What is 22.0838383... as a Fraction?

22.83 equals 21863990 as a fraction.

How do you turn 22.83 repeating into a fraction?

Detailed Answer:

Step 1: To convert 22.83 repeating into a fraction, begin writing this simple equation:

n = 22.83 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (83), so multiply both sides by 10² = 100.

100 × n = 2283.83 (equation 2)

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

100 × n = 2283.83
  1 × n = 22.83
 99 × n = 2261

n = 21863990 (answer)

22.83 = 21863990 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 21863990 is also equal to 2283990 when expressed as a mixed number.

The repeating decimal 22.83 (vinculum notation) has a repeated block length of 2. It is also represented as 22.838383... (ellipsis notation) which equals approximately 22.8383838383 (decimal approximation)(*).

The recurring decimal 22.83 can be written as a ratio of two integers having 21863 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.