What is 5 and 1/11 as a Decimal?

Fraction to Decimal Converter

What is 5 1/11 as a decimal?

Answer

Fraction 5 1/11 as a decimal is

5.09

≈ 5.09 to hundredths

Repeating decimal: denominator 11 has the factor 11, not 2 or 5 · the bar marks the period 09 — 2 digits repeat forever

Whole part 5 stays in front; divide the fraction part:

remainder	×10	= digit × 11 + new remainder	digit
1	10	0 × 11 + 10	0
10	100	9 × 11 + 1	9

Remainder 1 is back after the 2nd division → the 2 digits 09 repeat: 0.09.

5 + 0.09 = 5.09

Fraction 5 1/11 as a decimal is 5.(09)

To convert 5 1/11 to a decimal, divide the numerator by the denominator, 1 ÷ 11 = 0.(09), then add the whole part: 5 + 0.(09) = 5.(09).

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: 5 1/11 ≈ 509.09%.