What is 10.08383838383... as a Fraction?

10.83 equals 9983990 as a fraction.

How do you turn 10.83 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.83 repeating into a fraction, begin writing this simple equation:

n = 10.83 (equation 1)

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

100 × n = 1083.83 (equation 2)

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

100 × n = 1083.83
  1 × n = 10.83
 99 × n = 1073

n = 9983990 (answer)

10.83 = 9983990 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 9983990 is also equal to 1083990 when expressed as a mixed number.

The repeating decimal 10.83 (vinculum notation) has a repeated block length of 2. It is also represented as 10.838383... (ellipsis notation) which equals approximately 10.8383838383 (decimal approximation)(*).

The recurring decimal 10.83 can be written as a ratio of two integers having 9983 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.