What is 15.8714714714... as a Fraction?

15.8714 equals 264261665 as a fraction.

How do you turn 15.8714 repeating into a fraction?

Detailed Answer:

Step 1: To convert 15.8714 repeating into a fraction, begin writing this simple equation:

n = 15.8714 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (714) and 1 digit in the non-repeating part (8). Multiply both sides by 10⁴ = 10000.

10000 × n = 158714.714 (equation 2)

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

10000 × n = 158714.714
   10 × n = 15.8714
 9990 × n = 158556

1585569990 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 6 (the GCF - greatest common factor).

n = 1585569990 = 158556 ÷ 69990 ÷ 6 = 264261665. So,

15.8714 = 264261665 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 264261665 is also equal to 1514511665 when expressed as a mixed number.

The repeating decimal 15.8714 (vinculum notation) has a repeated block length of 3. It is also represented as 15.8714714714... (ellipsis notation) which equals approximately 15.8714714714714714 (decimal approximation)(*).

The recurring decimal 15.8714 can be written as a ratio of two integers having 26426 as the numerator and 1665 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.