What is 11.125714571457145714... as a Fraction?

11.125714 equals 5562301499950 as a fraction.

How do you turn 11.125714 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.125714 repeating into a fraction, begin writing this simple equation:

n = 11.125714 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (5714) and 2 digits in the non-repeating part (12). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 11125714.5714 (equation 2)

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

1000000 × n = 11125714.5714
    100 × n = 11.125714
 999900 × n = 11124602

11124602999900 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 = 11124602999900 = 11124602 ÷ 2999900 ÷ 2 = 5562301499950. So,

11.125714 = 5562301499950 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 5562301499950 is also equal to 1162851499950 when expressed as a mixed number.

The repeating decimal 11.125714 (vinculum notation) has a repeated block length of 4. It is also represented as 11.12571457145714... (ellipsis notation) which equals approximately 11.1257145714571457145714 (decimal approximation)(*).

The recurring decimal 11.125714 can be written as a ratio of two integers having 5562301 as the numerator and 499950 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.