What is 1.08333333... as a Fraction?

1.083 equals 1312 as a fraction.

How do you turn 1.083 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.083 repeating into a fraction, begin writing this simple equation:

n = 1.083 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (08). Multiply both sides by 10³ = 1000.

1000 × n = 1083.3 (equation 2)

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

1000 × n = 1083.3
 100 × n = 1.083
 900 × n = 975

975900 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 = 975900 = 975 ÷ 75900 ÷ 75 = 1312. So,

1.083 = 1312 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 1312 is also equal to 1112 when expressed as a mixed number.

The repeating decimal 1.083 (vinculum notation) has a repeated block length of 1. It is also represented as 1.08333... (ellipsis notation) which equals approximately 1.0833333 (decimal approximation)(*).

The recurring decimal 1.083 can be written as a ratio of two integers having 13 as the numerator and 12 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.