and Improper Fractions
An improper fraction has a numerator at least as large as its denominator. It can be rewritten as a mixed number. For example, 17/5 equals 3 2/5. The whole number comes from division. The remainder becomes the new numerator. Both forms are correct. Choose the form that best matches your task.
Improper fractions are often better for multiplication and division. Mixed numbers are often easier to read in daily measurements. The output options let you view both formats. This saves time when a worksheet, recipe, plan, or estimate requires a specific notation.
Repeating Values Need a Different Rule
Repeating decimals do not end. A number such as 0.333... equals 1/3. A repeating block can be converted by shifting the decimal and subtracting matching values. This removes the recurring section. The calculator accepts parentheses for the repeated digits, such as 0.(3) or 1.2(45). It then creates a reduced fraction.
Accuracy and Denominator Limits
Exact conversion is best when the original value is complete. Sometimes you only know a rounded decimal. In that situation, a denominator limit can produce a practical nearby fraction. For instance, 3.14159 may display as 355/113 when a suitable limit is selected. The result is an approximation, not the original exact value.
Always check the displayed decimal before using an approximation. A small difference may matter in engineering, dosage planning, or money calculations. Use a larger denominator limit when you need finer matching. Use a smaller limit when you want a simple, readable fraction.
Build Good Fraction Habits
Enter values carefully and select the matching input type. Read the result, simplified form, mixed form, and decimal check. Save the output when you need a record. Fractions make numeric relationships easier to understand and share.
Frequently Asked Questions
What does fraction notation mean?
Fraction notation writes a value as a numerator over a denominator. The numerator shows selected parts. The denominator shows equal total parts. A reduced fraction removes common factors while keeping the same value.
Can this convert a decimal into a fraction?
Yes. Choose Decimal, enter a value such as 0.625, and convert it. The calculator uses decimal place value, then reduces the resulting fraction.
How are percentages converted?
A percentage is divided by 100 before reduction. For example, 25% becomes 25/100, then reduces to 1/4.
How do I enter a repeating decimal?
Put the repeating digits inside parentheses. Enter 0.(3) for 0.333..., or 1.2(45) for 1.2454545.... Select Repeating decimal before converting.
Can I simplify an existing fraction?
Yes. Choose Fraction and enter a value like 18/24. The calculator reduces it to 3/4 and also shows the matching mixed number when relevant.
What is a mixed number?
A mixed number combines a whole number with a proper fraction. For example, 2 1/2 represents two full units and one half of another unit.
Why would I set a maximum denominator?
A denominator limit can turn a long exact fraction into a simpler nearby fraction. This is helpful when your decimal is rounded or when readability matters more than perfect exactness.
Is limited mode always exact?
No. Limited mode may create an approximation when the exact denominator is higher than your chosen limit. The result panel clearly notes when an approximation was applied.
Does the calculator support negative values?
Yes. Enter a minus sign before the number, such as -2.75 or -3 1/4. The calculator keeps the sign in every equivalent output form.
Why does my result show both fraction forms?
Simplified fractions are useful for calculations. Mixed numbers are easier to read for quantities above one. Showing both helps you choose the notation your work requires.
Can I save my conversion?
Yes. After a successful calculation, use Download CSV for spreadsheet data or Download PDF for a compact result record.