Fractions to Decimals — How to Convert Step by Step

To turn a fraction into a decimal, divide the numerator by the denominator: read $a/b$ as $a \div b$, provided $b \ne 0$. For example, $3/4$ means $3 \div 4$, so $3/4 = 0.75$.

When to use each approach

A fraction and a decimal can name the same value: $1/2$, $0.5$, and $50\%$ all describe the same amount. Decimals are easier to compare on a number line or use in measurements and calculators; fractions are better for showing exact parts. Two routes are available, and the denominator decides which is faster:

• If the denominator can be scaled to $10$, $100$, or $1000$, rewrite as an equivalent fraction and read the decimal off directly.
• If not, long division always works.

The procedure, step by step

Step 1: Read the fraction as division. Treat the numerator as the number being divided and the denominator as the divisor:

Step 2: Try an equivalent fraction first. If the denominator scales to base $10$, rewrite it:

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

Step 3: Use long division if needed, adding zeros after the decimal point until the quotient ends or begins to repeat.

Step 4: Check the size of the answer. If the fraction is less than $1$, the decimal should be less than $1$ too.

Worked example: convert $3/8$ all the way through

Start with the division $3 \div 8$. Since $8$ does not go into $3$, write $0.$ and add a zero, then divide $30$ by $8$:

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

So

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

Will it terminate or repeat?

In base 10, some fractions end and some repeat forever. A fraction such as $1/4 = 0.25$ terminates, while $1/3 = 0.333\ldots$ 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, it repeats. You do not need this rule to convert, but it tells you what to expect while dividing.

Where you get stuck, and how to self-check

Each step has a common slip:

• 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 $1$, so is the decimal. That quick check catches many errors.
• Forgetting to simplify before predicting the pattern. $3/6$ simplifies to $1/2$, so its decimal terminates even though the original denominator was $6$.

Run the whole procedure on $5/16$ and $2/3$ by hand: predict which terminates and which repeats before you divide. ($5/16 = 0.3125$ terminates because $16 = 2^4$, while $2/3 = 0.666\ldots$ repeats.)

Where you use fractions and decimals

These conversions show up in measurement, money, probability, test scores, and calculator work, and they make comparisons faster. For instance, $3/5$ and $5/8$ are easier to compare as $0.6$ and $0.625$.