What is 0.93846384638463846... as a Fraction?

0.93846 equals 3127933330 as a fraction.

How do you turn 0.93846 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.93846 repeating into a fraction, begin writing this simple equation:

n = 0.93846 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (3846) and 1 digit in the non-repeating part (9). Multiply both sides by 10⁵ = 100000.

100000 × n = 93846.3846 (equation 2)

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

100000 × n = 93846.3846
    10 × n = 0.93846
 99990 × n = 93837

9383799990 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 3 (the GCF - greatest common factor).

n = 9383799990 = 93837 ÷ 399990 ÷ 3 = 3127933330. So,

0.93846 = 3127933330 as the lowest possible fraction.

The repeating decimal 0.93846 (vinculum notation) has a repeated block length of 4. It is also represented as 0.9384638463846... (ellipsis notation) which equals approximately 0.938463846384638463846 (decimal approximation)(*).

The recurring decimal 0.93846 can be written as a ratio of two integers having 31279 as the numerator and 33330 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.