What is 11.13076307630763076... as a Fraction?

11.13076 equals 22259319998 as a fraction.

How do you turn 11.13076 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.13076 repeating into a fraction, begin writing this simple equation:

n = 11.13076 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (3076) and 1 digit in the non-repeating part (1). Multiply both sides by 10⁵ = 100000.

100000 × n = 1113076.3076 (equation 2)

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

100000 × n = 1113076.3076
    10 × n = 11.13076
 99990 × n = 1112965

111296599990 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 5 (the GCF - greatest common factor).

n = 111296599990 = 1112965 ÷ 599990 ÷ 5 = 22259319998. So,

11.13076 = 22259319998 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 22259319998 is also equal to 11261519998 when expressed as a mixed number.

The repeating decimal 11.13076 (vinculum notation) has a repeated block length of 4. It is also represented as 11.1307630763076... (ellipsis notation) which equals approximately 11.130763076307630763076 (decimal approximation)(*).

The recurring decimal 11.13076 can be written as a ratio of two integers having 222593 as the numerator and 19998 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.