What is 5.11571571571... as a Fraction?

5.11571 equals 255534995 as a fraction.

How do you turn 5.11571 repeating into a fraction?

Detailed Answer:

Step 1: To convert 5.11571 repeating into a fraction, begin writing this simple equation:

n = 5.11571 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (571) and 2 digits in the non-repeating part (11). Multiply both sides by 10⁵ = 100000.

100000 × n = 511571.571 (equation 2)

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

100000 × n = 511571.571
   100 × n = 5.11571
 99900 × n = 511060

51106099900 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 20 (the GCF - greatest common factor).

n = 51106099900 = 511060 ÷ 2099900 ÷ 20 = 255534995. So,

5.11571 = 255534995 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 255534995 is also equal to 55784995 when expressed as a mixed number.

The repeating decimal 5.11571 (vinculum notation) has a repeated block length of 3. It is also represented as 5.11571571571... (ellipsis notation) which equals approximately 5.11571571571571571 (decimal approximation)(*).

The recurring decimal 5.11571 can be written as a ratio of two integers having 25553 as the numerator and 4995 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.