What is 13.33076307630763076... as a Fraction?

13.33076 equals 133294399990 as a fraction.

How do you turn 13.33076 repeating into a fraction?

Detailed Answer:

Step 1: To convert 13.33076 repeating into a fraction, begin writing this simple equation:

n = 13.33076 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (3076) and 1 digit in the non-repeating part (3). Multiply both sides by 10⁵ = 100000.

100000 × n = 1333076.3076 (equation 2)

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

100000 × n = 1333076.3076
    10 × n = 13.33076
 99990 × n = 1332943

n = 133294399990 (answer)

13.33076 = 133294399990 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 133294399990 is also equal to 133307399990 when expressed as a mixed number.

The repeating decimal 13.33076 (vinculum notation) has a repeated block length of 4. It is also represented as 13.3307630763076... (ellipsis notation) which equals approximately 13.330763076307630763076 (decimal approximation)(*).

The recurring decimal 13.33076 can be written as a ratio of two integers having 1332943 as the numerator and 99990 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.