Fraction to Decimal Converter – Convert Fractions to Decimals
Convert any fraction or mixed number to a decimal with our free online fraction to decimal converter. Get exact or rounded decimal results instantly with the division shown.
Leave whole number as 0 for proper fractions
Fraction to Decimal Converter – Convert Fractions to Decimals
Converting fractions to decimals is straightforward: divide the numerator by the denominator. This calculator handles proper fractions, improper fractions, and mixed numbers. It shows the complete division process and identifies repeating decimals.
Some fractions produce terminating decimals (like 1/2 = 0.5). Others produce repeating decimals (like 1/3 = 0.333...). The calculator shows both the exact form with repeating notation and an approximate decimal value.
How Fraction to Decimal Conversion Works
- 1
Convert mixed numbers to improper fractions
Multiply the whole number by the denominator, add the numerator, and keep the same denominator. 2½ becomes 5/2.
- 2
Simplify if possible
Reduce the fraction by dividing both numerator and denominator by their greatest common divisor.
- 3
Divide numerator by denominator
Perform long division. If the remainder becomes zero, you have a terminating decimal. If remainders repeat, you have a repeating decimal.
Terminating vs Repeating Decimals
Terminating Decimals
A fraction produces a terminating decimal if its denominator (in simplest form) has only prime factors of 2 and/or 5.
Repeating Decimals
A fraction produces a repeating decimal if its denominator (in simplest form) has prime factors other than 2 or 5.
Worked Examples
Example 1: Convert 3/4
Example 2: Convert 1/3
Example 3: Convert 2½
Example 4: Convert 1/7
Quick Fact
The decimal system we use today was developed in India around the 6th century and spread to Europe through Arab mathematicians. The decimal point wasn't standardized until the 17th century – before that, mathematicians used various notations including placing a bar over the units digit.
Frequently Asked Questions
How do I know if a decimal will repeat?
Look at the denominator after simplifying the fraction. If it has any prime factors besides 2 or 5, the decimal will repeat. For example, 1/6 has denominator 6 = 2 × 3, so it repeats.
What does the parentheses notation mean?
Parentheses indicate the repeating part of a decimal. 0.(3) means 0.333... forever. 0.1(6) means 0.1666... The digits in parentheses repeat infinitely.
Can I convert improper fractions?
Yes. Enter the numerator larger than the denominator, or use the whole number field for mixed numbers. 7/4 = 1.75 and 3/2 = 1.5.
How many decimal places should I use?
For terminating decimals, use all places. For repeating decimals, use enough places for your purpose, or use the exact repeating notation. In science, match the precision of your measurements.
What about negative fractions?
Enter a negative numerator. The decimal will also be negative. -3/4 = -0.75. The calculator handles negative values correctly.
Why does 1/7 have such a long repeating pattern?
Prime denominators often produce long repeating patterns. For prime p, the maximum repeating length is p-1 digits. For 7, the pattern is 6 digits long (142857), which is the maximum possible.
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