What is 0.308585... as a Fraction?

0.3085 equals 6111980 as a fraction.

How do you turn 0.3085 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.3085 repeating into a fraction, begin writing this simple equation:

n = 0.3085 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (85) and 2 digits in the non-repeating part (30). Multiply both sides by 10⁴ = 10000.

10000 × n = 3085.85 (equation 2)

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

10000 × n = 3085.85
  100 × n = 0.3085
 9900 × n = 3055

30559900 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 5 (the GCF - greatest common factor).

n = 30559900 = 3055 ÷ 59900 ÷ 5 = 6111980. So,

0.3085 = 6111980 as the lowest possible fraction.

The repeating decimal 0.3085 (vinculum notation) has a repeated block length of 2. It is also represented as 0.30858585... (ellipsis notation) which equals approximately 0.308585858585 (decimal approximation)(*).

The recurring decimal 0.3085 can be written as a ratio of two integers having 611 as the numerator and 1980 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.