What is 0.0285285285... as a Fraction?

0.285 equals 19666 as a fraction.

How do you turn 0.285 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.285 repeating into a fraction, begin writing this simple equation:

n = 0.285 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (285), so multiply both sides by 10³ = 1000.

1000 × n = 285.285 (equation 2)

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

1000 × n = 285.285
   1 × n = 0.285
 999 × n = 285

285999 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 3 (the GCF - greatest common factor).

n = 285999 = 285 ÷ 3999 ÷ 3 = 19666. So,

0.285 = 19666 as the lowest possible fraction.

The repeating decimal 0.285 (vinculum notation) has a repeated block length of 3. It is also represented as 0.285285285... (ellipsis notation) which equals approximately 0.285285285285285 (decimal approximation)(*).

The recurring decimal 0.285 can be written as a ratio of two integers having 19 as the numerator and 666 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.