What is 85.11999... as a Fraction?

85.119 equals 212825 as a fraction.

How do you turn 85.119 repeating into a fraction?

Detailed Answer:

Step 1: To convert 85.119 repeating into a fraction, begin writing this simple equation:

n = 85.119 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (9) and 2 digits in the non-repeating part (11). Multiply both sides by 10³ = 1000.

1000 × n = 85119.9 (equation 2)

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

1000 × n = 85119.9
 100 × n = 85.119
 900 × n = 76608

76608900 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 36 (the GCF - greatest common factor).

n = 76608900 = 76608 ÷ 36900 ÷ 36 = 212825. So,

85.119 = 212825 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 212825 is also equal to 85325 when expressed as a mixed number.

The repeating decimal 85.119 (vinculum notation) has a repeated block length of 1. It is also represented as 85.11999... (ellipsis notation) which equals approximately 85.1199999 (decimal approximation)(*).

The recurring decimal 85.119 can be written as a ratio of two integers having 2128 as the numerator and 25 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.