What is 6 and 5/3 as a Decimal?

Fraction to Decimal Converter

What is 6 5/3 as a decimal?

Answer

Fraction 6 5/3 as a decimal is

7.6

≈ 7.67 to hundredths

Repeating decimal: denominator 3 has the factor 3, not 2 or 5 · the bar marks the period 6 — it repeats forever

5 = 1 × 3 + 2: whole part 6 + 1 = 7, then divide the remainder 2

remainder	×10	= digit × 3 + new remainder	digit
2	20	6 × 3 + 2	6

Remainder 2 is back after the 1st division → the digit 6 repeats forever: 0.6.

7 + 0.6 = 7.6

Fraction 6 5/3 as a decimal is 7.(6)

To convert 6 5/3 to a decimal, divide the numerator by the denominator, 5 ÷ 3 = 1.(6), then add the whole part: 6 + 1.(6) = 7.(6).

In lowest terms its denominator 3 has the prime factor 3, so the division never ends: a remainder comes back and the same digits repeat forever.

Multiply by 100: 6 5/3 ≈ 766.67%.