How to convert a fraction to a decimal

Converting a fraction to a decimal is just division. A fraction like 3/8 literally means “3 divided by 8.” When you perform that division, you get the decimal form (0.375). This calculator handles common cases (proper fractions, improper fractions, and mixed numbers), and it also shows the long-division steps so the result feels trustworthy—not like a black box.

The core formula

If a fraction is written as n/d (numerator over denominator), the decimal is:

decimal = n ÷ d

If the denominator is 0, the value is undefined (division by zero). If the fraction is negative, the decimal is negative.

Mixed numbers (like 1 1/2)

A mixed number has a whole part and a fraction part. For example: 1 1/2 = 1 + (1/2). Convert the fractional part to a decimal and add the whole part. This tool lets you type mixed numbers directly (like 1 1/2) or as an improper fraction (like 3/2).

Quick mental-math shortcuts

• Denominator 2, 4, 5, 8, 10 often gives a terminating decimal (it ends).
• Denominator 3 often repeats: 1/3 = 0.333…
• Denominator 6 can have repeating parts: 1/6 = 0.1666…
• Denominator 9 gives clean repeats: 1/9 = 0.111…

Terminating vs repeating decimals

Some fractions become decimals that stop (terminating decimals). Others repeat forever (repeating decimals). A fraction in simplest form has a terminating decimal only when the denominator’s prime factors are 2 and/or 5 (because our base-10 system is built on 2×5). If the simplified denominator has any other prime factor (3, 7, 11, …), the decimal repeats.

Examples:

• 3/8 → 0.375 (8 = 2³, so it terminates)
• 1/12 → 0.08333… (12 = 2²×3, includes 3, so it repeats)
• 7/20 → 0.35 (20 = 2²×5, so it terminates)

Step-by-step long division (the “show your work” method)

Long division converts n/d by dividing the numerator by the denominator:

1. Divide n by d. The integer part is the whole number portion (often 0 for proper fractions).
2. Keep the remainder r. The next digit comes from dividing r×10 by d.
3. Repeat: multiply the remainder by 10, divide by d, and record the next digit.
4. If a remainder becomes 0, the decimal terminates.
5. If a remainder repeats, the digits will start repeating from that point (a repeating decimal).

Example: 1/6

• 1 ÷ 6 = 0 remainder 1 → decimal starts with 0.
• Remainder 1 → 1×10 = 10. 10 ÷ 6 = 1 remainder 4 → next digit is 1.
• Remainder 4 → 4×10 = 40. 40 ÷ 6 = 6 remainder 4 → next digit is 6.
• Remainder 4 repeats, so the “6” repeats forever → 0.16666…

Converting the decimal to a percent

Once you have the decimal, turning it into a percent is easy: percent = decimal × 100. For example, 0.375 becomes 37.5%. This is useful for grades, discounts, and probability-style thinking.

Examples (common fractions)

FAQs

Why do some fractions repeat?

Because base-10 decimals can only terminate when the simplified denominator divides a power of 10 (10, 100, 1000, …). Those powers have only prime factors 2 and 5. Any other factor forces an infinite repeat.

Is 0.999… equal to 1?

Yes. A repeating 0.999… is exactly equal to 1. It’s a standard result in math, caused by how infinite repeating decimals are defined.

Does simplifying change the decimal value?

No. Simplifying (like turning 2/4 into 1/2) changes the representation, not the value. It can help you understand whether the decimal will terminate, and it’s often easier for mental math.

How many decimal places should I use?

It depends on the context. Money often uses 2 decimals, measurements might use 3–4, and scientific work can use more. This tool shows up to 12 digits by default and highlights repeating patterns when detected.

What about negative fractions?

The sign carries through: -3/8 = -0.375. You can enter negatives as -3/8 or with a negative numerator.