What is 100/3 as a Decimal?

Fraction to Decimal Converter

What is 100/3 as a decimal?

Answer

Fraction 100/3 as a decimal is

33.3

≈ 33.33 to hundredths

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

100 = 33 × 3 + 1: whole part 33, then divide the remainder 1

remainder	×10	= digit × 3 + new remainder	digit
1	10	3 × 3 + 1	3

Remainder 1 is back after the 1st division → the digit 3 repeats forever: 0.3.

33 + 0.3 = 33.3

Fraction 100/3 as a decimal is 33.(3)

To convert 100/3 to a decimal, divide the numerator by the denominator: 100 ÷ 3 = 33.(3).

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: 100/3 ≈ 3,333.33%.