What is 15.0090909090909... as a Fraction?

15.09 equals 1651110 as a fraction.

How do you turn 15.09 repeating into a fraction?

Detailed Answer:

Step 1: To convert 15.09 repeating into a fraction, begin writing this simple equation:

n = 15.09 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (09), so multiply both sides by 10² = 100.

100 × n = 1509.09 (equation 2)

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

100 × n = 1509.09
  1 × n = 15.09
 99 × n = 1494

149499 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 9 (the GCF - greatest common factor).

n = 149499 = 1494 ÷ 999 ÷ 9 = 1651110. So,

15.09 = 1651110 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 1651110 is also equal to 151110 when expressed as a mixed number.

The repeating decimal 15.09 (vinculum notation) has a repeated block length of 2. It is also represented as 15.090909... (ellipsis notation) which equals approximately 15.0909090909 (decimal approximation)(*).

The recurring decimal 15.09 can be written as a ratio of two integers having 1651 as the numerator and 110 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.