What is 8.88585... as a Fraction?

8.885 equals 8797990 as a fraction.

How do you turn 8.885 repeating into a fraction?

Detailed Answer:

Step 1: To convert 8.885 repeating into a fraction, begin writing this simple equation:

n = 8.885 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (85) and 1 digit in the non-repeating part (8). Multiply both sides by 10³ = 1000.

1000 × n = 8885.85 (equation 2)

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

1000 × n = 8885.85
  10 × n = 8.885
 990 × n = 8797

n = 8797990 (answer)

8.885 = 8797990 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 8797990 is also equal to 8877990 when expressed as a mixed number.

The repeating decimal 8.885 (vinculum notation) has a repeated block length of 2. It is also represented as 8.8858585... (ellipsis notation) which equals approximately 8.88585858585 (decimal approximation)(*).

The recurring decimal 8.885 can be written as a ratio of two integers having 8797 as the numerator and 990 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.