Fraction to Decimal Calculator

Converting a fraction to a decimal is one division: numerator divided by denominator. Three quarters is 3 ÷ 4 = 0.75; one eighth is 1 ÷ 8 = 0.125; one third is 1 ÷ 3 = 0.333…, repeating forever. The fraction to decimal calculator above does the division and shows the decimal to six places, and this page explains the method, the repeating cases, and the table of common conversions worth memorising.

The default example in the calculator is 3/4 + 1/2, which simplifies to 5/4 — and 5 ÷ 4 = 1.25. That is the pattern: the calculator simplifies first, then divides. A decimal is just the fraction’s value written in base ten, and the division is the bridge between the two forms.

How to Convert a Fraction to a Decimal

The method is the same for every fraction:

Decimal = numerator ÷ denominator

Divide the top number by the bottom number. For 3/4: 3 ÷ 4 = 0.75. For 5/8: 5 ÷ 8 = 0.625. For 7/20: 7 ÷ 20 = 0.35. If the numerator is bigger than the denominator, the decimal is bigger than 1: 5/4 is 5 ÷ 4 = 1.25, and 11/4 is 2.75. The division either ends — a terminating decimal — or repeats forever, and which one it is depends only on the denominator.

Step by Step: 3/4 to a Decimal

1. Set up the division. 3 ÷ 4 — the numerator is the dividend, the denominator is the divisor.
2. Divide. 4 goes into 3 zero times, so the answer starts 0. — then 4 goes into 30 seven times (28), leaving 2; bring down a zero, and 4 goes into 20 exactly five times.
3. Read the answer. 0.75, with no remainder — a terminating decimal.
4. Check it. 0.75 × 4 = 3, which brings you back to the numerator.

Common Fraction-to-Decimal Conversions

The table below covers the conversions worth knowing by heart. The halves, quarters, and eighths are the ones that appear in measurements, recipes, and money, and the thirds and sixths are the repeating cases.

The percentage column is the same conversion carried one step further: multiply the decimal by 100. The percentage calculator does that conversion with the working shown, and the Khan Academy — Fractions explains terminating and repeating decimals with visual models.

Terminating vs Repeating Decimals

Whether a decimal ends or repeats depends on the denominator after the fraction is simplified. If the denominator’s only prime factors are 2 and 5, the decimal terminates: 1/8 = 0.125 (8 = 2³), 3/20 = 0.15 (20 = 2² × 5), 7/40 = 0.175. If the denominator has any other prime factor — 3, 7, 11, and so on — the decimal repeats: 1/3 = 0.333…, 2/7 ≈ 0.2857 repeating, 5/6 = 0.8333….

Repeating decimals are written with a bar over the repeating digits, or with an ellipsis: 0.333…. For everyday use, round them: 1/3 is 0.33 to two decimal places, 2/3 is 0.67, and 1/6 is 0.17. But remember that a rounded decimal is an approximation — 0.33 × 3 is 0.99, not 1 — so keep the fraction for exact work and use the decimal only for measurement, money, or comparison. The calculator shows the decimal to six places, with trailing zeros trimmed, so a repeating decimal is visible as far as it goes.

Decimals Back to Fractions

The reverse conversion — decimal to fraction — is just as useful, and it follows the place value. Read the decimal as a fraction over a power of ten, then simplify: 0.75 is 75/100, which simplifies by 25 to 3/4. 0.125 is 125/1000, which simplifies by 125 to 1/8. 0.6 is 6/10, which simplifies to 3/5. 0.35 is 35/100, which simplifies to 7/20.

Repeating decimals convert differently: 0.333… is 1/3, and 0.666… is 2/3 — the repeating digit over 9 gives the fraction (3/9 = 1/3). For most everyday purposes the terminating cases above are the ones that matter, and the calculator’s decimal output is the fastest way to check your own conversion.

Common Mistakes

Most wrong fraction answers come from the same short list of errors. Check yours against it before trusting the result.

• Adding numerators and denominators. 1/2 + 1/3 is 5/6, not 2/5 — find a common denominator first.
• Forgetting to simplify. 6/12 is 1/2; an unsimplified answer is correct but unfinished.
• Multiplying by the wrong reciprocal. Dividing by 2/5 means multiplying by 5/2, not by 2/5.
• Mixing whole numbers and fractions. Convert mixed numbers to improper fractions before adding or multiplying.
• Dividing by zero. A denominator of zero has no meaning — check both denominators before calculating.
• Rounding a repeating decimal too early. 1/3 is 0.333…, not 0.33 — round only at the end, and say that it repeats.

Related Tools

Related tools on this site: the main fraction to decimal calculator for any fraction sum, the ratio calculator for the ratio behind a fraction, the percentage calculator to turn a fraction into a percent, and the basic calculator for decimal arithmetic.

Key Takeaways

If you remember nothing else from this page, remember these five points.

• 3/4 + 1/2 = 5/4 = 1 1/4: find a common denominator, add the numerators, simplify.
• 12/18 simplifies to 2/3 — divide numerator and denominator by their GCD, which is 6.
• 3/4 as a decimal is 0.75: divide the numerator by the denominator.
• 1 1/2 is 3/2 as an improper fraction: 1 × 2 + 1 = 3, over 2.
• Dividing by a fraction means multiplying by its reciprocal: 3/4 ÷ 2/5 = 15/8.

Try It Yourself

1. Enter the two fractions in the calculator above, whole parts included.
2. Pick the operation and read the answer with the step-by-step working.
3. Check the GCD shown to see how the answer was simplified.
4. Convert the answer to a decimal or a mixed number as needed.

Quick Reminders

• Never add denominators — only numerators, and only after they match.
• Convert mixed numbers to improper fractions before multiplying or dividing.
• A denominator of zero has no meaning — check both denominators.
• 1/3 is 0.333…, repeating — round only at the end.

Keep the fraction as a fraction for exact work and use the decimal only for measuring, money, or comparison — a rounded decimal is an approximation, and the fraction is the exact value.

Frequently Asked Questions

How do you convert a fraction to a decimal?

Divide the numerator by the denominator. For 3/4, 3 ÷ 4 = 0.75. For 5/8, 5 ÷ 8 = 0.625. If the numerator is bigger than the denominator, the decimal is bigger than 1 — 5/4 is 1.25.

What is 3/4 as a decimal?

0.75. The division is 3 ÷ 4 = 0.75, a terminating decimal. As a percentage that is 75%, and as a fraction in lowest terms it is already 3/4.

What is 7/8 as a decimal?

0.875. The division is 7 ÷ 8 = 0.875. The eighths run 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875 — each one an eighth (0.125) more than the last.

What is 1/3 as a decimal?

0.333…, repeating forever. The division never ends because 3 has the prime factor 3, so the decimal repeats. For everyday use it is rounded to 0.33, but the exact value is the fraction 1/3.

How do you convert a decimal back to a fraction?

Write the decimal over a power of ten, then simplify. 0.75 is 75/100, which simplifies by 25 to 3/4. 0.125 is 125/1,000, which simplifies by 125 to 1/8. A repeating decimal like 0.333… is 1/3.

Which fractions give terminating decimals?

Fractions whose simplified denominator has only the prime factors 2 and 5 — like 1/2, 3/4, 5/8, and 7/20. Any other prime factor in the denominator (3, 7, 11) makes the decimal repeat forever.

What is 1/8 as a decimal?

0.125. The division is 1 ÷ 8 = 0.125, a terminating decimal. The eighths run 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, and 0.875.

What is 2/5 as a decimal?

0.4. The division is 2 ÷ 5 = 0.4. As a percentage that is 40%, and the fraction is already in lowest terms.

Disclaimer: This calculator is for general information and education. Fractions are exact arithmetic, but measurements and quantities you enter should be checked against the original source.