What is 15.104285742857428574285742857... as a Fraction?

15.1042857 equals 1510413479999900 as a fraction.

How do you turn 15.1042857 repeating into a fraction?

Detailed Answer:

Step 1: To convert 15.1042857 repeating into a fraction, begin writing this simple equation:

n = 15.1042857 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (42857) and 2 digits in the non-repeating part (10). Multiply both sides by 10⁷ = 10000000.

10000000 × n = 151042857.42857 (equation 2)

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

10000000 × n = 151042857.42857
     100 × n = 15.1042857
 9999900 × n = 151041347

n = 1510413479999900 (answer)

15.1042857 = 1510413479999900 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 1510413479999900 is also equal to 1510428479999900 when expressed as a mixed number.

The repeating decimal 15.1042857 (vinculum notation) has a repeated block length of 5. It is also represented as 15.10428574285742857... (ellipsis notation) which equals approximately 15.104285742857428574285742857 (decimal approximation)(*).

The recurring decimal 15.1042857 can be written as a ratio of two integers having 151041347 as the numerator and 9999900 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.