What is 11.116333... as a Fraction?

11.1163 equals 333493000 as a fraction.

How do you turn 11.1163 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.1163 repeating into a fraction, begin writing this simple equation:

n = 11.1163 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 3 digits in the non-repeating part (116). Multiply both sides by 10⁴ = 10000.

10000 × n = 111163.3 (equation 2)

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

10000 × n = 111163.3
 1000 × n = 11.1163
 9000 × n = 100047

1000479000 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 3 (the GCF - greatest common factor).

n = 1000479000 = 100047 ÷ 39000 ÷ 3 = 333493000. So,

11.1163 = 333493000 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 333493000 is also equal to 113493000 when expressed as a mixed number.

The repeating decimal 11.1163 (vinculum notation) has a repeated block length of 1. It is also represented as 11.116333... (ellipsis notation) which equals approximately 11.11633333 (decimal approximation)(*).

The recurring decimal 11.1163 can be written as a ratio of two integers having 33349 as the numerator and 3000 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.