What is 5 and 1/7 as a Decimal?

Fraction to Decimal Converter

What is 5 1/7 as a decimal?

Answer

Fraction 5 1/7 as a decimal is

5.142857

≈ 5.14 to hundredths

Repeating decimal: denominator 7 has the factor 7, not 2 or 5 · the bar marks the period 142857 — 6 digits repeat forever

Whole part 5 stays in front; divide the fraction part:

remainder	×10	= digit × 7 + new remainder	digit
1	10	1 × 7 + 3	1
3	30	4 × 7 + 2	4
2	20	2 × 7 + 6	2
6	60	8 × 7 + 4	8
4	40	5 × 7 + 5	5
5	50	7 × 7 + 1	7

Remainder 1 is back after the 6th division → the 6 digits 142857 repeat: 0.142857.

5 + 0.142857 = 5.142857

Fraction 5 1/7 as a decimal is 5.(142857)

To convert 5 1/7 to a decimal, divide the numerator by the denominator, 1 ÷ 7 = 0.(142857), then add the whole part: 5 + 0.(142857) = 5.(142857).

In lowest terms its denominator 7 has the prime factor 7, so the division never ends: a remainder comes back and the same digits repeat forever.

Multiply by 100: 5 1/7 ≈ 514.29%.