What is 14.03636... as a Fraction?

14.36 equals 77255 as a fraction.

How do you turn 14.36 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.36 repeating into a fraction, begin writing this simple equation:

n = 14.36 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (36), so multiply both sides by 10² = 100.

100 × n = 1436.36 (equation 2)

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

100 × n = 1436.36
  1 × n = 14.36
 99 × n = 1422

142299 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 = 142299 = 1422 ÷ 999 ÷ 9 = 77255. So,

14.36 = 77255 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 77255 is also equal to 14255 when expressed as a mixed number.

The repeating decimal 14.36 (vinculum notation) has a repeated block length of 2. It is also represented as 14.363636... (ellipsis notation) which equals approximately 14.3636363636 (decimal approximation)(*).

The recurring decimal 14.36 can be written as a ratio of two integers having 772 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.