What is 0.252857128571285712857128571... as a Fraction?

0.2528571 equals 12642734999950 as a fraction.

How do you turn 0.2528571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.2528571 repeating into a fraction, begin writing this simple equation:

n = 0.2528571 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (28571) and 2 digits in the non-repeating part (25). Multiply both sides by 10⁷ = 10000000.

10000000 × n = 2528571.28571 (equation 2)

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

10000000 × n = 2528571.28571
     100 × n = 0.2528571
 9999900 × n = 2528546

25285469999900 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 2 (the GCF - greatest common factor).

n = 25285469999900 = 2528546 ÷ 29999900 ÷ 2 = 12642734999950. So,

0.2528571 = 12642734999950 as the lowest possible fraction.

The repeating decimal 0.2528571 (vinculum notation) has a repeated block length of 5. It is also represented as 0.25285712857128571... (ellipsis notation) which equals approximately 0.252857128571285712857128571 (decimal approximation)(*).

The recurring decimal 0.2528571 can be written as a ratio of two integers having 1264273 as the numerator and 4999950 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.