What is 11.1081818181... as a Fraction?

11.1081 equals 122191100 as a fraction.

How do you turn 11.1081 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.1081 repeating into a fraction, begin writing this simple equation:

n = 11.1081 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (81) and 2 digits in the non-repeating part (10). Multiply both sides by 10⁴ = 10000.

10000 × n = 111081.81 (equation 2)

Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.

10000 × n = 111081.81
  100 × n = 11.1081
 9900 × n = 109971

1099719900 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 9 (the GCF - greatest common factor).

n = 1099719900 = 109971 ÷ 99900 ÷ 9 = 122191100. So,

11.1081 = 122191100 as the lowest possible fraction.

As the numerator is greater than the denominator, we have an improper fraction, so we can also express it as a mixed number, thus 122191100 is also equal to 111191100 when expressed as a mixed number.

The repeating decimal 11.1081 (vinculum notation) has a repeated block length of 2. It is also represented as 11.10818181... (ellipsis notation) which equals approximately 11.108181818181 (decimal approximation)(*).

The recurring decimal 11.1081 can be written as a ratio of two integers having 12219 as the numerator and 1100 as the denominator. So, it is a rational number (named after ratio). It can be shown that a number is rational if its decimal representation is repeating or terminating.

(*) At present, there is no single universally accepted notation or phrasing for repeating decimals.