What is 1.383076307630763076... as a Fraction?

1.383076 equals 691469499950 as a fraction.

How do you turn 1.383076 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.383076 repeating into a fraction, begin writing this simple equation:

n = 1.383076 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (3076) and 2 digits in the non-repeating part (38). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 1383076.3076 (equation 2)

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

1000000 × n = 1383076.3076
    100 × n = 1.383076
 999900 × n = 1382938

1382938999900 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 2 (the GCF - greatest common factor).

n = 1382938999900 = 1382938 ÷ 2999900 ÷ 2 = 691469499950. So,

1.383076 = 691469499950 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 691469499950 is also equal to 1191519499950 when expressed as a mixed number.

The repeating decimal 1.383076 (vinculum notation) has a repeated block length of 4. It is also represented as 1.38307630763076... (ellipsis notation) which equals approximately 1.3830763076307630763076 (decimal approximation)(*).

The recurring decimal 1.383076 can be written as a ratio of two integers having 691469 as the numerator and 499950 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.