Fraction to Decimal Calculator

Q: How do I go from a decimal back to a fraction?

Use our Decimal to Fraction Calculator . It takes a decimal like 0.625 and gives you 5/8 in lowest terms.

Introduction

This Fraction to Decimal Calculator turns any fraction into a decimal in one click. Type a numerator and a denominator, and you get the answer right away. You can also switch to Mixed Number mode to convert numbers like 2 3/8.

The tool does more than give one number. It shows the fraction in lowest terms, the percent form, and the full step-by-step work. It also tells you if the decimal is terminating (it ends, like 0.375) or repeating (it goes on forever, like 0.8333…). Repeating answers are shown with the repeating digits in parentheses.

You can round to any number of decimal places, from 0 to 9, or keep the full value. Negative numbers work too. Use the ± buttons to flip a sign on the top, bottom, or whole number.

A picture of your fraction shows as you type, and a chart shows how big the value is. This makes the calculator handy for homework, test prep, cooking, measuring, and any job where you need fractions as decimals fast. If you need to go the other direction, use the Decimal to Fraction Calculator.

How to use our Fraction to Decimal Calculator

Type in your fraction, pick how many decimal places you want, and the calculator shows the decimal value, the percent value, and whether the decimal ends or repeats.

Fraction type: Click "Simple Fraction" for a plain fraction like 20/24. Click "Mixed Number" if your number has a whole part, like 2 3/8.

Whole Number: This box shows up in Mixed Number mode. Enter the whole part of your number. Use the ± button to make the whole mixed number negative.

Numerator: Enter the top number of the fraction. Use whole numbers only. Tap ± to switch it from positive to negative.

Denominator: Enter the bottom number of the fraction. It can be any whole number except zero, since you cannot divide by zero. Tap ± to change its sign.

Round to (Decimal Precision): Pick how many decimal places you want in the answer, from 0 to 9. Choose "Do Not Round" to see the full decimal, including repeating digits.

Calculate and Reset: Press Calculate to see your decimal answer, the percent, and the step-by-step work. Press Reset to clear everything and start over. Use the Copy button to copy your decimal result.

Fraction to Decimal Conversion Explained

A fraction shows a part of a whole. The top number is the numerator, and the bottom number is the denominator. A decimal shows the same value using a dot and place values like tenths, hundredths, and thousandths. Both write the same amount in different ways.

How to Change a Fraction Into a Decimal

Divide the numerator by the denominator. That is all the fraction bar means: 3/4 means 3 ÷ 4 = 0.75. If you want to see the divide worked out by hand, the Long Division Calculator shows every step. If the fraction has a whole number in front of it (a mixed number like 2 3/8), first turn it into an improper fraction. Multiply the whole number by the denominator, add the numerator, and keep the same bottom number: 2 3/8 becomes 19/8, and 19 ÷ 8 = 2.375.

Terminating and Repeating Decimals

Some divisions stop. Those answers are called terminating decimals, like 1/8 = 0.125. Others go on forever in a pattern. Those are repeating decimals, like 1/3 = 0.333… A quick trick: reduce the fraction to lowest terms and look at the bottom number. If its only prime factors are 2 and 5, the decimal will stop. If any other prime factor is there (like 3, 7, or 11), the decimal will repeat. You can break any denominator apart with the Prime Factorization Calculator.

Repeating digits are often written with a bar over them or inside parentheses. For example, 5/6 = 0.8(3), which means the 3 keeps going forever.

Negative Fractions

A fraction is negative when only one part is negative, either the top or the bottom. If both are negative, the two minus signs cancel out and the answer is positive.

Decimals and Percents

To turn a decimal into a percent, multiply by 100 and add a percent sign. So 3/4 = 0.75 = 75%. To go back, divide the percent by 100.

Common Fraction to Decimal Values

1/2 = 0.5 = 50%
1/3 = 0.333… = 33.33%
1/4 = 0.25 = 25%
1/5 = 0.2 = 20%
1/8 = 0.125 = 12.5%
2/3 = 0.666… = 66.67%
3/4 = 0.75 = 75%
5/8 = 0.625 = 62.5%

Rounding Your Answer

Long or repeating decimals are usually rounded. With half-up rounding, look at the digit just past the place you want. If it is 5 or more, round up. If it is 4 or less, keep the digit the same. For example, 2/3 rounded to two decimal places is 0.67.

Why This Matters

Decimals are easier to compare, add, and type into a calculator than fractions. Money, test scores, measurements, and data charts all use decimals. Knowing how to switch between fractions, decimals, and percents helps in math class, science, cooking, and shopping.

Formulas used

Mixed number to improper fraction

\pm w\,\frac{n}{d} = \pm\frac{w \times d + n}{d}

Simplify by the greatest common factor

\frac{n}{d} = \frac{n \div g}{d \div g}, \quad g = \gcd(n, d)

Fraction to decimal

x = \frac{n}{d} = n \div d

Percentage equivalent

P = \frac{n}{d} \times 100\%

Half-up rounding to p decimal places

\mathrm{round}_p\!\left(\frac{n}{d}\right) = \frac{\left\lfloor \dfrac{n \cdot 10^p}{d} + \dfrac{1}{2} \right\rfloor}{10^p}

Terminating decimal test

\frac{n}{d}\ \text{terminates} \iff d = 2^a \cdot 5^b \quad (a, b \ge 0),\ \gcd(n,d)=1

Long-division digit recurrence (remainder expansion)

r_0 = n \bmod d, \quad a_k = \left\lfloor \frac{10\,r_{k-1}}{d} \right\rfloor, \quad r_k = 10\,r_{k-1} \bmod d

Whole and fractional parts for the chart

W = \left\lfloor x \right\rfloor, \quad F = (x - W) \times 100\%

Frequently asked questions

What is 20/24 as a decimal?

20/24 equals 0.8333…, a repeating decimal. It is written as 0.8(3), and the 3 repeats forever. In lowest terms 20/24 is 5/6, and 5 ÷ 6 = 0.8333…

Why does the answer end with three dots (…)?

The dots mean the decimal keeps going. For repeating answers, the tool shows 15 digits and then dots. Look at the note under the result to see the exact repeating form in parentheses.

What happens if the numerator is 0?

The answer is 0. Zero parts of anything is nothing, so 0/9 = 0 and 0%. The minus sign is dropped because zero is neither positive nor negative.

Does rounding change the real value of my fraction?

Yes, a little. A rounded answer is close but not exact. Pick Do Not Round if you need the exact value, like when you check homework or do more math with the number.

How do I turn a tape measure fraction into a decimal?

Type the fraction as it is written. For example, 5/16 of an inch is 0.3125 inches. For adding up lengths, try the Feet and Inches Calculator.

Which fractions repeat forever?

Reduce the fraction, then check the bottom number. If it has a factor like 3, 7, 9, or 11, the decimal repeats. 1/7 repeats with a 6 digit cycle: 0.(142857).

How do I go from a decimal back to a fraction?

Use our Decimal to Fraction Calculator. It takes a decimal like 0.625 and gives you 5/8 in lowest terms.

Why does my mixed number stay negative when I flip the numerator?

In Mixed Number mode, the ± button on the whole number sets the sign for the full number. A number like -2 3/8 means the whole thing is negative, not just the fraction part.

Can I use very large numbers?

Yes. Each box holds up to 10 digits, and the math is exact, not rounded off by the computer. Long repeating patterns are found and shown correctly.

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