What is 0.2857128571285712857128571... as a Fraction?

0.28571 equals 2857199999 as a fraction.

How do you turn 0.28571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.28571 repeating into a fraction, begin writing this simple equation:

n = 0.28571 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (28571), so multiply both sides by 10⁵ = 100000.

100000 × n = 28571.28571 (equation 2)

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

100000 × n = 28571.28571
     1 × n = 0.28571
 99999 × n = 28571

n = 2857199999 (answer)

0.28571 = 2857199999 as the lowest possible fraction.

The repeating decimal 0.28571 (vinculum notation) has a repeated block length of 5. It is also represented as 0.285712857128571... (ellipsis notation) which equals approximately 0.2857128571285712857128571 (decimal approximation)(*).

The recurring decimal 0.28571 can be written as a ratio of two integers having 28571 as the numerator and 99999 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.