How to Convert Fractions to Decimals (and Decimals to Fractions)

Fractions and decimals are simply two different ways of writing the same value. The fraction one-half and the decimal 0.5 describe the exact same amount, but each form is useful in different situations. Knowing how to move smoothly between them helps you compare numbers, plug values into a calculator, measure ingredients, and check your work. In this guide you will learn a reliable method for converting any fraction into a decimal, how to turn a decimal back into a fraction, and how to handle the tricky case of repeating decimals.

What Fractions and Decimals Really Mean

A fraction has two parts: the numerator (top number) tells you how many parts you have, and the denominator (bottom number) tells you how many equal parts the whole is divided into. A decimal expresses that same idea using place value. The first digit after the decimal point is tenths, the next is hundredths, then thousandths, and so on. So 0.7 means seven tenths, which is the same as the fraction 7/10. If you understand place value, half the work is already done. For a deeper refresher on fraction basics, see our more guides section.

Converting a Fraction to a Decimal

The most dependable method is to remember that a fraction is a division problem. The bar between numerator and denominator means "divide." To convert any fraction to a decimal, divide the numerator by the denominator.

1. Write the numerator inside the division and the denominator outside.
2. Add a decimal point and zeros after the numerator as needed.
3. Divide as you would with whole numbers, carrying the decimal point straight up.
4. Continue until the remainder is zero or a pattern repeats.

Let us work through 3/8 step by step. We divide 3 by 8. Since 8 does not go into 3, we write 0 and a decimal point, then treat the value as 3.000. Eight goes into 30 three times (3 times 8 is 24), leaving a remainder of 6. Bring down a zero to make 60; 8 goes into 60 seven times (7 times 8 is 56), leaving 4. Bring down a zero to make 40; 8 goes into 40 exactly five times. So 3/8 equals 0.375. If you want to practice this division process, our practice problems are a great place to start, and the free math tools include calculators that show each step.

A Shortcut for Friendly Denominators

When the denominator is 10, 100, or 1000, you can skip division entirely. Just place the numerator and shift the decimal point by the number of zeros. For example, 47/100 is 0.47 because there are two zeros, so the point moves two places. You can also convert a fraction to an equivalent one with a power-of-ten denominator. The fraction 3/5 becomes 6/10 (multiply top and bottom by 2), which is simply 0.6.

Terminating Versus Repeating Decimals

Some fractions produce a decimal that ends cleanly, like 0.375. These are called terminating decimals. Others never end and instead repeat a digit or block of digits forever. For example, 1/3 equals 0.3333... where the 3 repeats endlessly. We write this with a bar over the repeating digit or simply note it as 0.3 repeating. The fraction 2/11 gives 0.181818..., where the block "18" repeats. A fraction will terminate only if, after fully simplifying, its denominator has no prime factors other than 2 and 5. Since 8 is 2 times 2 times 2, the fraction 3/8 terminates. Since 11 is a prime other than 2 or 5, the fraction 2/11 repeats.

Converting a Decimal Back to a Fraction

Going the other direction is mostly about reading the place value correctly.

1. Count the digits after the decimal point.
2. Write the digits (without the point) as the numerator.
3. Use 1 followed by that many zeros as the denominator.
4. Simplify the fraction by dividing top and bottom by their greatest common factor.

Take 0.64 as an example. There are two digits after the point, so we write 64/100. Both numbers are divisible by 4, giving 16/25, which cannot be reduced further. So 0.64 equals 16/25. For a number greater than one, such as 2.75, keep the whole number aside, convert 0.75 to 3/4, and combine to get 2 and 3/4, or the improper fraction 11/4.

Turning a Repeating Decimal into a Fraction

Repeating decimals require a small algebra trick. Suppose you want to convert 0.4444... into a fraction. Let x equal 0.4444... Multiply both sides by 10 to get 10x equals 4.4444... Subtract the first equation from the second: 10x minus x is 9x, and 4.4444... minus 0.4444... is exactly 4. So 9x equals 4, which means x equals 4/9. You can verify this by dividing 4 by 9 to recover the repeating decimal.

Common Mistakes to Avoid

• Dividing in the wrong order. Always divide the numerator by the denominator, not the other way around. For 3/8, divide 3 by 8, not 8 by 3.
• Forgetting to simplify. A decimal-to-fraction answer is not finished until it is reduced to lowest terms.
• Miscounting place value. The number 0.5 is five tenths, not five hundredths. Count decimal places carefully.
• Rounding too early. If you round a long decimal before finishing a calculation, your final answer drifts off. Keep extra digits until the end.

Frequently Asked Questions

How do I convert a fraction to a decimal without a calculator?

Use long division: divide the numerator by the denominator, adding zeros after the decimal point as needed. Continue until the remainder is zero or a pattern repeats.

Why does 1/3 never end as a decimal?

Because the denominator 3 is not made only of the prime factors 2 and 5. When a simplified denominator includes other primes, the decimal repeats forever instead of terminating.

Is 0.5 the same as 1/2?

Yes. The decimal 0.5 means five tenths, which simplifies to one half. They represent exactly the same value.

How do I convert a percentage to a fraction?

A percentage is just a fraction out of 100. So 40 percent is 40/100, which simplifies to 2/5. You can also write it as the decimal 0.40 first if that feels easier.

With these methods you can confidently move between fractions and decimals in any direction. Practice a few conversions by hand to build intuition, then use our free math tools to check your answers and speed up longer calculations.