What is 85.23333... as a Fraction?

85.233 equals 255730 as a fraction.

How do you turn 85.233 repeating into a fraction?

Detailed Answer:

Step 1: To convert 85.233 repeating into a fraction, begin writing this simple equation:

n = 85.233 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 2 digits in the non-repeating part (23). Multiply both sides by 10³ = 1000.

1000 × n = 85233.3 (equation 2)

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

1000 × n = 85233.3
 100 × n = 85.233
 900 × n = 76710

76710900 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 30 (the GCF - greatest common factor).

n = 76710900 = 76710 ÷ 30900 ÷ 30 = 255730. So,

85.233 = 255730 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 255730 is also equal to 85730 when expressed as a mixed number.

The repeating decimal 85.233 (vinculum notation) has a repeated block length of 1. It is also represented as 85.23333... (ellipsis notation) which equals approximately 85.2333333 (decimal approximation)(*).

The recurring decimal 85.233 can be written as a ratio of two integers having 2557 as the numerator and 30 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.