What is 0.1363636363636... as a Fraction?

0.136 equals 322 as a fraction.

How do you turn 0.136 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.136 repeating into a fraction, begin writing this simple equation:

n = 0.136 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (36) and 1 digit in the non-repeating part (1). Multiply both sides by 10³ = 1000.

1000 × n = 136.36 (equation 2)

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

1000 × n = 136.36
  10 × n = 0.136
 990 × n = 135

135990 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 45 (the GCF - greatest common factor).

n = 135990 = 135 ÷ 45990 ÷ 45 = 322. So,

0.136 = 322 as the lowest possible fraction.

The repeating decimal 0.136 (vinculum notation) has a repeated block length of 2. It is also represented as 0.1363636... (ellipsis notation) which equals approximately 0.13636363636 (decimal approximation)(*).

The recurring decimal 0.136 can be written as a ratio of two integers having 3 as the numerator and 22 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.