What is 11.122888... as a Fraction?

11.1228 equals 500534500 as a fraction.

How do you turn 11.1228 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.1228 repeating into a fraction, begin writing this simple equation:

n = 11.1228 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8) and 3 digits in the non-repeating part (122). Multiply both sides by 10⁴ = 10000.

10000 × n = 111228.8 (equation 2)

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

10000 × n = 111228.8
 1000 × n = 11.1228
 9000 × n = 100106

1001069000 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 2 (the GCF - greatest common factor).

n = 1001069000 = 100106 ÷ 29000 ÷ 2 = 500534500. So,

11.1228 = 500534500 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 500534500 is also equal to 115534500 when expressed as a mixed number.

The repeating decimal 11.1228 (vinculum notation) has a repeated block length of 1. It is also represented as 11.122888... (ellipsis notation) which equals approximately 11.12288888 (decimal approximation)(*).

The recurring decimal 11.1228 can be written as a ratio of two integers having 50053 as the numerator and 4500 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.