What is 1.23636... as a Fraction?

1.236 equals 6855 as a fraction.

How do you turn 1.236 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.236 repeating into a fraction, begin writing this simple equation:

n = 1.236 (equation 1)

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

1000 × n = 1236.36 (equation 2)

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

1000 × n = 1236.36
  10 × n = 1.236
 990 × n = 1224

1224990 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 18 (the GCF - greatest common factor).

n = 1224990 = 1224 ÷ 18990 ÷ 18 = 6855. So,

1.236 = 6855 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 6855 is also equal to 11355 when expressed as a mixed number.

The repeating decimal 1.236 (vinculum notation) has a repeated block length of 2. It is also represented as 1.2363636... (ellipsis notation) which equals approximately 1.23636363636 (decimal approximation)(*).

The recurring decimal 1.236 can be written as a ratio of two integers having 68 as the numerator and 55 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.