What is 0.5857857857... as a Fraction?

0.5857 equals 29264995 as a fraction.

How do you turn 0.5857 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.5857 repeating into a fraction, begin writing this simple equation:

n = 0.5857 (equation 1)

Step 2: Notice that there are 3 digits in the repeating block (857) and 1 digit in the non-repeating part (5). Multiply both sides by 10⁴ = 10000.

10000 × n = 5857.857 (equation 2)

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

10000 × n = 5857.857
   10 × n = 0.5857
 9990 × n = 5852

58529990 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 2 (the GCF - greatest common factor).

n = 58529990 = 5852 ÷ 29990 ÷ 2 = 29264995. So,

0.5857 = 29264995 as the lowest possible fraction.

The repeating decimal 0.5857 (vinculum notation) has a repeated block length of 3. It is also represented as 0.5857857857... (ellipsis notation) which equals approximately 0.5857857857857857 (decimal approximation)(*).

The recurring decimal 0.5857 can be written as a ratio of two integers having 2926 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.