What is 15.311515... as a Fraction?

15.3115 equals 12632825 as a fraction.

How do you turn 15.3115 repeating into a fraction?

Detailed Answer:

Step 1: To convert 15.3115 repeating into a fraction, begin writing this simple equation:

n = 15.3115 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (15) and 2 digits in the non-repeating part (31). Multiply both sides by 10⁴ = 10000.

10000 × n = 153115.15 (equation 2)

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

10000 × n = 153115.15
  100 × n = 15.3115
 9900 × n = 151584

1515849900 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 12 (the GCF - greatest common factor).

n = 1515849900 = 151584 ÷ 129900 ÷ 12 = 12632825. So,

15.3115 = 12632825 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 12632825 is also equal to 15257825 when expressed as a mixed number.

The repeating decimal 15.3115 (vinculum notation) has a repeated block length of 2. It is also represented as 15.31151515... (ellipsis notation) which equals approximately 15.311515151515 (decimal approximation)(*).

The recurring decimal 15.3115 can be written as a ratio of two integers having 12632 as the numerator and 825 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.