What is 13.18571857185718571... as a Fraction?

13.18571 equals 439483333 as a fraction.

How do you turn 13.18571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.18571 repeating into a fraction, begin writing this simple equation:

n = 13.18571 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (8571) and 1 digit in the non-repeating part (1). Multiply both sides by 10⁵ = 100000.

100000 × n = 1318571.8571 (equation 2)

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

100000 × n = 1318571.8571
    10 × n = 13.18571
 99990 × n = 1318440

131844099990 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 30 (the GCF - greatest common factor).

n = 131844099990 = 1318440 ÷ 3099990 ÷ 30 = 439483333. So,

13.18571 = 439483333 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 439483333 is also equal to 136193333 when expressed as a mixed number.

The repeating decimal 13.18571 (vinculum notation) has a repeated block length of 4. It is also represented as 13.1857185718571... (ellipsis notation) which equals approximately 13.185718571857185718571 (decimal approximation)(*).

The recurring decimal 13.18571 can be written as a ratio of two integers having 43948 as the numerator and 3333 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.