What is 11.9076076076... as a Fraction?

11.9076 equals 1189579990 as a fraction.

How do you turn 11.9076 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.9076 repeating into a fraction, begin writing this simple equation:

n = 11.9076 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (076) and 1 digit in the non-repeating part (9). Multiply both sides by 10⁴ = 10000.

10000 × n = 119076.076 (equation 2)

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

10000 × n = 119076.076
   10 × n = 11.9076
 9990 × n = 118957

n = 1189579990 (answer)

11.9076 = 1189579990 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 1189579990 is also equal to 1190679990 when expressed as a mixed number.

The repeating decimal 11.9076 (vinculum notation) has a repeated block length of 3. It is also represented as 11.9076076076... (ellipsis notation) which equals approximately 11.9076076076076076 (decimal approximation)(*).

The recurring decimal 11.9076 can be written as a ratio of two integers having 118957 as the numerator and 9990 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.