What is 85.0888... as a Fraction?

85.8 equals 382945 as a fraction.

How do you turn 85.8 repeating into a fraction?

Detailed Answer:

Step 1: To convert 85.8 repeating into a fraction, begin writing this simple equation:

n = 85.8 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (8), so multiply both sides by 10¹ = 10.

10 × n = 858.8 (equation 2)

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

10 × n = 858.8
 1 × n = 85.8
 9 × n = 773

n = 382945 (answer)

85.8 = 382945 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 382945 is also equal to 85445 when expressed as a mixed number.

The repeating decimal 85.8 (vinculum notation) has a repeated block length of 1. It is also represented as 85.888... (ellipsis notation) which equals approximately 85.88888 (decimal approximation)(*).

The recurring decimal 85.8 can be written as a ratio of two integers having 3829 as the numerator and 45 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.