What is 0.6818181818181... as a Fraction?

0.681 equals 1522 as a fraction.

How do you turn 0.681 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.681 repeating into a fraction, begin writing this simple equation:

n = 0.681 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (81) and 1 digit in the non-repeating part (6). Multiply both sides by 10³ = 1000.

1000 × n = 681.81 (equation 2)

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

1000 × n = 681.81
  10 × n = 0.681
 990 × n = 675

675990 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 45 (the GCF - greatest common factor).

n = 675990 = 675 ÷ 45990 ÷ 45 = 1522. So,

0.681 = 1522 as the lowest possible fraction.

The repeating decimal 0.681 (vinculum notation) has a repeated block length of 2. It is also represented as 0.6818181... (ellipsis notation) which equals approximately 0.68181818181 (decimal approximation)(*).

The recurring decimal 0.681 can be written as a ratio of two integers having 15 as the numerator and 22 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.