What is 0.118571857185718571... as a Fraction?

0.118571 equals 197616665 as a fraction.

How do you turn 0.118571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.118571 repeating into a fraction, begin writing this simple equation:

n = 0.118571 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (8571) and 2 digits in the non-repeating part (11). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 118571.8571 (equation 2)

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

1000000 × n = 118571.8571
    100 × n = 0.118571
 999900 × n = 118560

118560999900 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 60 (the GCF - greatest common factor).

n = 118560999900 = 118560 ÷ 60999900 ÷ 60 = 197616665. So,

0.118571 = 197616665 as the lowest possible fraction.

The repeating decimal 0.118571 (vinculum notation) has a repeated block length of 4. It is also represented as 0.11857185718571... (ellipsis notation) which equals approximately 0.1185718571857185718571 (decimal approximation)(*).

The recurring decimal 0.118571 can be written as a ratio of two integers having 1976 as the numerator and 16665 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.