What is 18.81818181... as a Fraction?

18.81 equals 20711 as a fraction.

How do you turn 18.81 repeating into a fraction?

Detailed Answer:

Step 1: To convert 18.81 repeating into a fraction, begin writing this simple equation:

n = 18.81 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (81), so multiply both sides by 10² = 100.

100 × n = 1881.81 (equation 2)

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

100 × n = 1881.81
  1 × n = 18.81
 99 × n = 1863

186399 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 = 186399 = 1863 ÷ 999 ÷ 9 = 20711. So,

18.81 = 20711 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 20711 is also equal to 18911 when expressed as a mixed number.

The repeating decimal 18.81 (vinculum notation) has a repeated block length of 2. It is also represented as 18.818181... (ellipsis notation) which equals approximately 18.8181818181 (decimal approximation)(*).

The recurring decimal 18.81 can be written as a ratio of two integers having 207 as the numerator and 11 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.