Decimal to Fraction Calculator
*Enter repeating decimals using parentheses.
e.g. 0.(6) for 0.6, 0.7(5) for 0.75.
About
This Decimal to Fraction Calculator is a fast, intelligent tool that instantly converts both terminating and repeating decimals into simplified fractions or mixed numbers—while clearly showing each step of the process. Whether you’re entering something like 1.75 or a repeating decimal such as -0.8(3), it provides accurate, beautifully formatted results in real time, right in your browser. No server requests, no loading time, and no privacy concerns—just instant, transparent computation.
Unlike other decimal to fraction converters that merely return an answer, this tool is designed to reveal the logic behind the conversion. You’ll see detailed, step-by-step explanations using intuitive formatting: overlined repeating digits, fractions in proper mathematical style, and clear mixed number conversions. Even tricky cases like simplifying with a GCD or placing a negative sign correctly are handled with precision—making it not just a calculator, but a learning tool.
Created to offer a faster, smoother, and more educational experience, this converter features a clean, modern interface optimized for all devices—including a specially tailored layout for mobile. Every interaction feels seamless, from typing a decimal to watching it transform, reflecting our dedication to both mathematical clarity and user-centered design.
We built this tool for those who value not just results, but understanding—and we’re continually refining every detail to make it the most trusted, enjoyable decimal-to-fraction converter available.
🔢 How to Input Repeating Decimals
To enter repeating decimals, simply enclose the repeating part in parentheses. This tells the calculator exactly which digits repeat and allows it to convert the decimal to a simplified fraction in real time.
For example:
- For a repeating decimal such as 0.333…, where the digit 3 repeats forever, just enter 0.(3) into the calculator — you’ll get the result 1/3.
- Similarly, if the repeating part of a repeating decimal is longer, like in 0.818181…, where 81 repeats, you can enter 0.(81), and the calculator will return 9/11.
- For repeating decimals with a non-repeating part before the repeating cycle, such as 0.1666… (where only the 6 repeats), enter 0.1(6) and you’ll get 1/6.
- You can also enter mixed repeating decimals like 2.457777… as 2.45(7), and get 2 103/225.
- For negative repeating decimals are supported too — for example, -0.8181… (where 81 repeats) ,just enter -0.(81), you’ll get the answer 9/11.
This simple input format using parentheses ensures accurate recognition of repeating digits, so you always get the correct simplified result, along with a clear explanation of each step.
How to Convert a Decimal to a Fraction
Identify the decimal: Take the decimal number you want to convert (e.g.,
1.75).Convert to fraction form:
Count the number of decimal places.
Multiply both the numerator (decimal value) and denominator by 10 for each decimal place.
For example:1.75→1.75 * 100 / 100→175 / 100.
Simplify the fraction:
Find the greatest common divisor (GCD) of the numerator and denominator.
Divide both the numerator and denominator by the GCD.
For example:GCD of 175 and 100is25.175 ÷ 25 = 7,100 ÷ 25 = 4→ Final fraction:7/4.
(Optional) Convert to a mixed number: If the numerator is larger than the denominator, express it as a mixed number.
For example:7/4→1 3/4.
This is the basic process of converting a decimal to a fraction. Or you can use our Decimal to Fraction Converter to automatically handle these steps for you and display the result!
Example: Converting 1.75 to a Fraction
Step 1: Original Decimal
We begin by noting the original decimal number: 1.75.
1.75= 1.75 1
Step 2: Convert to Fraction
To convert the decimal into a fraction, we multiply both the numerator and denominator by 100 (since there are two decimal places in 1.75). This gives us:
Step 3: Simplify the Fraction
Next, we simplify the fraction by finding the greatest common divisor (GCD) of 175 and 100, which is 25. We divide both the numerator and denominator by 25:
After simplifying, we get the fraction:
= 74
Step 4: Mixed Number
Finally, we convert the fraction 7/4 into a mixed number. Since 7 divided by 4 equals 1 with a remainder of 3, we can express the fraction as 1 3/4:
How to Convert a Repeating Decimal to a Fraction
Repeating decimals are numbers with one or more digits that repeat endlessly, such as 0.333… or 1.63(5). This calculator allows you to easily convert repeating decimals into simplified fractions or mixed numbers by using a clear algebraic method. Here’s how it works behind the scenes, using a few examples:
Example 1: Convert repeating decimal 0.3 to a fraction
Step 1: Original repeating decimal:
0.3
Step 2: Let X equal the decimal (Equation 1)
X = 0.3
Step 3: As 1 digit is repeating, multiply both sides by 10 (101)
10X = 3.3
Step 4: Subtract equation (1) from equation (2)
10X = 3.3
– X = 0.3
————————————
We get
9X = 3
Step 5: Solve for X
X = 3/9
Step 6: Simplify the fraction
X = 1/3
Step 7: Convert to mixed number (if needed)
X = 1/3
Step 8: Result
0.3 = 1/3
Example 2: Convert repeating decimal 0.16 to a fraction
This is a mixed repeating decimal: the digit 6 repeats after a non-repeating part. Decimal: 0.16
Step 1: Original repeating decimal
0.16
Step 2: Let X equal the decimal (Equation 1)
X = 0.16
Step 3: 1 digit repeats after 1 non-repeating digit, multiply by 10 once, then by 10 again
100X = 16.6
10X = 1.6
Step 4: Subtract Equation 2 from Equation 1
100X = 16.6
– 10X = 1.6
————————————
90X = 15
Step 5: Solve for X
X = 15/90
Step 6: Simplify the fraction
X = 1/6
Step 7: Convert to mixed number
X = 1/6
Step 8: Result
0.16 = 1/6
This structured approach is what the calculator uses behind the scenes to ensure accurate results for all types of repeating decimals—whether it’s a simple repeat like 0.(7), a complex repeating group like 0.(123), or a decimal with a non-repeating part before the repeat, like 0.12(3). Every step is clearly shown so you not only get the correct fraction, but also understand how it’s derived.
🔢 How to Convert a Negative Decimal to a Fraction
Converting a negative decimal to a fraction is just like converting a positive decimal—but don’t forget to keep the negative sign throughout the process. The steps are exactly the same, except you carry the minus sign along with the final result.
Summary
No matter whether it’s a regular or repeating decimal, just convert it as if it’s positive, and then add the negative sign to the final result.
Our Decimal to Fraction calculator already does this automatically—including the step-by-step explanation—so users can see exactly how the conversion is done and why the negative sign stays with the fraction.
More Calculators
To convert a fraction to a decimal use our Fraction to Decimal Calculator.