1/7 as a Decimal
The fraction 1/7 converted to a decimal, with a step-by-step solution.
How to Convert 1/7 to a Decimal (Long Division)
- 1
Set up the division of the numerator by the denominator.
1 ÷ 7
- 2
7 does not go into 1, so the whole-number part is 0. Write "0." and continue with a remainder of 1.
0 . …
- 3
Bring down a 0 to make 10. 7 goes into 10 1 time (1 × 7 = 7), remainder 3. (This is where the repeating block begins.)
10 ÷ 7 = 1, r 3
- 4
Bring down a 0 to make 30. 7 goes into 30 4 times (4 × 7 = 28), remainder 2.
30 ÷ 7 = 4, r 2
- 5
Bring down a 0 to make 20. 7 goes into 20 2 times (2 × 7 = 14), remainder 6.
20 ÷ 7 = 2, r 6
- 6
Bring down a 0 to make 60. 7 goes into 60 8 times (8 × 7 = 56), remainder 4.
60 ÷ 7 = 8, r 4
- 7
Bring down a 0 to make 40. 7 goes into 40 5 times (5 × 7 = 35), remainder 5.
40 ÷ 7 = 5, r 5
- 8
Bring down a 0 to make 50. 7 goes into 50 7 times (7 × 7 = 49), remainder 1. The remainder 1 has appeared before, so the digits from here on repeat forever.
50 ÷ 7 = 7, r 1
Is 1/7 a Terminating or Repeating Decimal?
1/7 is a repeating decimal. Written in full it is 0.(142857) — the digits 142857 repeat forever. The parentheses mark the repeating block.
1/7 Rounded to Each Place
| Rounded to | Value |
|---|---|
| Nearest tenth | 0.1 |
| Nearest hundredth | 0.14 |
| Nearest thousandth | 0.143 |
1/7 as a Mixed Number
1/7 is a proper fraction (the numerator is smaller than the denominator), so it is less than 1 and has no whole-number part — its value is just 0.142857.
Try Another Fraction
Step-by-Step Solution
- 1
Divide the numerator by the denominator.
1 ÷ 7 = 0.142857
- 2
Multiply by 100 to get the percentage.
0.142857 × 100 = 14.285714%
Frequently Asked Questions
What is 1/7 as a decimal?
1/7 as a decimal is 0.142857. You get it by dividing the numerator 1 by the denominator 7.
Is 1/7 a terminating or repeating decimal?
1/7 is a repeating decimal. Written out it is 0.(142857), where the digits 142857 repeat forever.
What is 1/7 rounded to the nearest thousandth?
Rounded to the nearest thousandth, 1/7 ≈ 0.143. To the nearest hundredth it is 0.14, and to the nearest tenth it is 0.1.
Is 1/7 a rational number?
Yes. 1/7 is a ratio of two integers (1 over 7), so it is a rational number — even though its decimal form repeats.