What is 1.15076923076923076923076923076923076923... as a Fraction?

1.15076923 equals 374325 as a fraction.

How do you turn 1.15076923 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.15076923 repeating into a fraction, begin writing this simple equation:

n = 1.15076923 (equation 1)

Step 2: Notice that there are 6 digits in the repeating block (076923) and 2 digits in the non-repeating part (15). Multiply both sides by 10⁸ = 100000000.

100000000 × n = 115076923.076923 (equation 2)

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

100000000 × n = 115076923.076923
      100 × n = 1.15076923
 99999900 × n = 115076808

11507680899999900 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 307692 (the GCF - greatest common factor).

n = 11507680899999900 = 115076808 ÷ 30769299999900 ÷ 307692 = 374325. So,

1.15076923 = 374325 as the lowest possible fraction.

As the numerator is greater than the denominator, we have an improper fraction, so we can also express it as a mixed number, thus 374325 is also equal to 149325 when expressed as a mixed number.

The repeating decimal 1.15076923 (vinculum notation) has a repeated block length of 6. It is also represented as 1.15076923076923076923... (ellipsis notation) which equals approximately 1.15076923076923076923076923076923 (decimal approximation)(*).

The recurring decimal 1.15076923 can be written as a ratio of two integers having 374 as the numerator and 325 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.