What is 12.03838... as a Fraction?

12.38 equals 5959495 as a fraction.

How do you turn 12.38 repeating into a fraction?

Detailed Answer:

Step 1: To convert 12.38 repeating into a fraction, begin writing this simple equation:

n = 12.38 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (38), so multiply both sides by 10² = 100.

100 × n = 1238.38 (equation 2)

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

100 × n = 1238.38
  1 × n = 12.38
 99 × n = 1226

n = 5959495 (answer)

12.38 = 5959495 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 5959495 is also equal to 1219495 when expressed as a mixed number.

The repeating decimal 12.38 (vinculum notation) has a repeated block length of 2. It is also represented as 12.383838... (ellipsis notation) which equals approximately 12.3838383838 (decimal approximation)(*).

The recurring decimal 12.38 can be written as a ratio of two integers having 5959 as the numerator and 495 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.