What is 3/4 as a decimal?

3/4 is 0.75. Divide 3 by 4: it goes 0 times with 3 left over, then 30 ÷ 4 = 7 remainder 2, then 20 ÷ 4 = 5 remainder 0 — the division ends at 0.75.

What is 1/3 as a decimal?

1/3 is 0.3333… — a repeating decimal written 0.(3) or with a bar over the 3. It never terminates because the denominator 3 has a prime factor other than 2 and 5, so the long division never reaches a remainder of zero.

Why do some fractions repeat and others stop?

A fraction in lowest terms gives a terminating decimal exactly when its denominator’s only prime factors are 2 and 5 — the primes of 10. So 7/8 (8 = 2³) and 3/20 (20 = 2²·5) stop, while 1/3, 1/6, and 1/7 repeat because their denominators bring in the primes 3 or 7.

How do you write a repeating decimal?

Write the repeating block once and mark it — a bar (vinculum) over the digits or parentheses around them. For example 1/3 = 0.3̄, 1/6 = 0.16̄, and 1/7 = 0.142857‾ (the whole six-digit block repeats).

How do you turn a mixed number like 2 3/4 into a decimal?

Convert the fractional part and add the whole number. 3/4 = 0.75, so 2 3/4 = 2.75. The calculator accepts a whole-number box for exactly this, folding the mixed number into one improper fraction internally.

How many decimal places does a fraction have?

A terminating decimal has at most as many places as the highest power of 2 or 5 in its denominator — 1/8 has three places (0.125). A repeating decimal has infinitely many places, but its repeating block has a fixed length called the period (1/7 has period 6).

Is converting a fraction to a decimal the same as dividing?

Yes — they are identical. Numerator ÷ denominator is the decimal. Converting a fraction to a decimal is just performing that division (by long division, mentally, or with this calculator).

Arithmetic

Fraction to Decimal Calculator

Turn any fraction or mixed number into a decimal by long division — instantly. See whether it terminates or repeats, the repeating block marked with a bar, the percent equivalent, and a lookup chart of the fractions people search most.

Enter a fraction

mixed numbers ok

Whole

Numerator

Denominator

Round to4 places

Decimal

0.75

Terminating decimal

Rounded (4 dp)

0.7500

As a percent

75.00%

Improper form

3/4

Lowest terms

already reduced

The fraction bar means divide — every fraction is 3 ÷ 4.

Try an example

No sign-up · Free

The basics

What does fraction to decimal mean?

A fraction and a decimal are two ways of writing the same value. The fraction bar is a division sign, so converting a fraction to a decimal is simply carrying out that division — numerator divided by denominator. The result either ends (a terminating decimal) or settles into a block of digits that repeats forever.

a / b = a ÷ b

The fraction bar is division

The top number, a, is divided by the bottom number, b. Every fraction is therefore a division problem whose quotient is its decimal form.

3/4 = 3 ÷ 4 = 0.75

ends · or · repeats

Two kinds of result

The division either reaches a remainder of zero and stops, or a remainder recurs and the digits cycle forever. Which one happens depends only on the denominator.

7/8 = 0.875 · 1/6 = 0.1(6)

Method

How to convert a fraction by hand

Long division turns any fraction into a decimal. The same four steps work whether it terminates or repeats.

1
Divide the numerator by the denominator
Set up a ÷ b. If the numerator is smaller, the whole-number part is 0 and you go straight to the decimal point.
3 ÷ 4 → 0 .
2
Bring down a zero and divide again
Multiply the remainder by 10 (write a 0 after the decimal point) and divide once more. The quotient digit goes after the decimal point.
30 ÷ 4 = 7 remainder 2
3
Repeat with each new remainder
Keep bringing down zeros and dividing. Track the remainders — there are only finitely many possible values.
20 ÷ 4 = 5 remainder 0
4
Stop at zero, or mark the repeat
If a remainder reaches zero, the decimal ends. If a remainder you have seen before comes back, the digits from that point repeat — draw a bar over the block.
3/4 = 0.75

Worked examples

See all three outcomes

The same long division handles a clean terminating fraction, a repeating one, and a mixed number. Switch between them — each is computed from scratch.

Convert 3/8 — this one ends exactly.

Set up the division: 3 ÷ 8.

Bring down zeros and keep dividing: digits 3 7 5.

The remainder hits zero, so the decimal ends.

3/8 = 0.375

Quick chart

What is X/Y as a decimal?

Every proper fraction in a denominator family, with its decimal and whether it terminates or repeats. Pick a family of halves, thirds, quarters, and on up to sixteenths.

1/2

0.5

halves · denominator 2overline = the digits that repeat forever

Reference

The most common fraction conversions

The handful of fractions worth memorising. A bar over the digits marks the repeating block.

1/2 · terminates

0.5

1/3 · repeats

0.3

2/3 · repeats

0.6

1/4 · terminates

0.25

3/4 · terminates

0.75

1/5 · terminates

0.2

1/6 · repeats

0.16

1/7 · repeats

0.142857

1/8 · terminates

0.125

3/8 · terminates

0.375

5/8 · terminates

0.625

1/9 · repeats

0.1

1/10 · terminates

0.1

1/16 · terminates

0.0625

3/16 · terminates

0.1875

5/16 · terminates

0.3125

Where it shows up

Why you convert fractions

Decimals line up for comparison and arithmetic in places fractions are awkward.

¢ = 0.01 dollars

Money & receipts

Prices, tax, and tips live in two decimal places. A recipe or a quote written in eighths has to become a decimal before it touches a calculator or a till.

mm · in

Measurement

Tape measures and drill bits use sixteenths and thirty-seconds; CAD and machining want the decimal inch. Converting the fraction is step one of every cut.

% grade

Test scores & odds

A score of 17/20 or a probability of 3/8 is easiest to read once it is a decimal — and a decimal is one short step from a percentage.

Worth knowing

Rules that make it quick

A few facts let you predict the answer before you finish dividing.

denominator = 2ᵃ · 5ᵇ

When it terminates

In lowest terms, a fraction ends exactly when the denominator is built only from 2s and 5s. Any other prime factor forces it to repeat.

period < denominator

How long the block is

The repeating block is never longer than one less than the denominator, because there are only that many possible non-zero remainders.

reduce first

Reduce before you divide

Cancel common factors first — 6/8 is 3/4, a far easier division. Reducing never changes the decimal, only the work.

× 100 = %

Decimal to percent

A decimal is a percentage waiting to happen: shift the point two places right. So a fraction is one division and one shift away from a percent.

÷ 10ⁿ

Powers of ten are free

Tenths, hundredths, and thousandths convert by sight — the denominator already matches the place value, no division needed.

0.999… = 1

A repeating edge case

An endlessly repeating 9 equals the next whole number. It is the one place where two decimals name the same value.

Common mistakes

Where conversions go wrong

The errors that turn a right fraction into a wrong decimal.

b ÷ a ✗

Dividing the wrong way

The numerator goes inside the division — a ÷ b, not the reverse. Flipping it gives the reciprocal, a completely different number.

0.3 ≠ 0.3̄

Rounding a repeat too soon

Cutting off 1/3 at 0.3 loses value. Keep the bar (or enough places) when the exact figure matters; round only at the very end.

2 3/4 ≠ 2.34

Mashing mixed numbers together

The whole number and the fraction are added, not concatenated. Convert 3/4 to 0.75 first, then add the 2 to get 2.75.

÷ 0 ✗

A zero denominator

A denominator of zero has no decimal at all — division by zero is undefined, not zero or infinity. Check the bottom number first.

FAQ

Common questions

Divide the numerator by the denominator. The fraction bar is a division sign, so 3/4 means 3 ÷ 4 = 0.75. If the division doesn’t come out evenly, keep bringing down zeros until the remainder reaches zero or a remainder repeats.

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