What is 7 and 8/11 as a Decimal?

Fraction to Decimal Converter

What is 7 8/11 as a decimal?

Answer

Fraction 7 8/11 as a decimal is

7.72

≈ 7.73 to hundredths

Repeating decimal: denominator 11 has the factor 11, not 2 or 5 · the bar marks the period 72 — 2 digits repeat forever

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

remainder	×10	= digit × 11 + new remainder	digit
8	80	7 × 11 + 3	7
3	30	2 × 11 + 8	2

Remainder 8 is back after the 2nd division → the 2 digits 72 repeat: 0.72.

7 + 0.72 = 7.72

Fraction 7 8/11 as a decimal is 7.(72)

To convert 7 8/11 to a decimal, divide the numerator by the denominator, 8 ÷ 11 = 0.(72), then add the whole part: 7 + 0.(72) = 7.(72).

In lowest terms its denominator 11 has the prime factor 11, so the division never ends: a remainder comes back and the same digits repeat forever.

Multiply by 100: 7 8/11 ≈ 772.73%.