What is 13.2857285728572857... as a Fraction?

13.2857 equals 1328449999 as a fraction.

How do you turn 13.2857 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.2857 repeating into a fraction, begin writing this simple equation:

n = 13.2857 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (2857), so multiply both sides by 10⁴ = 10000.

10000 × n = 132857.2857 (equation 2)

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

10000 × n = 132857.2857
    1 × n = 13.2857
 9999 × n = 132844

n = 1328449999 (answer)

13.2857 = 1328449999 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 1328449999 is also equal to 1328579999 when expressed as a mixed number.

The repeating decimal 13.2857 (vinculum notation) has a repeated block length of 4. It is also represented as 13.285728572857... (ellipsis notation) which equals approximately 13.28572857285728572857 (decimal approximation)(*).

The recurring decimal 13.2857 can be written as a ratio of two integers having 132844 as the numerator and 9999 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.