Decimal to Fraction Calculator

Introduction

The Decimal to Fraction Calculator converts any decimal number into a fraction in its simplest form. Just type in a decimal like 0.75, and the calculator will show you that it equals 3/4. It works with terminating decimals (like 0.5) and repeating decimals (like 0.333...). Every decimal number can be written as a fraction, and this tool does the math for you in seconds. It also reduces the fraction to its lowest terms, so you always get the cleanest answer. This is helpful for homework, cooking, measuring, or any time you need to switch between decimals and fractions. If you need to perform operations with fractions after converting, try our Fraction Calculator.

How to use our Decimal to Fraction Calculator

Enter a decimal number and this calculator will convert it to a simplified fraction, mixed number, and percentage — with a full step-by-step solution.

Decimal Value: Type the decimal number you want to convert into a fraction. You can enter numbers like 0.375, 1.625, or 5.72. Use the +/− button next to the input field to switch between a positive and negative number.

Repeating Trailing Digits: Enter how many digits at the end of your decimal repeat forever. For example, if you have 0.6 and the 6 repeats (0.666...), type 1. If you have 0.36 and both digits repeat (0.3636...), type 2. Leave this set to 0 if your decimal does not repeat.

Round to Denominator (Optional): If you need your answer as a fraction with a specific bottom number, type it here. For instance, enter 16 to get your result in sixteenths, or 8 to get it in eighths. This is helpful for tasks like woodworking or measuring. Leave this field blank if you do not need rounding.

Convert: Click this button to run the calculation. The calculator will show your simplified fraction, mixed number, percentage, a visual bar and pie chart, and a detailed step-by-step breakdown of how the conversion was done.

Reset: Click this button to clear all your entries and return the calculator to its default settings.

Decimal to Fraction Calculator

A decimal to fraction conversion turns a number like 0.75 into a fraction like 3/4. Every decimal number can be written as a fraction. The key idea is simple: the digits after the decimal point tell you how many parts you are dividing something into. For example, 0.75 means 75 out of 100, which simplifies to 3/4 once you divide both numbers by their greatest common divisor (25). You can use our GCF Calculator to quickly find the greatest common factor of any two numbers.

How to Convert a Decimal to a Fraction

To convert a terminating decimal (one that ends) to a fraction, count the number of digits after the decimal point. Then write the number without the decimal point on top, and a 1 followed by that many zeros on the bottom. For example, 0.625 has three decimal places, so it becomes 625/1000. You then simplify by finding the greatest common divisor (GCD) of 625 and 1000, which is 125. Divide both by 125, and you get 5/8.

Repeating Decimals

Some decimals go on forever in a repeating pattern, like 0.333... or 0.1666.... These are called repeating decimals, and they can also be written as exact fractions. The method uses a simple algebra trick: you multiply the number by powers of 10 to line up the repeating parts, then subtract to cancel them out. For instance, if x = 0.333..., then 10x = 3.333.... Subtracting gives 9x = 3, so x = 3/9 = 1/3.

Simplifying Fractions

After converting, you should always simplify the fraction to its lowest terms. You do this by dividing both the numerator (top number) and the denominator (bottom number) by their GCD. A fraction is fully simplified when no number other than 1 divides evenly into both the numerator and the denominator. Finding the least common multiple (LCM) and prime factorization of numbers can also be useful when working with fractions.

Rounding to a Specific Denominator

Sometimes you need a fraction with a particular denominator. This is common in woodworking (where measurements use 16ths or 32nds of an inch), cooking (where recipes use halves, thirds, or quarters), and engineering. To round to a specific denominator, you multiply the decimal by that denominator, round to the nearest whole number, and place it over the denominator. For example, 0.34 rounded to eighths becomes 3/8, because 0.34 × 8 = 2.72, which rounds to 3. For construction and woodworking projects, tools like the Board Foot Calculator and Square Footage Calculator often require fractional measurements.

Mixed Numbers

When the fraction's numerator is larger than its denominator, the value is greater than 1. You can express this as a mixed number — a whole number combined with a proper fraction. To convert, divide the numerator by the denominator. The quotient is the whole number part, and the remainder goes over the original denominator. For example, 7/4 becomes 1 3/4 because 7 ÷ 4 = 1 with a remainder of 3. Understanding the modulo operation can help you quickly determine the remainder in these conversions.

Common Decimal to Fraction Conversions

Here are some frequently used conversions that are helpful to memorize:

• 0.5 = 1/2
• 0.25 = 1/4
• 0.75 = 3/4
• 0.125 = 1/8
• 0.2 = 1/5
• 0.333... = 1/3
• 0.666... = 2/3
• 0.1 = 1/10

This calculator handles terminating decimals, repeating decimals, and negative numbers. It shows the simplified fraction, mixed number, percentage, a step-by-step solution, and a visual representation so you can clearly see and understand the result. You may also find our Percentage Calculator and Ratio Calculator useful for related conversions, or our Scientific Notation Calculator if you're working with very large or very small decimal values.

Frequently Asked Questions

What is a fraction?

A fraction is a way to show a part of a whole. It has two numbers separated by a line. The top number is called the numerator, and it tells you how many parts you have. The bottom number is called the denominator, and it tells you how many equal parts the whole is divided into. For example, 3/4 means you have 3 out of 4 equal parts.

Why does 0.999... equal 1?

This is a famous math fact. If you set x = 0.999..., then 10x = 9.999.... Subtract x from 10x and you get 9x = 9, so x = 1. The repeating decimal 0.999... and the number 1 are the same value. There is no gap between them. This is not a trick — it is how the math works out.

Can every decimal be turned into a fraction?

Every terminating decimal (like 0.75) and every repeating decimal (like 0.333...) can be written as a fraction. However, some decimals never end and never repeat, like pi (3.14159...). These are called irrational numbers, and they cannot be written as an exact fraction.

What is the difference between a terminating and repeating decimal?

A terminating decimal stops after a certain number of digits, like 0.25 or 0.625. A repeating decimal has one or more digits that repeat forever, like 0.333... or 0.142857142857.... Both types can be converted to exact fractions.

How do I know if my fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator share no common factor other than 1. For example, 6/8 is not simplified because both 6 and 8 can be divided by 2, giving you 3/4. If you cannot find any number greater than 1 that divides evenly into both the top and bottom, the fraction is in its simplest form.

What does the Repeating Trailing Digits field do?

This field tells the calculator how many digits at the end of your decimal repeat forever. For example, if you type 0.16 and set repeating digits to 1, the calculator treats it as 0.1666... (only the 6 repeats). If you set it to 2, it treats it as 0.161616... (both 1 and 6 repeat). Leave it at 0 if your decimal stops and does not repeat.

What is a mixed number?

A mixed number is a whole number combined with a fraction. For example, 1 3/4 is a mixed number. It means 1 whole plus 3/4. You get a mixed number when the fraction's numerator is bigger than its denominator. The calculator shows this automatically when it applies.

Why would I round to a specific denominator?

Some tasks need fractions with a set denominator. In woodworking, measurements often use 16ths or 32nds of an inch. In cooking, you might need halves, thirds, or quarters. The "Round to Denominator" option finds the closest fraction with the bottom number you choose, so the result fits the tools or recipe you are using.

How do I convert a negative decimal to a fraction?

Enter the decimal number and click the +/− button to make it negative. The calculator will convert the absolute value to a fraction and then apply the negative sign. For example, −0.75 becomes −3/4.

What is the GCD and why does it matter?

GCD stands for Greatest Common Divisor. It is the largest number that divides evenly into both the numerator and denominator. The calculator uses the GCD to simplify your fraction. For example, the GCD of 625 and 1000 is 125. Dividing both by 125 turns 625/1000 into 5/8.

Can I enter a number in scientific notation?

Yes. You can type a number like 5.72e2 in the decimal field, which means 5.72 × 10² = 572. The calculator will read it correctly and convert it to a fraction.

What does the visual bar and pie chart show?

The visual bar shows your fraction as a filled portion of a horizontal bar, so you can see how much of a whole it represents. The pie chart does the same thing in a circular format. Both help you quickly understand the size of the fraction at a glance.

How do I convert a fraction back to a decimal?

Divide the numerator by the denominator. For example, to convert 3/8 back to a decimal, divide 3 by 8 and you get 0.375. The calculator shows a "Decimal (Verified)" row so you can confirm the conversion is correct.

What if my decimal has many digits after the decimal point?

The calculator can handle decimals with many digits. It counts the decimal places, creates the fraction over the correct power of 10, and then simplifies. For example, 0.0625 has four decimal places, so it starts as 625/10000 and simplifies to 1/16.

Is 0.5 the same as 1/2?

Yes. The decimal 0.5 means 5 out of 10, which is 5/10. Simplify by dividing both by 5, and you get 1/2. They are the same value written in different ways.