Dual-Direction Conversion Tool
Decimal to Fraction Calculator
Convert any terminating or repeating decimal into an exact, simplified fraction with instant step-by-step mathematical solutions.
Switch seamlessly between decimal-to-fraction and fraction-to-decimal modes to solve math problems, verify engineering specs, or reduce ratios.
Simplified Fraction Result
3/4
Input Decimal
0.75
Simplified Fraction
3/4
Mixed Number
Not Applicable
Step-by-Step Calculation
Decimal Result
0.75
Input Fraction
3/4
Decimal Type
Terminating Decimal
Simplified Fraction
3/4
Step-by-Step Calculation
How to Convert a Decimal to a Fraction
Follow these three essential mathematical steps to convert any terminating decimal into a reduced fraction.
1
Count Decimal Places
Determine the total digits appearing after the decimal point (e.g.,
0.75 has two decimal places).
2
Write Over a Power of 10
Remove the decimal dot and place the resulting integer over 10 raised to the decimal count (e.g.,
75 / 100).
3
Simplify Using the GCD
Divide both numerator and denominator by their Greatest Common Divisor (e.g., GCD of 75 and 100 is 25, yielding
3/4).
Worked Example: Convert 1.25 into a Simplified Fraction
1. Count decimal places:
2. Place over 100:
3. Divide top & bottom by GCD (25):
1.25 → 2 decimal places.2. Place over 100:
125 / 100.3. Divide top & bottom by GCD (25):
(125 ÷ 25) / (100 ÷ 25) = 5/4 (or mixed number 1 1/4).
How to Simplify a Fraction
Reduce any fraction to its lowest terms (irreducible form) using the Greatest Common Divisor (GCD).
1
Find Greatest Common Divisor (GCD)
Identify the largest integer that divides evenly into both numerator and denominator (e.g. for
24/36, GCD is 12).
2
Divide Top and Bottom
Divide both numbers by the GCD:
(24 ÷ 12) / (36 ÷ 12) = 2/3.
3
Verify Lowest Terms
Ensure the only common factor remaining between numerator and denominator is 1.
2/3 is fully simplified!
Worked Example: Simplify 75/100
1. Factors of 75: 1, 3, 5, 15, 25, 75.
2. Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
3. Greatest Common Divisor (GCD) = 25.
4. Simplify:
2. Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
3. Greatest Common Divisor (GCD) = 25.
4. Simplify:
(75 ÷ 25) / (100 ÷ 25) = 3/4.
How to Convert a Fraction to a Decimal
Perform division by dividing the top number (numerator) by the bottom number (denominator).
Category 1
Terminating Decimals
Decimals with a finite number of digits following the decimal point.
Examples: 3/4 = 0.75, 1/8 = 0.125, 1/2 = 0.5.
Examples: 3/4 = 0.75, 1/8 = 0.125, 1/2 = 0.5.
Category 2
Repeating Decimals
Decimals with digits that repeat infinitely in a recurring sequence.
Examples: 1/3 = 0.333..., 1/6 = 0.1666..., 2/3 = 0.666....
Examples: 1/3 = 0.333..., 1/6 = 0.1666..., 2/3 = 0.666....
Fraction to Decimal Formula
Division Formula: Decimal Value = Numerator ÷ Denominator
Example: For fraction 3/8, calculate
Example: For fraction 3/8, calculate
3 ÷ 8 = 0.375 (Terminating Decimal).
Terminating vs. Repeating Decimals
Understand the structural differences between finite terminating decimals and recurring repeating decimals.
Terminating Decimal
Finite Decimal Expansion
Decimals that end cleanly after a specific number of decimal places. Occurs when a reduced fraction's denominator contains only prime factors of 2 and 5.
Key Examples:
• 1/2 = 0.5 (1 decimal place)
• 3/4 = 0.75 (2 decimal places)
• 1/8 = 0.125 (3 decimal places)
Key Examples:
• 1/2 = 0.5 (1 decimal place)
• 3/4 = 0.75 (2 decimal places)
• 1/8 = 0.125 (3 decimal places)
Repeating Decimal
Infinite Recurring Pattern
Decimals with digits that repeat infinitely in a periodic cycle. Occurs when a reduced fraction's denominator contains prime factors other than 2 or 5 (like 3, 7, 11). Represented using a vinculum bar over repeating digits.
Key Examples:
• 1/3 = 0.333...
• 1/6 = 0.1666...
• 1/7 = 0.142857...
Key Examples:
• 1/3 = 0.333...
• 1/6 = 0.1666...
• 1/7 = 0.142857...
Mixed Numbers and Improper Fractions
How decimals greater than 1 convert into improper fractions and whole-plus-fraction mixed numbers.
Form 1
Improper Fraction
A fraction where the numerator is greater than or equal to the denominator (e.g.,
7/4, 15/8). When converting a decimal like 1.75 to a fraction:
1.75 = 175 / 100 = 7/4
Form 2
Mixed Number
Combines a whole number integer with a proper fraction (e.g.,
1 3/4, 1 7/8). To convert an improper fraction to a mixed number, divide numerator by denominator:
7 ÷ 4 = 1 remainder 3 → 1 3/4
Step-by-Step Conversion: Decimal 2.375 to Mixed Number
1. Separate integer and fractional decimal: Whole Part =
2. Convert decimal part:
3. Simplify fraction using GCD (125):
4. Combine whole part and simplified fraction: 2 3/8 (or improper fraction 19/8).
2, Decimal Part = 0.375.2. Convert decimal part:
0.375 = 375 / 1000.3. Simplify fraction using GCD (125):
(375 ÷ 125) / (1000 ÷ 125) = 3/8.4. Combine whole part and simplified fraction: 2 3/8 (or improper fraction 19/8).
Common Decimal to Fraction Examples
Explore instant conversion results for the most frequently calculated terminating and repeating decimals:
0.25 Decimal
0.25 = 25/100 = 1/40.5 Decimal
0.5 = 5/10 = 1/20.75 Decimal
0.75 = 75/100 = 3/40.125 Decimal
0.125 = 125/1000 = 1/80.375 Decimal
0.375 = 375/1000 = 3/80.625 Decimal
0.625 = 625/1000 = 5/80.875 Decimal
0.875 = 875/1000 = 7/80.333... (Repeating)
0.333... = 3/9 = 1/30.666... (Repeating)
0.666... = 6/9 = 2/31.25 Decimal
1.25 = 125/100 = 5/4 (1 1/4)Decimal to Fraction Conversion Reference Table
Below is a quick reference table of common decimal-to-fraction equivalents frequently used in math, engineering, and science:
| Decimal | Unsimplified Fraction | Simplified Fraction | Decimal Type |
|---|---|---|---|
| 0.1 | 10/100 | 1/10 | Terminating |
| 0.2 | 2/10 | 1/5 | Terminating |
| 0.25 | 25/100 | 1/4 | Terminating |
| 0.333... | 333/999 | 1/3 | Repeating |
| 0.5 | 5/10 | 1/2 | Terminating |
| 0.6 | 6/10 | 3/5 | Terminating |
| 0.666... | 666/999 | 2/3 | Repeating |
| 0.75 | 75/100 | 3/4 | Terminating |
| 0.8 | 8/10 | 4/5 | Terminating |
| 0.875 | 875/1000 | 7/8 | Terminating |
| 1.25 | 125/100 | 5/4 (1 1/4) | Terminating |
| 1.5 | 15/10 | 3/2 (1 1/2) | Terminating |
| 1.75 | 175/100 | 7/4 (1 3/4) | Terminating |
Common Fraction to Decimal Examples
Reference key division results and decimal equivalents for essential fractions:
1/2 Fraction
1 ÷ 2 = 0.51/3 Fraction
1 ÷ 3 = 0.333...1/4 Fraction
1 ÷ 4 = 0.251/5 Fraction
1 ÷ 5 = 0.21/6 Fraction
1 ÷ 6 = 0.1666...3/4 Fraction
3 ÷ 4 = 0.752/3 Fraction
2 ÷ 3 = 0.666...5/8 Fraction
5 ÷ 8 = 0.6257/8 Fraction
7 ÷ 8 = 0.8759/10 Fraction
9 ÷ 10 = 0.9Fraction to Decimal Conversion Reference Table
Below is a quick reference table of common fraction-to-decimal values, division operations, and percentage equivalents:
| Fraction | Division Expression | Decimal Equivalent | Percentage | Decimal Type |
|---|---|---|---|---|
| 1/2 | 1 ÷ 2 | 0.5 | 50% | Terminating |
| 1/3 | 1 ÷ 3 | 0.333... | 33.33% | Repeating |
| 1/4 | 1 ÷ 4 | 0.25 | 25% | Terminating |
| 1/5 | 1 ÷ 5 | 0.2 | 20% | Terminating |
| 1/6 | 1 ÷ 6 | 0.1666... | 16.67% | Repeating |
| 1/8 | 1 ÷ 8 | 0.125 | 12.5% | Terminating |
| 2/3 | 2 ÷ 3 | 0.666... | 66.67% | Repeating |
| 3/4 | 3 ÷ 4 | 0.75 | 75% | Terminating |
| 4/5 | 4 ÷ 5 | 0.8 | 80% | Terminating |
| 5/6 | 5 ÷ 6 | 0.8333... | 83.33% | Repeating |
| 7/8 | 7 ÷ 8 | 0.875 | 87.5% | Terminating |
| 9/10 | 9 ÷ 10 | 0.9 | 90% | Terminating |
Frequently Asked Questions
Write the decimal as a fraction over a power of 10 equal to the number of decimal places, then divide numerator and denominator by their Greatest Common Divisor (GCD).
Divide the numerator (top number) by the denominator (bottom number) using long division.
Yes! Select the "Repeating Decimal" option in our calculator tab, specify the repeating digits, and the calculator applies algebraic equations to find the exact simplified fraction.
A fraction represents a part of a whole as a ratio of two integers (e.g., 3/4), while a decimal represents numbers using place values based on tenths, hundredths, and thousandths (e.g., 0.75). Both express identical numerical values.