What is 14.01616... as a Fraction?

14.16 equals 6938495 as a fraction.

How do you turn 14.16 repeating into a fraction?

Detailed Answer:

Step 1: To convert 14.16 repeating into a fraction, begin writing this simple equation:

n = 14.16 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (16), so multiply both sides by 10² = 100.

100 × n = 1416.16 (equation 2)

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

100 × n = 1416.16
  1 × n = 14.16
 99 × n = 1402

n = 6938495 (answer)

14.16 = 6938495 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 6938495 is also equal to 148495 when expressed as a mixed number.

The repeating decimal 14.16 (vinculum notation) has a repeated block length of 2. It is also represented as 14.161616... (ellipsis notation) which equals approximately 14.1616161616 (decimal approximation)(*).

The recurring decimal 14.16 can be written as a ratio of two integers having 6938 as the numerator and 495 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.