Decimal to Fraction Calculator
Convert a decimal number to a fraction.
About Decimal to Fraction Calculator
Convert a decimal to a fraction by placing it over a power of 10, then simplifying by the GCD.
$$decimal \rightarrow \frac{p}{q}$$
How to use this calculator
- Enter the decimal number you want to convert, such as 0.6 or 3.125.
- Click the convert button to get the fraction form.
- Read the result, and simplify it if the fraction is not already in lowest terms.
- Check the decimal again if you want to verify the fraction matches the original value.
The formula explained
The conversion finds a fraction \(\frac{p}{q}\) that has the same value as the decimal. For terminating decimals, the number can be written exactly as a fraction and then reduced to simplest form.
- decimal = the decimal number being converted
- p = the numerator of the fraction
- q = the denominator of the fraction
Step by step method
- Write the decimal as a fraction with a power of 10 in the denominator. For example, 0.75 = 75/100.
- Remove the decimal point and divide by the appropriate power of 10, then simplify.
- Reduce the fraction by dividing the numerator and denominator by their greatest common factor.
Worked example
Problem. Convert 2.125 to a fraction.
- Write 2.125 as 2125/1000 because there are three digits after the decimal point.
- Simplify 2125/1000 by dividing the numerator and denominator by 125 to get 17/8.
- Check that 17 divided by 8 equals 2.125.
Answer. 2.125 = 17/8
Tips and common mistakes
- Always simplify the fraction to lowest terms, because calculators may show an unreduced result first.
- If the decimal repeats forever, it usually needs a different method than a simple terminating-decimal conversion.
Frequently asked questions
How do I convert a decimal to a fraction with this calculator?+
Enter the decimal value, and the tool converts it into a fraction of the form p/q. It also simplifies the fraction when possible, so 0.75 becomes 3/4.
What does the formula decimal to p over q mean?+
It means the calculator is finding two integers, p and q, so that p divided by q equals the decimal. For example, 0.125 equals 125/1000 at first, then simplifies to 1/8.
Can this calculator handle repeating decimals?+
It can convert many decimals to fractions, but a repeating decimal like 0.3333 may only be recognized based on the digits you type. If you enter enough repeating digits, it may give the expected fraction, such as 1/3.
Why did a decimal like 0.1 not turn into a simple fraction exactly in some cases?+
Some decimals are exact in base 10 but can be awkward in binary computer representation, so the displayed value may reflect rounding. If needed, enter the decimal with the precision you want the calculator to use.
What is the difference between a decimal and a fraction?+
A decimal writes a number using place value, like 0.6, while a fraction writes the same number as one integer over another, like 3/5. This calculator helps show that the two forms can represent the same value.
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