What is 15.5714714714... as a Fraction?

15.5714 equals 518533330 as a fraction.

How do you turn 15.5714 repeating into a fraction?

Detailed Answer:

Step 1: To convert 15.5714 repeating into a fraction, begin writing this simple equation:

n = 15.5714 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (714) and 1 digit in the non-repeating part (5). Multiply both sides by 10⁴ = 10000.

10000 × n = 155714.714 (equation 2)

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

10000 × n = 155714.714
   10 × n = 15.5714
 9990 × n = 155559

1555599990 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 = 1555599990 = 155559 ÷ 39990 ÷ 3 = 518533330. So,

15.5714 = 518533330 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 518533330 is also equal to 1519033330 when expressed as a mixed number.

The repeating decimal 15.5714 (vinculum notation) has a repeated block length of 3. It is also represented as 15.5714714714... (ellipsis notation) which equals approximately 15.5714714714714714 (decimal approximation)(*).

The recurring decimal 15.5714 can be written as a ratio of two integers having 51853 as the numerator and 3330 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.