What is 10.9383838... as a Fraction?

10.938 equals 10829990 as a fraction.

How do you turn 10.938 repeating into a fraction?

Detailed Answer:

Step 1: To convert 10.938 repeating into a fraction, begin writing this simple equation:

n = 10.938 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (38) and 1 digit in the non-repeating part (9). Multiply both sides by 10³ = 1000.

1000 × n = 10938.38 (equation 2)

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

1000 × n = 10938.38
  10 × n = 10.938
 990 × n = 10829

n = 10829990 (answer)

10.938 = 10829990 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 10829990 is also equal to 10929990 when expressed as a mixed number.

The repeating decimal 10.938 (vinculum notation) has a repeated block length of 2. It is also represented as 10.9383838... (ellipsis notation) which equals approximately 10.93838383838 (decimal approximation)(*).

The recurring decimal 10.938 can be written as a ratio of two integers having 10829 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.