What is 10.81428142814281428... as a Fraction?

10.81428 equals 360443333 as a fraction.

How do you turn 10.81428 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.81428 repeating into a fraction, begin writing this simple equation:

n = 10.81428 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (1428) and 1 digit in the non-repeating part (8). Multiply both sides by 10⁵ = 100000.

100000 × n = 1081428.1428 (equation 2)

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

100000 × n = 1081428.1428
    10 × n = 10.81428
 99990 × n = 1081320

108132099990 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 30 (the GCF - greatest common factor).

n = 108132099990 = 1081320 ÷ 3099990 ÷ 30 = 360443333. So,

10.81428 = 360443333 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 360443333 is also equal to 1027143333 when expressed as a mixed number.

The repeating decimal 10.81428 (vinculum notation) has a repeated block length of 4. It is also represented as 10.8142814281428... (ellipsis notation) which equals approximately 10.814281428142814281428 (decimal approximation)(*).

The recurring decimal 10.81428 can be written as a ratio of two integers having 36044 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.