1/7 as a Decimal
1/7 = 0.1̅4̅2̅8̅5̅7̅
1/7 as a decimal is 0.1̅4̅2̅8̅5̅7̅ — the digits 142857 repeat forever (≈ 0.142857).
Step by step
- Divide 1 by 7: 0 whole (so the answer starts 0.), remainder 1.
- Bring down a 0: 10 ÷ 7 = 1, remainder 3.
- Bring down a 0: 30 ÷ 7 = 4, remainder 2.
- Bring down a 0: 20 ÷ 7 = 2, remainder 6.
- Bring down a 0: 60 ÷ 7 = 8, remainder 4.
- Bring down a 0: 40 ÷ 7 = 5, remainder 5.
- Bring down a 0: 50 ÷ 7 = 7, remainder 1.
- Result: 1/7 = 0.1̅4̅2̅8̅5̅7̅ (repeating).
Why it repeats: after removing factors of 2 and 5, the denominator 7 still has the factor 7, so the division never ends and the remainders cycle. The repeating block “142857” has 6 digits; round it to the precision you need, for example 0.14 or 0.1429.
Details
- Decimal (rounded)
- 0.142857
- Percent
- 14.2857%
- Type
- Repeating (142857 repeats)
- Equivalent fractions
- 2/14, 3/21, 4/28
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 1/7 as a decimal?
1/7 = 0.1̅4̅2̅8̅5̅7̅, which rounds to 0.1429.
How do you convert 1/7 to a decimal?
Divide 1 by 7. 1 ÷ 7 = 0.142857….
What is 1/7 as a percent?
14.2857%.
Is 1/7 a terminating or repeating decimal?
Repeating — the block “142857” repeats forever.