What is 11.51414... as a Fraction?

11.514 equals 11399990 as a fraction.

How do you turn 11.514 repeating into a fraction?

Detailed Answer:

Step 1: To convert 11.514 repeating into a fraction, begin writing this simple equation:

n = 11.514 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (14) and 1 digit in the non-repeating part (5). Multiply both sides by 10³ = 1000.

1000 × n = 11514.14 (equation 2)

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

1000 × n = 11514.14
  10 × n = 11.514
 990 × n = 11399

n = 11399990 (answer)

11.514 = 11399990 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 11399990 is also equal to 11509990 when expressed as a mixed number.

The repeating decimal 11.514 (vinculum notation) has a repeated block length of 2. It is also represented as 11.5141414... (ellipsis notation) which equals approximately 11.51414141414 (decimal approximation)(*).

The recurring decimal 11.514 can be written as a ratio of two integers having 11399 as the numerator and 990 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.