Fractions to Decimals — How to Convert Step by Step

To convert a fraction to a decimal, divide the numerator by the denominator. In other words, read $a/b$ as $a \div b$, as long as $b \ne 0$.

For example, $3/4$ means $3 \div 4$, so $3/4 = 0.75$.

If the denominator can be turned into $10$, $100$, or $1000$, you can often convert faster by writing an equivalent fraction. If not, long division always works.

How Fraction To Decimal Conversion Works

A fraction and a decimal can name the same value in different forms. For example, $1/2$, $0.5$, and $50\%$ all describe the same amount.

Decimals are usually easier to compare on a number line or use in measurements and calculators. Fractions are often better for showing exact parts. Converting between them lets you use the form that fits the problem.

The Main Rule

Read

$$\frac{a}{b}$$

as

$$a \div b$$

as long as $b \ne 0$.

That gives the decimal form of the fraction.

Convert $3/8$ To A Decimal Step By Step

Convert $3/8$ to a decimal.

Start with the division:

$$3 \div 8$$

Since $8$ does not go into $3$, write $0.$ and add a zero. Now divide $30$ by $8$.

• $8$ goes into $30$ three times, because $3 \times 8 = 24$.
• Subtract: $30 - 24 = 6$.
• Bring down another $0$ to make $60$.
• $8$ goes into $60$ seven times, because $7 \times 8 = 56$.
• Subtract: $60 - 56 = 4$.
• Bring down another $0$ to make $40$.
• $8$ goes into $40$ five times.

So

$$\frac{3}{8} = 0.375$$

This answer makes sense because $3/8$ is less than $1/2$, and $0.375$ is less than $0.5$.

Use An Equivalent Fraction When The Denominator Fits Base 10

Sometimes you do not need long division at all. If the denominator can be scaled to $10$, $100$, or $1000$, rewrite the fraction first.

For example:

$$\frac{7}{20} = \frac{35}{100} = 0.35$$

This works because multiplying the numerator and denominator by the same nonzero number does not change the value of the fraction.

When A Fraction Gives A Terminating Or Repeating Decimal

In base 10, some fractions end and some repeat forever.

• A fraction such as $1/4 = 0.25$ terminates.
• A fraction such as $1/3 = 0.333\ldots$ repeats.

After simplifying the fraction first, the decimal terminates only when the denominator has no prime factors other than $2$ and $5$. If other prime factors remain, the decimal repeats.

You do not need that rule to convert fractions, but it helps you know what to expect while dividing.

Common Mistakes When Converting Fractions To Decimals

Reversing the division

$3/8$ means $3 \div 8$, not $8 \div 3$.

Stopping too early

If there is a remainder, the division is not finished. Add a zero and keep going.

Misplacing the decimal point

If the fraction is less than $1$, the decimal must also be less than $1$. That quick check catches many errors.

Forgetting to simplify when predicting the pattern

For example, $3/6$ simplifies to $1/2$, so its decimal terminates even though the original denominator was $6$.

Where You Use Fractions And Decimals

Fractions to decimals show up in measurement, money, probability, test scores, and calculator work. They also help when you want to compare two fractions quickly.

For example, it is often easier to compare $3/5$ and $5/8$ by converting them to $0.6$ and $0.625$.

Try Your Own Version

Try converting $5/16$ and $2/3$ on paper. One will terminate, and one will repeat. Predict which is which before you divide.

If you want one more check after doing it by hand, try your own version in a solver and compare each division step with your result.