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.
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 numerator and denominator by 10 for each digit after the decimal point. For 0.75, there are two digits, so you multiply by 100 to get 75/100.
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 a mixed number (if greater than 1)
If the decimal is greater than 1 (e.g., 2.75), the result is an improper fraction (275/100 = 11/4). You can optionally express it as a mixed number: 2 3/4.
Special Cases
Repeating Decimals
Repeating decimals (like 0.333…) require an algebraic method: let x equal the repeating decimal, multiply by the right power of 10 to shift the repeating block, subtract to eliminate the repeating part, and solve for x. Example: 0.333… = 1/3. See the repeating-decimal converter for details.
Very Long Decimals
Irrational numbers like π (3.14159…) and √2 (1.41421…) never terminate or repeat. They cannot be expressed as exact fractions. You must round to a specific number of decimal places 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 0.5 Reveal Answer
Answer: 1/2
0.5 = 5/10 → GCD(5, 10) = 5 → (5 ÷ 5)/(10 ÷ 5) = 1/2
Problem 2: Convert 0.25 Reveal Answer
Answer: 1/4
0.25 = 25/100 → GCD(25, 100) = 25 → (25 ÷ 25)/(100 ÷ 25) = 1/4
Problem 3: Convert 0.125 Reveal Answer
Answer: 1/8
0.125 = 125/1000 → GCD(125, 1000) = 125 → (125 ÷ 125)/(1000 ÷ 125) = 1/8
Problem 4: Convert 0.75 Reveal Answer
Answer: 3/4
0.75 = 75/100 → GCD(75, 100) = 25 → (75 ÷ 25)/(100 ÷ 25) = 3/4
Problem 5: Convert 1.25 Reveal Answer
Answer: 5/4 = 1 1/4
1.25 = 125/100 → GCD(125, 100) = 25 → (125 ÷ 25)/(100 ÷ 25) = 5/4 = 1 1/4
Problem 6: Convert 2.375 Reveal Answer
Answer: 19/8 = 2 3/8
2.375 = 2375/1000 → GCD(2375, 1000) = 125 → (2375 ÷ 125)/(1000 ÷ 125) = 19/8 = 2 3/8
Problem 7: Convert -0.6 Reveal Answer
Answer: -3/5
0.6 = 6/10 → GCD(6, 10) = 2 → (6 ÷ 2)/(10 ÷ 2) = 3/5 → -3/5
For repeating decimals like 0.333… or 0.1666…, this place-value method does not apply directly. See our repeating-decimal converter for the algebraic approach, or the terminating-decimal guide for finite decimals specifically.
Related Tools
📝 Practice Step-by-Step
Enter a decimal to see the full manual conversion process.
Visual Representation
Frequently Asked Questions
Common questions about manual decimal-to-fraction conversion
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01 What is the first step in converting a decimal to a fraction?
Count the number of digits after the decimal point. That count tells you the power of 10 to use as the denominator. For example, 0.75 has two decimal digits, so write it as 75/100. Then simplify by dividing both numbers by their greatest common divisor.
02 How do I remove the decimal point when converting?
Multiply both the numerator and denominator by 10 for each digit after the decimal point. With one digit (e.g., 0.8), multiply by 10 to get 8/10. With two digits (e.g., 0.75), multiply by 100 to get 75/100. With three digits (e.g., 0.125), multiply by 1000 to get 125/1000.
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 are common mistakes when converting a decimal to a fraction?
The two most common mistakes are: (1) miscounting decimal places — for example, treating 0.125 as having two places instead of three, which gives 125/100 instead of the correct 125/1000; and (2) not simplifying fully — for example, writing 6/10 instead of reducing to 3/5.
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 What is the difference between a terminating and a repeating decimal?
A terminating decimal has a finite number of digits after the decimal point (e.g., 0.25, 0.875). A repeating decimal has one or more digits that cycle indefinitely (e.g., 0.333… or 0.142857142857…). Both types can be converted to fractions, but they use different methods: the place-value method for terminating decimals, and an algebraic method for repeating decimals.