Converting a decimal to a fraction turns a base-10 number like 0.75 into its equivalent fraction form, 3/4 — a conversion that comes up constantly in math coursework, cooking measurements, construction, and anywhere a precise fractional value is more useful than a decimal approximation. This page covers how to change a decimal to a fraction step by step, several worked examples, and a decimal to fraction chart for commonly needed values. Browse all calculators if you need a different tool, or use fraction to decimal to go the other way.
How to Change a Decimal to a Fraction
The Conversion Method
Converting a decimal to a fraction follows three steps:
- Write the decimal as a fraction over 1 — for example, 0.75 becomes 0.75/1
- Multiply the numerator and denominator by 10 for each digit after the decimal point — 0.75 has two decimal digits, so multiply by 100: 75/100
- Simplify the fraction to its lowest terms by dividing both numerator and denominator by their greatest common divisor
Simplifying the Result
The last step is what turns an unwieldy fraction like 75/100 into its cleanest form. The greatest common divisor of 75 and 100 is 25, so dividing both by 25 gives the simplified fraction 3/4 — this simplification step is essential, since an unsimplified fraction, while mathematically correct, isn't the standard way a converted decimal is expressed.
Decimal to Fraction Calculator: Step by Step
This calculator automates the full process above — enter any decimal, and it returns the equivalent fraction already simplified to its lowest terms, without needing to manually find the greatest common divisor.
Worked Examples: Converting Common Decimals
Example: 0.75 to a Fraction
0.75 = 75/100
GCD of 75 and 100 = 25
75/100 simplifies to 3/4
Example: 0.125 to a Fraction
0.125 = 125/1000
GCD of 125 and 1000 = 125
125/1000 simplifies to 1/8
Example: 0.6 to a Fraction
0.6 = 6/10
GCD of 6 and 10 = 2
6/10 simplifies to 3/5
Decimal to Fraction Chart: Common Values
Decimal to Fraction Table
A quick reference table for some of the most commonly needed decimal to fraction conversions:
| Decimal | Fraction |
|---|---|
| 0.1 | 1/10 |
| 0.2 | 1/5 |
| 0.25 | 1/4 |
| 0.333... | 1/3 |
| 0.4 | 2/5 |
| 0.5 | 1/2 |
| 0.6 | 3/5 |
| 0.666... | 2/3 |
| 0.75 | 3/4 |
| 0.8 | 4/5 |
| 0.875 | 7/8 |
| 0.9 | 9/10 |
Repeating Decimals as Fractions
Converting a Repeating Decimal Like 0.333...
Repeating decimals require a slightly different approach than terminating decimals, since the standard "multiply by a power of 10" method doesn't directly apply to an infinitely repeating digit. For a simple repeating decimal like 0.333... (where 3 repeats forever), the fraction is 1/3 — this and other common repeating decimals (like 0.666... = 2/3, or 0.111... = 1/9) follow recognizable patterns that this calculator handles correctly, converting them to their exact fraction equivalent rather than a rounded approximation.
Frequently Asked Questions
How do I convert a decimal to a fraction?
Write the decimal over 1, multiply the numerator and denominator by 10 for each digit after the decimal point, then simplify the resulting fraction to its lowest terms.
How do I convert 0.75 to a fraction?
0.75 equals 75/100, which simplifies to 3/4.
How do I convert 0.125 to a fraction?
0.125 equals 125/1000, which simplifies to 1/8.
Does this calculator simplify the fraction automatically?
Yes. Any decimal entered returns its fraction equivalent already simplified to lowest terms.
How are repeating decimals converted to fractions?
Common repeating decimals follow recognizable patterns. For example, 0.333 repeating converts to exactly 1/3, and 0.666 repeating converts to exactly 2/3.
Is there a chart for common decimal to fraction conversions?
Yes, a reference table covering common values like 0.25 equals 1/4, 0.5 equals 1/2, and 0.75 equals 3/4 is included.
Can this calculator handle decimals with many digits?
Yes. Any decimal, including longer ones, converts to its exact fraction equivalent using the same method, then simplifies to lowest terms.
Is this decimal to fraction converter free to use?
Yes. It is free, requires no sign-up, and converts decimals to fractions instantly.