What is 0.122857285728572857... as a Fraction?

0.122857 equals 24569199980 as a fraction.

How do you turn 0.122857 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.122857 repeating into a fraction, begin writing this simple equation:

n = 0.122857 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (2857) and 2 digits in the non-repeating part (12). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 122857.2857 (equation 2)

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

1000000 × n = 122857.2857
    100 × n = 0.122857
 999900 × n = 122845

122845999900 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 5 (the GCF - greatest common factor).

n = 122845999900 = 122845 ÷ 5999900 ÷ 5 = 24569199980. So,

0.122857 = 24569199980 as the lowest possible fraction.

The repeating decimal 0.122857 (vinculum notation) has a repeated block length of 4. It is also represented as 0.12285728572857... (ellipsis notation) which equals approximately 0.1228572857285728572857 (decimal approximation)(*).

The recurring decimal 0.122857 can be written as a ratio of two integers having 24569 as the numerator and 199980 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.