Decimal to Fraction Calculator

How to Convert a Decimal to a Fraction

Every terminating decimal (a decimal with a finite number of digits) can be converted to a fraction in just three steps. This process works for any decimal, whether it's less than 1 (like 0.75), greater than 1 (like 1.25), or negative (like −0.4).

Step One: Create the Starting Fraction

Write the decimal as a fraction with the decimal number as the numerator and 1 as the denominator.

Example: Convert 0.75 to a fraction.

0.75 = 0.75 / 1

Step Two: Multiply by 10 to Remove the Decimal

Multiply both the numerator and denominator by 10 repeatedly until the numerator is a whole number. The number of times you multiply equals the number of decimal places.

Continuing the example:

• 0.75 has 2 decimal places → multiply by 10² = 100
• 0.75 / 1 = (0.75 × 100) / (1 × 100) = 75 / 100

Step Three: Reduce the Fraction

Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it to get the simplest form.

Completing the example:

• GCD(75, 100) = 25
• 75 / 100 = (75 ÷ 25) / (100 ÷ 25) = 3/4

So 0.75 = 3/4. ✓

More Worked Examples

• 0.625: 625/1000 → GCD = 125 → 5/8
• 0.4: 4/10 → GCD = 2 → 2/5
• 1.25: 125/100 → GCD = 25 → 5/4 → as mixed number: 1 1/4
• 2.375: 2375/1000 → GCD = 125 → 19/8 → as mixed number: 2 3/8
• 0.333: 333/1000 → GCD = 1 → 333/1000 (not exact — see repeating decimals below)

Converting Decimals Greater Than 1

Decimals larger than 1 produce improper fractions (where the numerator is larger than the denominator). You can convert these to mixed numbers:

1. Follow the same three steps to get the improper fraction.
2. Divide the numerator by the denominator — the quotient is the whole number, the remainder is the new numerator.

Example: 1.75 → 175/100 → GCD = 25 → 7/4 → 7 ÷ 4 = 1 remainder 3 → 1 3/4

How to Convert a Repeating Decimal to a Fraction

A repeating decimal is a decimal that goes on forever with a repeating pattern, like 0.333… (= 1/3) or 0.142857142857… (= 1/7). These require a different algebraic approach:

1. Let x = the repeating decimal (e.g., x = 0.333…)
2. Multiply both sides by a power of 10 to shift the repeating part (e.g., 10x = 3.333…)
3. Subtract the original equation: 10x − x = 3.333… − 0.333… → 9x = 3
4. Solve for x: x = 3/9 = 1/3

Another example: 0.1666… (where 6 repeats)

• x = 0.1666…
• 10x = 1.666… and 100x = 16.666…
• 100x − 10x = 16.666… − 1.666… → 90x = 15
• x = 15/90 = 1/6

How to Convert a Negative Decimal

For negative decimals, simply ignore the minus sign, convert the absolute value to a fraction using the steps above, then add the negative sign back to the result.

Example: −0.4 → convert 0.4 → 4/10 = 2/5 → −2/5

Common Decimal to Fraction Conversions

Here are some frequently used conversions for quick reference:

• 0.1 = 1/10  |  0.125 = 1/8  |  0.2 = 1/5
• 0.25 = 1/4  |  0.333… = 1/3  |  0.375 = 3/8
• 0.4 = 2/5  |  0.5 = 1/2  |  0.625 = 5/8
• 0.666… = 2/3  |  0.75 = 3/4  |  0.875 = 7/8

Frequently Asked Questions

When do you need to convert decimals to fractions?

You'll need to convert decimals to fractions in construction (measurements in inches), cooking (recipe quantities like 1/3 cup), finance (interest rates), and in math courses when simplifying expressions or solving equations. Fractions are also essential when working with ratios.

What are the benefits of using fractions over decimals?

Fractions are exact — 1/3 is precise, while 0.333… is an approximation. Fractions also make it easier to see relationships between numbers (3/4 immediately tells you "three out of four parts"), and they simplify certain calculations like finding common denominators for adding fractions.

How do you convert a decimal greater than 1 to a fraction?

Follow the same three steps (write over 1, multiply by 10, reduce). The result will be an improper fraction that you can convert to a mixed number. For example, 2.5 → 25/10 → 5/2 → 2 1/2.

What is 0.333… as a fraction?

0.333… (repeating) = 1/3. Similarly, 0.666… = 2/3 and 0.999… = 1 (exactly). These are repeating decimals that require the algebraic method described above.

Can every decimal be expressed as a fraction?

Every terminating decimal and every repeating decimal can be expressed as a fraction (rational number). However, irrational numbers like π (3.14159…) and √2 (1.41421…) cannot be expressed as exact fractions because their decimal expansions never terminate or repeat.