What is 0.2571571571... as a Fraction?

0.2571 equals 25699990 as a fraction.

How do you turn 0.2571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.2571 repeating into a fraction, begin writing this simple equation:

n = 0.2571 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (571) and 1 digit in the non-repeating part (2). Multiply both sides by 10⁴ = 10000.

10000 × n = 2571.571 (equation 2)

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

10000 × n = 2571.571
   10 × n = 0.2571
 9990 × n = 2569

n = 25699990 (answer)

0.2571 = 25699990 as the lowest possible fraction.

The repeating decimal 0.2571 (vinculum notation) has a repeated block length of 3. It is also represented as 0.2571571571... (ellipsis notation) which equals approximately 0.2571571571571571 (decimal approximation)(*).

The recurring decimal 0.2571 can be written as a ratio of two integers having 2569 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.