What is 10 and 2/3 as a Decimal?

Fraction to Decimal Converter

What is 10 2/3 as a decimal?

Answer

Fraction 10 2/3 as a decimal is

10.6

≈ 10.67 to hundredths

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

Whole part 10 stays in front; divide the fraction part:

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.

10 + 0.6 = 10.6

Fraction 10 2/3 as a decimal is 10.(6)

To convert 10 2/3 to a decimal, divide the numerator by the denominator, 2 ÷ 3 = 0.(6), then add the whole part: 10 + 0.(6) = 10.(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: 10 2/3 ≈ 1,066.67%.