What is 3 and 8/3 as a Decimal?

Fraction to Decimal Converter

What is 3 8/3 as a decimal?

Answer

Fraction 3 8/3 as a decimal is

5.6

≈ 5.67 to hundredths

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

8 = 2 × 3 + 2: whole part 3 + 2 = 5, 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.

5 + 0.6 = 5.6

Fraction 3 8/3 as a decimal is 5.(6)

To convert 3 8/3 to a decimal, divide the numerator by the denominator, 8 ÷ 3 = 2.(6), then add the whole part: 3 + 2.(6) = 5.(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: 3 8/3 ≈ 566.67%.