What is 1.163076307630763076... as a Fraction?

1.163076 equals 5814849995 as a fraction.

How do you turn 1.163076 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.163076 repeating into a fraction, begin writing this simple equation:

n = 1.163076 (equation 1)

Step 2: Notice that there are 4 digits in the repeating block (3076) and 2 digits in the non-repeating part (16). Multiply both sides by 10⁶ = 1000000.

1000000 × n = 1163076.3076 (equation 2)

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

1000000 × n = 1163076.3076
    100 × n = 1.163076
 999900 × n = 1162960

1162960999900 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 20 (the GCF - greatest common factor).

n = 1162960999900 = 1162960 ÷ 20999900 ÷ 20 = 5814849995. So,

1.163076 = 5814849995 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 5814849995 is also equal to 1815349995 when expressed as a mixed number.

The repeating decimal 1.163076 (vinculum notation) has a repeated block length of 4. It is also represented as 1.16307630763076... (ellipsis notation) which equals approximately 1.1630763076307630763076 (decimal approximation)(*).

The recurring decimal 1.163076 can be written as a ratio of two integers having 58148 as the numerator and 49995 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.