What is 0.6131313... as a Fraction?

0.613 equals 607990 as a fraction.

How do you turn 0.613 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.613 repeating into a fraction, begin writing this simple equation:

n = 0.613 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (13) and 1 digit in the non-repeating part (6). Multiply both sides by 10³ = 1000.

1000 × n = 613.13 (equation 2)

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

1000 × n = 613.13
  10 × n = 0.613
 990 × n = 607

n = 607990 (answer)

0.613 = 607990 as the lowest possible fraction.

The repeating decimal 0.613 (vinculum notation) has a repeated block length of 2. It is also represented as 0.6131313... (ellipsis notation) which equals approximately 0.61313131313 (decimal approximation)(*).

The recurring decimal 0.613 can be written as a ratio of two integers having 607 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.