What is 0.8828282... as a Fraction?

0.882 equals 437495 as a fraction.

How do you turn 0.882 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.882 repeating into a fraction, begin writing this simple equation:

n = 0.882 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (82) and 1 digit in the non-repeating part (8). Multiply both sides by 10³ = 1000.

1000 × n = 882.82 (equation 2)

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

1000 × n = 882.82
  10 × n = 0.882
 990 × n = 874

874990 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 2 (the GCF - greatest common factor).

n = 874990 = 874 ÷ 2990 ÷ 2 = 437495. So,

0.882 = 437495 as the lowest possible fraction.

The repeating decimal 0.882 (vinculum notation) has a repeated block length of 2. It is also represented as 0.8828282... (ellipsis notation) which equals approximately 0.88282828282 (decimal approximation)(*).

The recurring decimal 0.882 can be written as a ratio of two integers having 437 as the numerator and 495 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.