What is 18.6857857857... as a Fraction?

18.6857 equals 1866719990 as a fraction.

How do you turn 18.6857 repeating into a fraction?

Detailed Answer:

Step 1: To convert 18.6857 repeating into a fraction, begin writing this simple equation:

n = 18.6857 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (857) and 1 digit in the non-repeating part (6). Multiply both sides by 10⁴ = 10000.

10000 × n = 186857.857 (equation 2)

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

10000 × n = 186857.857
   10 × n = 18.6857
 9990 × n = 186671

n = 1866719990 (answer)

18.6857 = 1866719990 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 1866719990 is also equal to 1868519990 when expressed as a mixed number.

The repeating decimal 18.6857 (vinculum notation) has a repeated block length of 3. It is also represented as 18.6857857857... (ellipsis notation) which equals approximately 18.6857857857857857 (decimal approximation)(*).

The recurring decimal 18.6857 can be written as a ratio of two integers having 186671 as the numerator and 9990 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.