What is 0.076923076923076923076923076923076923... as a Fraction?

0.076923 equals 113 as a fraction.

How do you turn 0.076923 repeating into a fraction?

Detailed Answer:

Step 1: To convert 0.076923 repeating into a fraction, begin writing this simple equation:

n = 0.076923 (equation 1)

Step 2: Notice that there are 6 digits in the repeating block (076923), so multiply both sides by 10⁶ = 1000000.

1000000 × n = 76923.076923 (equation 2)

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

1000000 × n = 76923.076923
      1 × n = 0.076923
 999999 × n = 76923

76923999999 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 76923 (the GCF - greatest common factor).

n = 76923999999 = 76923 ÷ 76923999999 ÷ 76923 = 113. So,

0.076923 = 113 as the lowest possible fraction.

The repeating decimal 0.076923 (vinculum notation) has a repeated block length of 6. It is also represented as 0.076923076923076923... (ellipsis notation) which equals approximately 0.076923076923076923076923076923 (decimal approximation)(*).

The recurring decimal 0.076923 can be written as a ratio of two integers having 1 as the numerator and 13 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.