What is 18.58571857185718571... as a Fraction?

18.58571 equals 30973116665 as a fraction.

How do you turn 18.58571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 18.58571 repeating into a fraction, begin writing this simple equation:

n = 18.58571 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (8571) and 1 digit in the non-repeating part (5). Multiply both sides by 10⁵ = 100000.

100000 × n = 1858571.8571 (equation 2)

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

100000 × n = 1858571.8571
    10 × n = 18.58571
 99990 × n = 1858386

185838699990 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 6 (the GCF - greatest common factor).

n = 185838699990 = 1858386 ÷ 699990 ÷ 6 = 30973116665. So,

18.58571 = 30973116665 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 30973116665 is also equal to 18976116665 when expressed as a mixed number.

The repeating decimal 18.58571 (vinculum notation) has a repeated block length of 4. It is also represented as 18.5857185718571... (ellipsis notation) which equals approximately 18.585718571857185718571 (decimal approximation)(*).

The recurring decimal 18.58571 can be written as a ratio of two integers having 309731 as the numerator and 16665 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.