What is 2.08571485714857148571485714... as a Fraction?

2.85714 equals 1042847499995 as a fraction.

How do you turn 2.85714 repeating into a fraction?

Detailed Answer:

Step 1: To convert 2.85714 repeating into a fraction, begin writing this simple equation:

n = 2.85714 (equation 1)

Step 2: Notice that there are 5 digits in the repeating block (85714), so multiply both sides by 10⁵ = 100000.

100000 × n = 285714.85714 (equation 2)

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

100000 × n = 285714.85714
     1 × n = 2.85714
 99999 × n = 285712

n = 1042847499995 (answer)

2.85714 = 1042847499995 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 1042847499995 is also equal to 242857499995 when expressed as a mixed number.

The repeating decimal 2.85714 (vinculum notation) has a repeated block length of 5. It is also represented as 2.857148571485714... (ellipsis notation) which equals approximately 2.8571485714857148571485714 (decimal approximation)(*).

The recurring decimal 2.85714 can be written as a ratio of two integers having 1042847 as the numerator and 499995 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.