What is 0.63846384638463846... as a Fraction?

0.63846 equals 21283333 as a fraction.

How do you turn 0.63846 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.63846 repeating into a fraction, begin writing this simple equation:

n = 0.63846 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (3846) and 1 digit in the non-repeating part (6). Multiply both sides by 10⁵ = 100000.

100000 × n = 63846.3846 (equation 2)

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

100000 × n = 63846.3846
    10 × n = 0.63846
 99990 × n = 63840

6384099990 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 30 (the GCF - greatest common factor).

n = 6384099990 = 63840 ÷ 3099990 ÷ 30 = 21283333. So,

0.63846 = 21283333 as the lowest possible fraction.

The repeating decimal 0.63846 (vinculum notation) has a repeated block length of 4. It is also represented as 0.6384638463846... (ellipsis notation) which equals approximately 0.638463846384638463846 (decimal approximation)(*).

The recurring decimal 0.63846 can be written as a ratio of two integers having 2128 as the numerator and 3333 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.