What is 11.106222... as a Fraction?

11.1062 equals 249892250 as a fraction.

How do you turn 11.1062 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.1062 repeating into a fraction, begin writing this simple equation:

n = 11.1062 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 3 digits in the non-repeating part (106). Multiply both sides by 10⁴ = 10000.

10000 × n = 111062.2 (equation 2)

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

10000 × n = 111062.2
 1000 × n = 11.1062
 9000 × n = 99956

999569000 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 4 (the GCF - greatest common factor).

n = 999569000 = 99956 ÷ 49000 ÷ 4 = 249892250. So,

11.1062 = 249892250 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 249892250 is also equal to 112392250 when expressed as a mixed number.

The repeating decimal 11.1062 (vinculum notation) has a repeated block length of 1. It is also represented as 11.106222... (ellipsis notation) which equals approximately 11.10622222 (decimal approximation)(*).

The recurring decimal 11.1062 can be written as a ratio of two integers having 24989 as the numerator and 2250 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.