What is 7 and 4/7 as a Decimal?

Fraction to Decimal Converter

What is 7 4/7 as a decimal?

Answer

Fraction 7 4/7 as a decimal is

7.571428

≈ 7.57 to hundredths

Repeating decimal: denominator 7 has the factor 7, not 2 or 5 · the bar marks the period 571428 — 6 digits repeat forever

Whole part 7 stays in front; divide the fraction part:

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

Remainder 4 is back after the 6th division → the 6 digits 571428 repeat: 0.571428.

7 + 0.571428 = 7.571428

Fraction 7 4/7 as a decimal is 7.(571428)

To convert 7 4/7 to a decimal, divide the numerator by the denominator, 4 ÷ 7 = 0.(571428), then add the whole part: 7 + 0.(571428) = 7.(571428).

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: 7 4/7 ≈ 757.14%.