What is 0.42857128571285712857128571... as a Fraction?

0.428571 equals 428567999990 as a fraction.

How do you turn 0.428571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.428571 repeating into a fraction, begin writing this simple equation:

n = 0.428571 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (28571) and 1 digit in the non-repeating part (4). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 428571.28571 (equation 2)

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

1000000 × n = 428571.28571
     10 × n = 0.428571
 999990 × n = 428567

n = 428567999990 (answer)

0.428571 = 428567999990 as the lowest possible fraction.

The repeating decimal 0.428571 (vinculum notation) has a repeated block length of 5. It is also represented as 0.4285712857128571... (ellipsis notation) which equals approximately 0.42857128571285712857128571 (decimal approximation)(*).

The recurring decimal 0.428571 can be written as a ratio of two integers having 428567 as the numerator and 999990 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.