What is 0.3428571428571428571428571428571428571... as a Fraction?

0.3428571 equals 1235 as a fraction.

How do you turn 0.3428571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.3428571 repeating into a fraction, begin writing this simple equation:

n = 0.3428571 (equation 1)

Step 2: Notice that there are 6 digits in the repeating block (428571) and 1 digit in the non-repeating part (3). Multiply both sides by 10⁷ = 10000000.

10000000 × n = 3428571.428571 (equation 2)

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

10000000 × n = 3428571.428571
      10 × n = 0.3428571
 9999990 × n = 3428568

34285689999990 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 285714 (the GCF - greatest common factor).

n = 34285689999990 = 3428568 ÷ 2857149999990 ÷ 285714 = 1235. So,

0.3428571 = 1235 as the lowest possible fraction.

The repeating decimal 0.3428571 (vinculum notation) has a repeated block length of 6. It is also represented as 0.3428571428571428571... (ellipsis notation) which equals approximately 0.3428571428571428571428571428571 (decimal approximation)(*).

The recurring decimal 0.3428571 can be written as a ratio of two integers having 12 as the numerator and 35 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.