How to Convert Decimal to Fraction
Learn how to convert any decimal to a fraction step by step. Includes conversion formula, method, examples, and practice problems.
📝 Practice Step-by-Step
Enter a decimal to see the full manual conversion process.
Visual Representation
The Conversion Formula
Where n is the number of digits after the decimal point. Afterwards, simplify by dividing by the Greatest Common Divisor (GCD).
Step-by-Step Conversion Method
1 Write Decimal Over 1
Start by writing the decimal number over 1. This creates a fraction that is mathematically equal to the decimal.
1
2 Multiply to Remove Decimal Point
Multiply both the top (numerator) and bottom (denominator) by 10 for every digit after the decimal point. For 0.75, there are two digits, so multiply by 100.
1 × 100 100
3 Find the Greatest Common Divisor (GCD)
Find the largest number that divides exactly into both the numerator and denominator. For 75 and 100, the GCD is 25.
4 Simplify the Fraction
Divide both numbers by the GCD to get the simplified fraction.
100 ÷ 25 4
5 Convert to Mixed Number (If > 1)
If your original decimal was greater than 1 (e.g., 2.75), you would now have an improper fraction (11/4). Convert it to a mixed number: 2 3/4.
Special Cases
Repeating Decimals
To convert repeating decimals (like 0.333...), set it to a variable x, multiply by 10 to shift the decimal, subtract the original x to cancel the repeating part, and solve for x. (e.g., 0.333... = 1/3)
Very Long Decimals
For irrational numbers (like Pi = 3.14159...), an exact fraction isn't possible. You must round to a specific precision first before converting.
Negative Decimals
Simply ignore the negative sign during calculation, and apply it to the final fraction at the end. (e.g., -0.25 becomes -1/4)
Quick Reference Guide
| Decimal | Fraction |
|---|---|
| 0.1 | 1/10 |
| 0.125 | 1/8 |
| 0.2 | 1/5 |
| 0.25 | 1/4 |
| 0.333... | 1/3 |
| 0.5 | 1/2 |
| 0.75 | 3/4 |
Practice Problems
Test your decimal to fraction conversion skills. Click to reveal the answer!
Problem 1: Convert 0.4 Reveal Answer
Answer: 2/5
0.4 = 4/10. Divide both by GCD of 2 to get 2/5.
Problem 2: Convert 0.125 Reveal Answer
Answer: 1/8
0.125 = 125/1000. Divide both by GCD of 125 to get 1/8.
Problem 3: Convert 1.75 Reveal Answer
Answer: 1 3/4 or 7/4
1.75 = 175/100. Divide both by 25 to get 7/4. Convert to mixed: 1 3/4.
Problem 4: Convert 0.666... Reveal Answer
Answer: 2/3
Let x = 0.666... Then 10x = 6.666... Subtract x: 9x = 6. So x = 6/9 = 2/3.
Problem 5: Convert 2.35 Reveal Answer
Answer: 2 7/20 or 47/20
2.35 = 235/100. Divide both by 5 to get 47/20. Convert to mixed: 2 7/20.
Related Tools
Frequently Asked Questions
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01 What is the first step in converting a decimal to a fraction?
The first step is to write down the decimal divided by 1, like this: 0.75 / 1.
02 How do I eliminate the decimal point?
Multiply both the top and bottom by 10 for every digit after the decimal point. For example, if there are two digits, multiply by 100.
03 Why is simplifying the fraction necessary?
Simplifying or reducing the fraction to its lowest terms makes it easier to read and use in further mathematical equations. It presents the result in standard simplified mathematical form.
04 What is the most common mistake when converting?
A common mistake is not simplifying the fraction completely, or miscounting the number of decimal places when multiplying by a power of 10.
05 How do I handle repeating decimals?
Repeating decimals require a different algebraic approach, usually involving setting the decimal to a variable x, multiplying by a power of 10 to align repeating digits, and subtracting equations.
06 How to convert decimal to fraction step by step?
To convert a decimal to a fraction step by step: (1) Count the number of decimal places. (2) Write the decimal number as a numerator over a denominator of 10 raised to the number of decimal places (e.g., 0.375 becomes 375/1000). (3) Find the greatest common divisor (GCD) of the numerator and denominator. (4) Divide both by the GCD to get the simplified fraction (375÷125 / 1000÷125 = 3/8).
07 Can decimals be fractions?
Yes — every terminating or repeating decimal can be expressed as a fraction. Decimals are simply another way of writing fractions whose denominators are powers of 10. For example, 0.5 = 5/10 = 1/2, and 0.333... = 1/3. The only numbers that cannot be written as exact fractions are irrational numbers like π or √2, whose decimal expansions never terminate or repeat.
08 How can you convert fractions to decimals?
To convert a fraction to a decimal, divide the numerator by the denominator. For instance, 3/4 = 3 ÷ 4 = 0.75. Some fractions produce terminating decimals (like 1/8 = 0.125), while others produce repeating decimals (like 1/3 = 0.333...). You can perform this division by hand using long division, or use our fraction to decimal calculator for instant results.
09 How do I convert a decimal to a fraction?
Write the decimal over 1 (e.g., 0.75/1), then multiply both the numerator and denominator by 10 for each decimal place (75/100). Next, find the greatest common divisor (GCD) of the numerator and denominator, and divide both by it to simplify. For 75/100, the GCD is 25, giving you 3/4. For repeating decimals, use an algebraic method instead.