What is 0.13076076076... as a Fraction?

0.13076 equals 1306399900 as a fraction.

How do you turn 0.13076 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.13076 repeating into a fraction, begin writing this simple equation:

n = 0.13076 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (076) and 2 digits in the non-repeating part (13). Multiply both sides by 10⁵ = 100000.

100000 × n = 13076.076 (equation 2)

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

100000 × n = 13076.076
   100 × n = 0.13076
 99900 × n = 13063

n = 1306399900 (answer)

0.13076 = 1306399900 as the lowest possible fraction.

The repeating decimal 0.13076 (vinculum notation) has a repeated block length of 3. It is also represented as 0.13076076076... (ellipsis notation) which equals approximately 0.13076076076076076 (decimal approximation)(*).

The recurring decimal 0.13076 can be written as a ratio of two integers having 13063 as the numerator and 99900 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.