Decimal to Fraction Calculator — Convert Decimals to Fractions & Mixed Numbers with Live Interactive Visuals

What does a decimal to fraction calculator do?

A decimal to fraction calculator turns a number written in decimal form — such as 0.375, 1.625 or 0.333… — into an equivalent fraction written as a numerator over a denominator. The fraction is usually reduced to its simplest form, and if the value is greater than 1 it is also shown as a mixed number. The conversion works for every terminating decimal and every repeating decimal, and this tool shows the exact arithmetic at each step.

Decimals and fractions are two ways of writing the same number. 0.5 and 1/2 are the same value. 0.25 and 1/4 are the same value. 0.333… and 1/3 are the same value. The decimal form is convenient for arithmetic and calculators; the fraction form is exact and is often preferred in cooking, woodworking, engineering drawings, music notation, and any calculation where you want to avoid rounding.

How to convert a decimal to a fraction — the three-step method

The algorithm is the same for every terminating decimal. It has three steps.

Step 1 — Write the decimal over 1

Place the decimal number as the numerator and 1 as the denominator:

Step 2 — Multiply both parts by a power of 10

Count how many digits are to the right of the decimal point. Call that number n. Multiply both the numerator and the denominator by 10ⁿ:

Step 3 — Reduce by the greatest common divisor

Find the largest number that divides both the numerator and the denominator exactly. That is the greatest common divisor (GCD), also called the greatest common factor (GCF). Divide both by it:

If the numerator is larger than the denominator, divide to extract the whole part and write the remainder over the denominator:

Terminating vs repeating decimals

Every decimal falls into one of three families, and the family determines whether the fraction is exact or approximate.

Terminating decimals

A terminating decimal has a finite number of digits after the decimal point. It stops. Examples: 0.5, 0.25, 0.375, 1.625, 2.75, 0.1. Every terminating decimal can be written as an exact fraction whose denominator is a power of 10, then reduced.

Repeating decimals

A repeating decimal (also called a recurring decimal) has a block of digits that repeats forever. Examples: 0.333… (the 3 repeats), 0.142857142857… (the 142857 repeats), 1.8333… (the 3 repeats after the 8). Every repeating decimal can be written as an exact fraction. The fraction's denominator, in lowest terms, always has a prime factor other than 2 and 5.

Non-terminating, non-repeating decimals

Some decimals neither terminate nor repeat — π = 3.14159265…, √2 = 1.41421356…, and e = 2.71828182…. These are irrational numbers, and they cannot be written as exact fractions. They can only be approximated by fractions such as 22/7 or 355/113. If you enter a finite decimal in this calculator, it is by definition terminating (you typed a finite number of digits), so the result is exact.

How to convert a repeating decimal to a fraction

The three-step method above works for terminating decimals. Repeating decimals need a different approach using algebra. The idea is to create two equations whose difference cancels the repeating tail.

Take 0.3(3) = 0.3333…

For a repeating decimal with a non-repeating prefix and a longer repeating block, multiply by two different powers of 10 first. Take 1.2(34) = 1.2343434…

The general formula used by this calculator is:

Mixed numbers and improper fractions

When the decimal is greater than 1, the conversion produces an improper fraction — a fraction where the numerator is larger than the denominator. For example, 1.625 = 1625/1000 = 13/8. The fraction 13/8 is correct, but many people prefer to see it as a mixed number: 1 5/8.

To convert an improper fraction to a mixed number:

1. Divide the numerator by the denominator. The quotient is the whole part.
2. The remainder becomes the numerator of the fractional part.
3. The denominator stays the same.

For 13/8: 13 ÷ 8 = 1 remainder 5, so 13/8 = 1 5/8. This calculator shows both forms — the improper fraction and the mixed number — because different contexts prefer different formats. Cooking recipes usually use mixed numbers (1 1/2 cups); engineering drawings often use improper fractions or decimals; algebra problems often use improper fractions.

Negative decimals

The conversion works exactly the same way for negative numbers. Remove the minus sign, convert the positive value to a fraction, then re-apply the minus sign to the result. So −0.75 = −3/4, −1.5 = −3/2 = −1 1/2, and −0.625 = −5/8. The sign applies to the whole mixed number: −1 5/8 means −(1 + 5/8) = −13/8, not (−1) + 5/8.

Simplifying fractions with the GCD

The raw conversion always produces a fraction over a power of 10, such as 375/1000 or 1625/1000. That fraction is correct but not in its simplest form. The greatest common divisor (GCD) of the numerator and denominator is the largest number that divides both exactly. Dividing both parts by the GCD gives the simplest equivalent fraction.

If the GCD is 1, the fraction is already in simplest form. For example 333/1000 has GCD 1, so it cannot be reduced further. This calculator's settings include a toggle to turn simplification on or off, so you can see the raw and reduced forms side by side.

Reading fractions aloud — the word form

The word form of a fraction is what you'd say if you read it out loud. The numerator is read as a normal number, and the denominator becomes an ordinal word — halves, thirds, quarters/fourths, fifths, sixths, sevenths, eighths, ninths, tenths, elevenths, twelfths… For a mixed number, add "and" between the whole part and the fraction.

Note that "half" and "quarter" are the common exceptions. Technically "two fourths" is also correct, but "a half" and "a quarter" are what people actually say. The fraction word form is used in legal documents, banking (write the amount in words), recipes and education.

Fractions as ratios

Every fraction a/b is also a ratio a:b. So 3/8 is the ratio 3:8, 1/4 is the ratio 1:4, and 13/8 is the ratio 13:8. Ratios appear everywhere in engineering (gear ratios, screen aspect ratios, scale drawings), mixing instructions (2:1 paint, 4:1 epoxy), sports (odds, win-loss ratios) and cooking (rice-to-water ratios). The ratio display in this calculator gives you the reduced form directly, so 0.5 → 1/2 → 1:2 rather than 5:10.

Prime factorization of the fraction

Every positive integer can be written uniquely as a product of prime numbers. For the fraction's numerator and denominator, this reveals why simplification works:

The GCD is the product of the common prime factors (each raised to its minimum power). Dividing out the common factors leaves only the primes that appear in the numerator or the denominator — the fraction in lowest terms. This is exactly what the calculator shows in the "Prime factorization" panel: both factorizations side by side, and the common primes highlighted. It makes the simplification step visually obvious instead of a mysterious "divide by 125".

Worked examples

Example 1 — 0.375

Decimal places: 3. Raw fraction: 375/1000. GCD: 125. Simplified: 3/8. Result: 0.375 = 3/8.

Example 2 — 1.625

Decimal places: 3. Raw fraction: 1625/1000. GCD: 125. Simplified improper: 13/8. Mixed: 1 5/8.

Example 3 — 2.5

Decimal places: 1. Raw fraction: 25/10. GCD: 5. Simplified improper: 5/2. Mixed: 2 1/2.

Example 4 — 0.333…

This is a repeating decimal, not the terminating decimal 0.333. Use repeating mode with 0.3(3): x = 0.333…, 10x = 3.333…, 9x = 3, x = 1/3. If you enter 0.333 in decimal mode you get 333/1000 (a different number).

Example 5 — 0.142857142857…

The repeating block is 142857 (six digits). x = 0.142857…, 10⁶x = 142857.142857…, 999999x = 142857, x = 142857/999999 = 1/7. The repeating block of 1/7 is exactly 142857.

Example 6 — −0.75

Ignore the sign: 0.75 = 75/100 = 3/4. Re-apply the sign: −3/4.

Example 7 — 0.08(3)

Non-repeating digits: 08 (p = 2), repeating digits: 3 (q = 1). Numerator = 8 × (10 − 1) + 3 = 75. Denominator = 100 × 9 = 900. 75/900 = 1/12. So 0.08333… = 1/12.

Common decimal to fraction conversions

Decimal to fraction inches chart

In woodworking, machining and construction, decimal inches are often converted to the nearest fraction on a ruler. Rulers are marked in halves, quarters, eighths, sixteenths, thirty-seconds and sixty-fourths. The table below gives the common decimal-to-inch-fraction equivalents.

Converting a fraction back to a decimal

The reverse operation is a simple division: divide the numerator by the denominator. For 5/8, 5 ÷ 8 = 0.625. For 13/8, 13 ÷ 8 = 1.625. For a mixed number, add the whole part: 1 5/8 = 1 + 5 ÷ 8 = 1.625.

The interest is in what happens when the division does not terminate. 1/3 = 0.333… with the 3 repeating forever. 1/7 = 0.142857142857… with the 6-digit block 142857 repeating. The repeating block is the sequence of remainders in the long division — when a remainder repeats, the digits from that point repeat too. This is exactly what the Fraction → Decimal tab of this calculator detects: it runs the long division, records each remainder, and reports where the cycle begins and how long the repeating block is.

Common mistakes

• Not reducing the fraction. 375/1000 is correct but 3/8 is simpler. Always divide by the GCD unless you specifically need the raw form.
• Miscounting decimal places. 0.375 has three digits after the point, so the denominator is 1000, not 100. Count carefully, especially with leading zeros: 0.0125 has four decimal places, so the denominator is 10000, giving 125/10000 = 1/80.
• Treating 0.333 as exactly 1/3. The terminating decimal 0.333 is 333/1000. The repeating decimal 0.333… is exactly 1/3. They are different numbers, and 0.333 < 1/3.
• Forgetting the negative sign. −0.75 is −3/4, not 3/4. For a negative mixed number, the sign applies to the whole number: −1 5/8 = −13/8.
• Simplifying a fraction that is already simplest. 333/1000 has GCD 1, so it cannot be reduced. A fraction is in simplest form when the only common divisor is 1.
• Using the wrong denominator for inches. A decimal of 0.375 inch is exactly 3/8 inch, but 0.4 inch is not exactly 3/8 — it rounds to 13/32 on a 1/32 ruler. Match the ruler precision to the measurement precision.
• Confusing a mixed number with multiplication. 1 5/8 means 1 + 5/8, not 1 × 5/8. The whole number and the fraction are added.
• Assuming every decimal has an exact fraction. Terminating and repeating decimals do; irrational numbers like π do not. This calculator only accepts terminating decimals (which you type) or explicitly marked repeating decimals.

Where decimal-to-fraction conversion is used

• Woodworking and carpentry. Tape measures and rulers are marked in fractions. A laser measure or calculator reports 0.375 inch; you need 3/8 inch to set a saw or drill.
• Engineering and machining. Drill sizes, bolt diameters, sheet thicknesses and tolerances are often specified in both decimal inches and fractions.
• Cooking and baking. A recipe calls for 0.75 cup; the measuring cups are marked in 1/4, 1/3, 1/2 and 1 cup. 0.75 cup = 3/4 cup.
• Music theory. Note values and time signatures use fractions: a quarter note is 1/4, a dotted half note is 3/4, a triplet is 1/3 of a beat.
• Finance. Stock prices, interest rates and exchange rates are quoted in decimals, but fractional-share calculations and historical prices sometimes use fractions (especially in the US bond market, where prices are quoted in 32nds).
• Education. Converting between decimals and fractions is a core skill in primary and middle-school mathematics, and showing the steps is exactly what this calculator provides.

Privacy

Every calculation, visualization, conversion and export runs in your browser with plain JavaScript. Nothing you type is uploaded, logged or sent to a server. There is no account and no network request after the page loads. Recent calculations are optionally kept in your browser's localStorage so you can reload them, and clearing them removes them permanently from your device.

Limitations

• The decimal input must be a terminating decimal (a finite number of digits) or a repeating decimal entered with parentheses. A non-terminating, non-repeating decimal (π, √2) cannot be written as an exact fraction.
• Very long decimals are handled exactly with BigInt, but the display is rounded to a sensible number of significant figures. The underlying fraction is exact.
• The nearest-fraction table uses the value's fractional part (the part after the decimal point). For negative numbers it uses the absolute value.
• The inch-fraction table is an approximation to the nearest 1/2, 1/4, 1/8, 1/16, 1/32 and 1/64. It does not round to 1/128 or finer.
• Extremely large numbers may lose precision in the visualization, though the fraction result remains exact.

Frequently asked questions

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