What is 15.13076076076... as a Fraction?

15.13076 equals 151156399900 as a fraction.

How do you turn 15.13076 repeating into a fraction?

Detailed Answer:

Step 1: To convert 15.13076 repeating into a fraction, begin writing this simple equation:

n = 15.13076 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (076) and 2 digits in the non-repeating part (13). Multiply both sides by 10⁵ = 100000.

100000 × n = 1513076.076 (equation 2)

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

100000 × n = 1513076.076
   100 × n = 15.13076
 99900 × n = 1511563

n = 151156399900 (answer)

15.13076 = 151156399900 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 151156399900 is also equal to 151306399900 when expressed as a mixed number.

The repeating decimal 15.13076 (vinculum notation) has a repeated block length of 3. It is also represented as 15.13076076076... (ellipsis notation) which equals approximately 15.13076076076076076 (decimal approximation)(*).

The recurring decimal 15.13076 can be written as a ratio of two integers having 1511563 as the numerator and 99900 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.