What is 13.04285428542854285... as a Fraction?

13.4285 equals 26083119998 as a fraction.

How do you turn 13.4285 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.4285 repeating into a fraction, begin writing this simple equation:

n = 13.4285 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (4285), so multiply both sides by 10⁴ = 10000.

10000 × n = 134285.4285 (equation 2)

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

10000 × n = 134285.4285
    1 × n = 13.4285
 9999 × n = 134272

n = 26083119998 (answer)

13.4285 = 26083119998 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 26083119998 is also equal to 1385719998 when expressed as a mixed number.

The repeating decimal 13.4285 (vinculum notation) has a repeated block length of 4. It is also represented as 13.428542854285... (ellipsis notation) which equals approximately 13.42854285428542854285 (decimal approximation)(*).

The recurring decimal 13.4285 can be written as a ratio of two integers having 260831 as the numerator and 19998 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.