What is 13.8838383... as a Fraction?

13.883 equals 2749198 as a fraction.

How do you turn 13.883 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.883 repeating into a fraction, begin writing this simple equation:

n = 13.883 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (83) and 1 digit in the non-repeating part (8). Multiply both sides by 10³ = 1000.

1000 × n = 13883.83 (equation 2)

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

1000 × n = 13883.83
  10 × n = 13.883
 990 × n = 13745

13745990 could be the answer, but it still can be put in the simplest form, i.e., reduced.

To simplify this fraction, divide the numerator and denominator by 5 (the GCF - greatest common factor).

n = 13745990 = 13745 ÷ 5990 ÷ 5 = 2749198. So,

13.883 = 2749198 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 2749198 is also equal to 13175198 when expressed as a mixed number.

The repeating decimal 13.883 (vinculum notation) has a repeated block length of 2. It is also represented as 13.8838383... (ellipsis notation) which equals approximately 13.88383838383 (decimal approximation)(*).

The recurring decimal 13.883 can be written as a ratio of two integers having 2749 as the numerator and 198 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.