Decimal to Fraction Calculator

Convert decimal numbers to fractions in their simplest form with our easy-to-use calculator.

How to Use This Calculator

Enter the decimal number you want to convert to a fraction
Select the maximum denominator for precision or choose a custom value
Choose whether to display the result as a mixed number when applicable
Click "Convert" to see the fraction representation of your decimal

Formula Used

Decimal × 10^n = Fraction

Where:

n = Number of decimal places
The resulting fraction is then simplified to its lowest terms
For repeating decimals, special algorithms are applied to find the exact fraction

Example Calculation

Real-World Scenario:

Converting 0.375 to a fraction for a woodworking measurement

Given:

Decimal = 0.375
Maximum denominator = 1000

Calculation:

0.375 × 1000 = 375/1000

Simplify by dividing numerator and denominator by their greatest common divisor (125):

375 ÷ 125 = 3

1000 ÷ 125 = 8

Result: 3/8 (which equals 0.375)

Why This Calculation Matters

Practical Applications

Cooking and baking measurements
Construction and woodworking
Engineering and technical drawings

Key Benefits

Precise measurements without rounding errors
Easy to understand fractional representations
Useful for teaching mathematical concepts

Common Mistakes & Tips

Using a maximum denominator that's too small can result in an inaccurate fraction. For example, converting 0.125 with a maximum denominator of 10 would give 1/8, but with a maximum denominator of 100, it would correctly give 1/8. Always use a denominator large enough for your decimal's precision.

Terminating decimals (like 0.25) have a finite number of digits and can be represented exactly as a fraction. Repeating decimals (like 0.333...) have an infinite number of digits and require special algorithms to convert to fractions. Make sure to include enough digits of repeating decimals for accurate conversion.

Frequently Asked Questions

For a repeating decimal like 0.333..., you can set x = 0.333..., then multiply both sides by 10 to get 10x = 3.333..., subtract the original equation to get 9x = 3, and solve for x to get x = 3/9 = 1/3. For more complex repeating patterns, similar algebraic methods can be used.

A decimal has an exact fractional representation if it terminates (has a finite number of digits) or repeats a pattern. Decimals that neither terminate nor repeat are irrational numbers and cannot be expressed as exact fractions. Examples of irrational numbers include π (3.14159...) and √2 (1.41421...).

A proper fraction has a numerator smaller than its denominator (e.g., 3/4). An improper fraction has a numerator equal to or larger than its denominator (e.g., 5/4). A mixed number combines a whole number and a proper fraction (e.g., 1 1/4). Our calculator can display results as mixed numbers when applicable.

References & Disclaimer

Mathematical Disclaimer

This calculator provides conversions based on standard mathematical algorithms. For educational purposes, results are accurate to the precision specified. For critical applications, verify calculations independently.

References

Converting Decimals to Fractions - Math Is Fun: A comprehensive guide on converting decimals to fractions with examples
Fractions and Decimals - Khan Academy: Video tutorials on the relationship between fractions and decimals
Repeating Decimal - Wikipedia: Mathematical explanation of repeating decimals and their fractional representations

Accuracy Notice

This calculator uses standard algorithms for decimal-to-fraction conversion. Results are accurate to the precision specified by the maximum denominator setting. For very large or very small numbers, some precision may be lost due to floating-point limitations.

About the Author

Kumaravel Madhavan

Web developer and data researcher creating accurate, easy-to-use calculators across health, finance, education, and construction and more. Works with subject-matter experts to ensure formulas meet trusted standards like WHO, NIH, and ISO.

Connect with LinkedIn

Tags:

math arithmetic decimal fraction equation formula calculation

Related Calculators