How to Convert a Decimal to a Fraction (Step-by-Step with Examples)
Learn how to convert decimal to fraction step by step, including simplifying and repeating decimals, plus try our free decimal to fraction calculator.
A tape measure reading, a recipe ratio, or a homework problem will occasionally hand you a decimal when what you actually need is a clean fraction, like an eighth of an inch instead of 0.125. Knowing how to convert decimal to fraction by hand is a short process once you see the pattern, and it works the same way regardless of how many digits the decimal has.
This guide covers terminating decimals, simplifying a fraction to its lowest terms, the algebraic trick for repeating decimals, converting a fraction back to a decimal, and a reference table of common conversions worth memorizing.
What Is a Decimal and What Is a Fraction?
A decimal expresses a value using place values to the right of a decimal point, such as tenths, hundredths, and thousandths. A fraction expresses the same value as one number divided by another, a numerator over a denominator. Both are simply different notations for the same underlying quantity, which is exactly why a clean conversion between the two is always possible for terminating and repeating decimals.
How to Convert a Terminating Decimal to a Fraction
The basic method
Fraction = Decimal × 10^(decimal places) ÷ 10^(decimal places)
Count how many digits sit after the decimal point, then place the decimal's digits (without the decimal point) over a denominator of 10 raised to that count. For 0.625, there are 3 digits after the decimal point, so it becomes 625 over 1,000, written as 625/1000. This is the unsimplified fraction, and it is mathematically correct, just not in its simplest form yet.
How to Simplify a Fraction to Its Lowest Terms
Simplifying means dividing both the numerator and denominator by their greatest common divisor (GCD), the largest number that divides evenly into both. For 625/1000, the greatest common divisor is 125. Dividing both numbers by 125 gives 5/8, which is the simplified fraction.
Worked example
625 ÷ 125 = 5, and 1000 ÷ 125 = 8, so 625/1000 = 5/8
If you do not immediately know the greatest common divisor, you can divide by any common factor you can spot (like 5 or 25 first), and repeat the process with the smaller numbers until no common factor remains.
Try it yourself
Decimal to Fraction Calculator
Enter any decimal to get the simplified fraction, the unsimplified version, and a mixed number instantly, with every simplification step shown and a reverse fraction-to-decimal mode.
How to Convert a Repeating Decimal to a Fraction
Repeating decimals need a different, algebraic approach, since they never terminate. Take 0.333..., where the 3 repeats forever.
- Let x = 0.333...
- Multiply both sides by 10, since one digit repeats: 10x = 3.333...
- Subtract the original equation from this new one: 10x − x = 3.333... − 0.333..., which gives 9x = 3.
- Solve for x: x = 3/9, which simplifies to 1/3.
The key step is multiplying by a power of 10 that shifts the repeating block exactly one full cycle to the left, so that subtracting the original value cancels out the infinite repeating part entirely, leaving a normal, solvable equation.
How to Convert a Fraction Back to a Decimal
The reverse direction
Decimal = Numerator ÷ Denominator
This direction is simpler: divide the numerator by the denominator using long division or a calculator. For 5/8, dividing 5 by 8 gives 0.625, confirming the same value we started with in the earlier example, just in the opposite notation.
Common Decimal to Fraction Conversions Reference Table
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/3 | 0.333... |
| 2/3 | 0.667... |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/8 | 0.125 |
| 3/8 | 0.375 |
| 1/16 | 0.0625 |
These come up often enough in measurement and construction work that memorizing the eighths and sixteenths in particular can save you from redoing the same conversion repeatedly.
Frequently asked questions
Why do decimals like 0.1 sometimes show tiny rounding errors in software?
Computers store decimals in binary, and many decimal fractions that look clean in base 10, like 0.1, cannot be represented exactly in binary. This is a computing quirk rather than a math problem, and it does not affect the manual conversion method described in this guide, which works directly with the digits as written.
How do I know if a decimal is terminating or repeating?
A terminating decimal ends after a finite number of digits, such as 0.625. A repeating decimal has one or more digits that repeat infinitely, such as 0.333... or 0.142857142857.... If the decimal you are working with simply stops, it is terminating, and the basic conversion method applies directly.
What is the fastest way to simplify a fraction?
Find the greatest common divisor of the numerator and denominator, then divide both numbers by it in a single step. This is faster than repeatedly dividing by small numbers like 2 or 3 one at a time, especially for larger fractions.
Can every decimal be converted into a fraction?
Every terminating and every repeating decimal can be expressed as a fraction. Non-repeating, non-terminating decimals, such as the digits of pi, cannot be expressed as an exact fraction, since they are irrational numbers by definition.
Now that you know how to convert decimal to fraction for both terminating and repeating decimals, simplifying any result down to its lowest terms is just a matter of finding the right greatest common divisor. Use the Decimal to Fraction Calculator above to get the simplified fraction, the unsimplified version, and a mixed number instantly, with every step shown.
For other measurement conversions, see how to calculate the square footage of a room , or for comparing two values as a percentage, see how to calculate a percentage increase.