What is 11.02323... as a Fraction?

11.23 equals 10913990 as a fraction.

How do you turn 11.23 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.23 repeating into a fraction, begin writing this simple equation:

n = 11.23 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (23), so multiply both sides by 10² = 100.

100 × n = 1123.23 (equation 2)

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

100 × n = 1123.23
  1 × n = 11.23
 99 × n = 1112

n = 10913990 (answer)

11.23 = 10913990 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 10913990 is also equal to 1123990 when expressed as a mixed number.

The repeating decimal 11.23 (vinculum notation) has a repeated block length of 2. It is also represented as 11.232323... (ellipsis notation) which equals approximately 11.2323232323 (decimal approximation)(*).

The recurring decimal 11.23 can be written as a ratio of two integers having 10913 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.