What is 2.02323... as a Fraction?

2.23 equals 2003990 as a fraction.

How do you turn 2.23 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.23 repeating into a fraction, begin writing this simple equation:

n = 2.23 (equation 1)

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

100 × n = 223.23 (equation 2)

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

100 × n = 223.23
  1 × n = 2.23
 99 × n = 221

n = 2003990 (answer)

2.23 = 2003990 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 2003990 is also equal to 223990 when expressed as a mixed number.

The repeating decimal 2.23 (vinculum notation) has a repeated block length of 2. It is also represented as 2.232323... (ellipsis notation) which equals approximately 2.2323232323 (decimal approximation)(*).

The recurring decimal 2.23 can be written as a ratio of two integers having 2003 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.