What is 11.25857857857... as a Fraction?

11.25857 equals 28118324975 as a fraction.

How do you turn 11.25857 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.25857 repeating into a fraction, begin writing this simple equation:

n = 11.25857 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (857) and 2 digits in the non-repeating part (25). Multiply both sides by 10⁵ = 100000.

100000 × n = 1125857.857 (equation 2)

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

100000 × n = 1125857.857
   100 × n = 11.25857
 99900 × n = 1124732

112473299900 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 = 112473299900 = 1124732 ÷ 499900 ÷ 4 = 28118324975. So,

11.25857 = 28118324975 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 28118324975 is also equal to 11645824975 when expressed as a mixed number.

The repeating decimal 11.25857 (vinculum notation) has a repeated block length of 3. It is also represented as 11.25857857857... (ellipsis notation) which equals approximately 11.25857857857857857 (decimal approximation)(*).

The recurring decimal 11.25857 can be written as a ratio of two integers having 281183 as the numerator and 24975 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.