What is 13.0461461461... as a Fraction?

13.461 equals 1303319990 as a fraction.

How do you turn 13.461 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.461 repeating into a fraction, begin writing this simple equation:

n = 13.461 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (461), so multiply both sides by 10³ = 1000.

1000 × n = 13461.461 (equation 2)

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

1000 × n = 13461.461
   1 × n = 13.461
 999 × n = 13448

n = 1303319990 (answer)

13.461 = 1303319990 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 1303319990 is also equal to 134619990 when expressed as a mixed number.

The repeating decimal 13.461 (vinculum notation) has a repeated block length of 3. It is also represented as 13.461461461... (ellipsis notation) which equals approximately 13.461461461461461 (decimal approximation)(*).

The recurring decimal 13.461 can be written as a ratio of two integers having 130331 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.