Fraction to Decimal
Convert proper fractions, improper fractions, and mixed numbers into decimals with detailed calculation work shown.
Decimal Result
Showing the work
How to Use This Calculator
- Simple Fractions: If you have a standard fraction like 3/4, leave the “Whole” box empty. Just enter 3 in the top box (Numerator) and 4 in the bottom box (Denominator).
- Mixed Numbers: For numbers like 2 1/2, enter 2 in the “Whole” field, then input the fraction parts separately. The calculator automatically converts this into an improper fraction for the calculation.
- Rounding: By default, the tool shows the exact result (or as many digits as possible). If you need a specific precision for engineering or science say, 3 decimal places—select that from the dropdown menu.
- Repeating Decimals: If the result has a repeating pattern (like 1/3 = 0.333…), the calculator detects it and places a bar (vinculum) over the repeating digits to show the exact mathematical value.
The Math Behind the Conversion
Method 1: The Long Division (The Standard Way)
This is the method used by this calculator to generate the “Show Work” steps. To convert any fraction, you divide the numerator (the top number) by the denominator (the bottom number).
Example: Convert 5/8 to a decimal.
- Set up the division: 5 ÷ 8.
- Since 8 doesn’t go into 5, we add a decimal point and a zero to make it 5.0.
- 8 goes into 50 six times (6 × 8 = 48), leaving a remainder of 2.
- Bring down another zero to make 20.
- 8 goes into 20 two times (2 × 8 = 16), leaving a remainder of 4.
- Bring down a final zero to make 40.
- 8 goes into 40 exactly five times.
Result: 0.625
Method 2: The Power of 10 Shortcut
If you can easily multiply the denominator to become 10, 100, or 1000, you can convert the fraction without long division. This works best for denominators like 2, 4, 5, 20, 25, or 50.
Formula:
Numerator × Factor / Denominator × Factor = New Numerator / Power of 10Example: Convert 3/5
- We know that 5 × 2 = 10.
- Multiply both the top and bottom by 2.
- (3 × 2) / (5 × 2) = 6/10
- Six-tenths is written as 0.6.
Handling Mixed Numbers
Mixed numbers represent a sum of a whole integer and a proper fraction. To convert these, you generally have two options:
Option A: Keep the Whole Number Separate
Calculate the decimal for the fraction part only, then tack it onto the end of the whole number. For 5 3/4, you know 3/4 is 0.75, so the answer is 5.75.
Option B: Convert to Improper Fraction (The Calculator’s Method)
This is safer for complex calculations. We convert the mixed number into a single numerator before dividing.
Formula:
Total Numerator = (Whole Number × Denominator) + Numerator
For example, taking 2 3/5:
- Multiply 2 × 5 = 10.
- Add the numerator: 10 + 3 = 13.
- New Fraction: 13/5.
- Divide 13 ÷ 5 = 2.6.
Terminating vs. Repeating Decimals
Not all fractions result in a clean ending. Understanding the difference helps you interpret your results.
Terminating Decimals
These are decimals that end (terminate) after a certain number of digits. This happens only when the denominator’s prime factors are exclusively 2 and 5. Examples include:
- 1/2 = 0.5
- 1/8 = 0.125
- 1/20 = 0.05
Repeating Decimals
If the denominator contains prime factors other than 2 or 5 (like 3, 7, or 11), the division will never end. Instead, a sequence of digits will repeat infinitely.
- 1/3 = 0.33333… (The 3 repeats forever)
- 1/7 = 0.142857142857… (The sequence 142857 repeats)
Notation: Mathematicians use a bar called a vinculum over the repeating part. This calculator automatically applies this notation so you can distinguish between a rounded number and an exact repeating value.
Conversion Reference Table
Here are the decimal equivalents for the most common fractions used in construction, cooking, and schoolwork.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
Sources: Calculator Soup, RapidTables, Calculator.net, GraphCalc, Inch Calculator, Math Salamanders.