What is 1.108333... as a Fraction?

1.1083 equals 133120 as a fraction.

How do you turn 1.1083 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.1083 repeating into a fraction, begin writing this simple equation:

n = 1.1083 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 3 digits in the non-repeating part (108). Multiply both sides by 10⁴ = 10000.

10000 × n = 11083.3 (equation 2)

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

10000 × n = 11083.3
 1000 × n = 1.1083
 9000 × n = 9975

99759000 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 75 (the GCF - greatest common factor).

n = 99759000 = 9975 ÷ 759000 ÷ 75 = 133120. So,

1.1083 = 133120 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 133120 is also equal to 113120 when expressed as a mixed number.

The repeating decimal 1.1083 (vinculum notation) has a repeated block length of 1. It is also represented as 1.108333... (ellipsis notation) which equals approximately 1.10833333 (decimal approximation)(*).

The recurring decimal 1.1083 can be written as a ratio of two integers having 133 as the numerator and 120 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.