What is 17.563636363... as a Fraction?

17.563 equals 96655 as a fraction.

How do you turn 17.563 repeating into a fraction?

Detailed Answer:

Step 1: To convert 17.563 repeating into a fraction, begin writing this simple equation:

n = 17.563 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (63) and 1 digit in the non-repeating part (5). Multiply both sides by 10³ = 1000.

1000 × n = 17563.63 (equation 2)

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

1000 × n = 17563.63
  10 × n = 17.563
 990 × n = 17388

17388990 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 18 (the GCF - greatest common factor).

n = 17388990 = 17388 ÷ 18990 ÷ 18 = 96655. So,

17.563 = 96655 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 96655 is also equal to 173155 when expressed as a mixed number.

The repeating decimal 17.563 (vinculum notation) has a repeated block length of 2. It is also represented as 17.5636363... (ellipsis notation) which equals approximately 17.56363636363 (decimal approximation)(*).

The recurring decimal 17.563 can be written as a ratio of two integers having 966 as the numerator and 55 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.