What is 2.33636... as a Fraction?

2.336 equals 257110 as a fraction.

How do you turn 2.336 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.336 repeating into a fraction, begin writing this simple equation:

n = 2.336 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (36) and 1 digit in the non-repeating part (3). Multiply both sides by 10³ = 1000.

1000 × n = 2336.36 (equation 2)

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

1000 × n = 2336.36
  10 × n = 2.336
 990 × n = 2313

2313990 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 9 (the GCF - greatest common factor).

n = 2313990 = 2313 ÷ 9990 ÷ 9 = 257110. So,

2.336 = 257110 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 257110 is also equal to 237110 when expressed as a mixed number.

The repeating decimal 2.336 (vinculum notation) has a repeated block length of 2. It is also represented as 2.3363636... (ellipsis notation) which equals approximately 2.33636363636 (decimal approximation)(*).

The recurring decimal 2.336 can be written as a ratio of two integers having 257 as the numerator and 110 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.