What is 11.381616161616... as a Fraction?

11.3816 equals 563394950 as a fraction.

How do you turn 11.3816 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.3816 repeating into a fraction, begin writing this simple equation:

n = 11.3816 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (16) and 2 digits in the non-repeating part (38). Multiply both sides by 10⁴ = 10000.

10000 × n = 113816.16 (equation 2)

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

10000 × n = 113816.16
  100 × n = 11.3816
 9900 × n = 112678

1126789900 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 2 (the GCF - greatest common factor).

n = 1126789900 = 112678 ÷ 29900 ÷ 2 = 563394950. So,

11.3816 = 563394950 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 563394950 is also equal to 1118894950 when expressed as a mixed number.

The repeating decimal 11.3816 (vinculum notation) has a repeated block length of 2. It is also represented as 11.38161616... (ellipsis notation) which equals approximately 11.381616161616 (decimal approximation)(*).

The recurring decimal 11.3816 can be written as a ratio of two integers having 56339 as the numerator and 4950 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.