What is 13.9571571571... as a Fraction?

13.9571 equals 697164995 as a fraction.

How do you turn 13.9571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.9571 repeating into a fraction, begin writing this simple equation:

n = 13.9571 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (571) and 1 digit in the non-repeating part (9). Multiply both sides by 10⁴ = 10000.

10000 × n = 139571.571 (equation 2)

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

10000 × n = 139571.571
   10 × n = 13.9571
 9990 × n = 139432

1394329990 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 = 1394329990 = 139432 ÷ 29990 ÷ 2 = 697164995. So,

13.9571 = 697164995 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 697164995 is also equal to 1347814995 when expressed as a mixed number.

The repeating decimal 13.9571 (vinculum notation) has a repeated block length of 3. It is also represented as 13.9571571571... (ellipsis notation) which equals approximately 13.9571571571571571 (decimal approximation)(*).

The recurring decimal 13.9571 can be written as a ratio of two integers having 69716 as the numerator and 4995 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.