What is 84.0888... as a Fraction?

84.8 equals 378445 as a fraction.

How do you turn 84.8 repeating into a fraction?

Detailed Answer:

Step 1: To convert 84.8 repeating into a fraction, begin writing this simple equation:

n = 84.8 (equation 1)

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

10 × n = 848.8 (equation 2)

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

10 × n = 848.8
 1 × n = 84.8
 9 × n = 764

n = 378445 (answer)

84.8 = 378445 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 378445 is also equal to 84445 when expressed as a mixed number.

The repeating decimal 84.8 (vinculum notation) has a repeated block length of 1. It is also represented as 84.888... (ellipsis notation) which equals approximately 84.88888 (decimal approximation)(*).

The recurring decimal 84.8 can be written as a ratio of two integers having 3784 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.