What is 0.234285742857428574285742857... as a Fraction?

0.2342857 equals 11714174999950 as a fraction.

How do you turn 0.2342857 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.2342857 repeating into a fraction, begin writing this simple equation:

n = 0.2342857 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (42857) and 2 digits in the non-repeating part (23). Multiply both sides by 10⁷ = 10000000.

10000000 × n = 2342857.42857 (equation 2)

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

10000000 × n = 2342857.42857
     100 × n = 0.2342857
 9999900 × n = 2342834

23428349999900 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 = 23428349999900 = 2342834 ÷ 29999900 ÷ 2 = 11714174999950. So,

0.2342857 = 11714174999950 as the lowest possible fraction.

The repeating decimal 0.2342857 (vinculum notation) has a repeated block length of 5. It is also represented as 0.23428574285742857... (ellipsis notation) which equals approximately 0.234285742857428574285742857 (decimal approximation)(*).

The recurring decimal 0.2342857 can be written as a ratio of two integers having 1171417 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.