What is 11.1428142814281428... as a Fraction?

11.1428 equals 371393333 as a fraction.

How do you turn 11.1428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.1428 repeating into a fraction, begin writing this simple equation:

n = 11.1428 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (1428), so multiply both sides by 10⁴ = 10000.

10000 × n = 111428.1428 (equation 2)

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

10000 × n = 111428.1428
    1 × n = 11.1428
 9999 × n = 111417

1114179999 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 3 (the GCF - greatest common factor).

n = 1114179999 = 111417 ÷ 39999 ÷ 3 = 371393333. So,

11.1428 = 371393333 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 371393333 is also equal to 114763333 when expressed as a mixed number.

The repeating decimal 11.1428 (vinculum notation) has a repeated block length of 4. It is also represented as 11.142814281428... (ellipsis notation) which equals approximately 11.14281428142814281428 (decimal approximation)(*).

The recurring decimal 11.1428 can be written as a ratio of two integers having 37139 as the numerator and 3333 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.