What is 20.6838383... as a Fraction?

20.683 equals 20477990 as a fraction.

How do you turn 20.683 repeating into a fraction?

Detailed Answer:

Step 1: To convert 20.683 repeating into a fraction, begin writing this simple equation:

n = 20.683 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (83) and 1 digit in the non-repeating part (6). Multiply both sides by 10³ = 1000.

1000 × n = 20683.83 (equation 2)

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

1000 × n = 20683.83
  10 × n = 20.683
 990 × n = 20477

n = 20477990 (answer)

20.683 = 20477990 as the lowest possible fraction.

As the numerator is greater than the denominator, we have an improper fraction, so we can also express it as a mixed number, thus 20477990 is also equal to 20677990 when expressed as a mixed number.

The repeating decimal 20.683 (vinculum notation) has a repeated block length of 2. It is also represented as 20.6838383... (ellipsis notation) which equals approximately 20.68383838383 (decimal approximation)(*).

The recurring decimal 20.683 can be written as a ratio of two integers having 20477 as the numerator and 990 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.