What is 0.2323... as a Fraction?

0.23 equals 2399 as a fraction.

How do you turn 0.23 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.23 repeating into a fraction, begin writing this simple equation:

n = 0.23 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (23), so multiply both sides by 10² = 100.

100 × n = 23.23 (equation 2)

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

100 × n = 23.23
  1 × n = 0.23
 99 × n = 23

n = 2399 (answer)

0.23 = 2399 as the lowest possible fraction.

The repeating decimal 0.23 (vinculum notation) has a repeated block length of 2. It is also represented as 0.232323... (ellipsis notation) which equals approximately 0.2323232323 (decimal approximation)(*).

The recurring decimal 0.23 can be written as a ratio of two integers having 23 as the numerator and 99 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.