What is 12.0307307307... as a Fraction?

12.307 equals 1201879990 as a fraction.

How do you turn 12.307 repeating into a fraction?

Detailed Answer:

Step 1: To convert 12.307 repeating into a fraction, begin writing this simple equation:

n = 12.307 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (307), so multiply both sides by 10³ = 1000.

1000 × n = 12307.307 (equation 2)

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

1000 × n = 12307.307
   1 × n = 12.307
 999 × n = 12295

n = 1201879990 (answer)

12.307 = 1201879990 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 1201879990 is also equal to 123079990 when expressed as a mixed number.

The repeating decimal 12.307 (vinculum notation) has a repeated block length of 3. It is also represented as 12.307307307... (ellipsis notation) which equals approximately 12.307307307307307 (decimal approximation)(*).

The recurring decimal 12.307 can be written as a ratio of two integers having 120187 as the numerator and 9990 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.