What is 11.12307307307... as a Fraction?

11.12307 equals 22223919980 as a fraction.

How do you turn 11.12307 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.12307 repeating into a fraction, begin writing this simple equation:

n = 11.12307 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (307) and 2 digits in the non-repeating part (12). Multiply both sides by 10⁵ = 100000.

100000 × n = 1112307.307 (equation 2)

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

100000 × n = 1112307.307
   100 × n = 11.12307
 99900 × n = 1111195

111119599900 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 5 (the GCF - greatest common factor).

n = 111119599900 = 1111195 ÷ 599900 ÷ 5 = 22223919980. So,

11.12307 = 22223919980 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 22223919980 is also equal to 11245919980 when expressed as a mixed number.

The repeating decimal 11.12307 (vinculum notation) has a repeated block length of 3. It is also represented as 11.12307307307... (ellipsis notation) which equals approximately 11.12307307307307307 (decimal approximation)(*).

The recurring decimal 11.12307 can be written as a ratio of two integers having 222239 as the numerator and 19980 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.