What is 14.14384384384... as a Fraction?

14.14384 equals 470993330 as a fraction.

How do you turn 14.14384 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.14384 repeating into a fraction, begin writing this simple equation:

n = 14.14384 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (384) and 2 digits in the non-repeating part (14). Multiply both sides by 10⁵ = 100000.

100000 × n = 1414384.384 (equation 2)

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

100000 × n = 1414384.384
   100 × n = 14.14384
 99900 × n = 1412970

141297099900 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 30 (the GCF - greatest common factor).

n = 141297099900 = 1412970 ÷ 3099900 ÷ 30 = 470993330. So,

14.14384 = 470993330 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 470993330 is also equal to 144793330 when expressed as a mixed number.

The repeating decimal 14.14384 (vinculum notation) has a repeated block length of 3. It is also represented as 14.14384384384... (ellipsis notation) which equals approximately 14.14384384384384384 (decimal approximation)(*).

The recurring decimal 14.14384 can be written as a ratio of two integers having 47099 as the numerator and 3330 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.