What is 18.4615461546154615... as a Fraction?

18.4615 equals 1845979999 as a fraction.

How do you turn 18.4615 repeating into a fraction?

Detailed Answer:

Step 1: To convert 18.4615 repeating into a fraction, begin writing this simple equation:

n = 18.4615 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (4615), so multiply both sides by 10⁴ = 10000.

10000 × n = 184615.4615 (equation 2)

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

10000 × n = 184615.4615
    1 × n = 18.4615
 9999 × n = 184597

n = 1845979999 (answer)

18.4615 = 1845979999 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 1845979999 is also equal to 1846159999 when expressed as a mixed number.

The repeating decimal 18.4615 (vinculum notation) has a repeated block length of 4. It is also represented as 18.461546154615... (ellipsis notation) which equals approximately 18.46154615461546154615 (decimal approximation)(*).

The recurring decimal 18.4615 can be written as a ratio of two integers having 184597 as the numerator and 9999 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.