What is 16.84615461546154615... as a Fraction?

16.84615 equals 168444799990 as a fraction.

How do you turn 16.84615 repeating into a fraction?

Detailed Answer:

Step 1: To convert 16.84615 repeating into a fraction, begin writing this simple equation:

n = 16.84615 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (4615) and 1 digit in the non-repeating part (8). Multiply both sides by 10⁵ = 100000.

100000 × n = 1684615.4615 (equation 2)

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

100000 × n = 1684615.4615
    10 × n = 16.84615
 99990 × n = 1684447

n = 168444799990 (answer)

16.84615 = 168444799990 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 168444799990 is also equal to 168460799990 when expressed as a mixed number.

The repeating decimal 16.84615 (vinculum notation) has a repeated block length of 4. It is also represented as 16.8461546154615... (ellipsis notation) which equals approximately 16.846154615461546154615 (decimal approximation)(*).

The recurring decimal 16.84615 can be written as a ratio of two integers having 1684447 as the numerator and 99990 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.