What is 13.93846384638463846... as a Fraction?

13.93846 equals 46456933330 as a fraction.

How do you turn 13.93846 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.93846 repeating into a fraction, begin writing this simple equation:

n = 13.93846 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (3846) and 1 digit in the non-repeating part (9). Multiply both sides by 10⁵ = 100000.

100000 × n = 1393846.3846 (equation 2)

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

100000 × n = 1393846.3846
    10 × n = 13.93846
 99990 × n = 1393707

139370799990 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 = 139370799990 = 1393707 ÷ 399990 ÷ 3 = 46456933330. So,

13.93846 = 46456933330 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 46456933330 is also equal to 133127933330 when expressed as a mixed number.

The repeating decimal 13.93846 (vinculum notation) has a repeated block length of 4. It is also represented as 13.9384638463846... (ellipsis notation) which equals approximately 13.938463846384638463846 (decimal approximation)(*).

The recurring decimal 13.93846 can be written as a ratio of two integers having 464569 as the numerator and 33330 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.