What is 0.72857128571285712857128571... as a Fraction?

0.728571 equals 364282499995 as a fraction.

How do you turn 0.728571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.728571 repeating into a fraction, begin writing this simple equation:

n = 0.728571 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (28571) and 1 digit in the non-repeating part (7). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 728571.28571 (equation 2)

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

1000000 × n = 728571.28571
     10 × n = 0.728571
 999990 × n = 728564

728564999990 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 = 728564999990 = 728564 ÷ 2999990 ÷ 2 = 364282499995. So,

0.728571 = 364282499995 as the lowest possible fraction.

The repeating decimal 0.728571 (vinculum notation) has a repeated block length of 5. It is also represented as 0.7285712857128571... (ellipsis notation) which equals approximately 0.72857128571285712857128571 (decimal approximation)(*).

The recurring decimal 0.728571 can be written as a ratio of two integers having 364282 as the numerator and 499995 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.