What is 11.113222... as a Fraction?

11.1132 equals 1000199000 as a fraction.

How do you turn 11.1132 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.1132 repeating into a fraction, begin writing this simple equation:

n = 11.1132 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 3 digits in the non-repeating part (113). Multiply both sides by 10⁴ = 10000.

10000 × n = 111132.2 (equation 2)

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

10000 × n = 111132.2
 1000 × n = 11.1132
 9000 × n = 100019

n = 1000199000 (answer)

11.1132 = 1000199000 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 1000199000 is also equal to 1110199000 when expressed as a mixed number.

The repeating decimal 11.1132 (vinculum notation) has a repeated block length of 1. It is also represented as 11.113222... (ellipsis notation) which equals approximately 11.11322222 (decimal approximation)(*).

The recurring decimal 11.1132 can be written as a ratio of two integers having 100019 as the numerator and 9000 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.