1/3 as a Decimal
1/3 = 0.3̅
1/3 as a decimal is 0.3̅ — the digit 3 repeat forever (≈ 0.333333).
Step by step
- Divide 1 by 3: 0 whole (so the answer starts 0.), remainder 1.
- Bring down a 0: 10 ÷ 3 = 3, remainder 1.
- Bring down a 0: 10 ÷ 3 = 3, remainder 1.
- Bring down a 0: 10 ÷ 3 = 3, remainder 1.
- Bring down a 0: 10 ÷ 3 = 3, remainder 1.
- Bring down a 0: 10 ÷ 3 = 3, remainder 1.
- Bring down a 0: 10 ÷ 3 = 3, remainder 1.
- Result: 1/3 = 0.3̅ (repeating).
Why it repeats: after removing factors of 2 and 5, the denominator 3 still has the factor 3, so the division never ends and the remainders cycle. The repeating block “3” has 1 digit; round it to the precision you need, for example 0.33 or 0.3333.
Details
- Decimal (rounded)
- 0.333333
- Percent
- 33.3333%
- Type
- Repeating (3 repeats)
- Equivalent fractions
- 2/6, 3/9, 4/12
How it works
A fraction means division: the numerator (top) divided by the denominator (bottom). Use long division, adding zeros after the decimal point until the remainder is zero or a remainder repeats. If the simplified denominator has only 2 and 5 as prime factors, the decimal terminates; otherwise it repeats forever, and the repeating digits are marked with a bar.
Nearby values
Related conversions
Frequently asked questions
What is 1/3 as a decimal?
1/3 = 0.3̅, which rounds to 0.3333.
How do you convert 1/3 to a decimal?
Divide 1 by 3. 1 ÷ 3 = 0.333333….
What is 1/3 as a percent?
33.3333%.
Is 1/3 a terminating or repeating decimal?
Repeating — the block “3” repeats forever.