What is 77.0888... as a Fraction?

77.8 equals 346945 as a fraction.

How do you turn 77.8 repeating into a fraction?

Detailed Answer:

Step 1: To convert 77.8 repeating into a fraction, begin writing this simple equation:

n = 77.8 (equation 1)

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

10 × n = 778.8 (equation 2)

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

10 × n = 778.8
 1 × n = 77.8
 9 × n = 701

n = 346945 (answer)

77.8 = 346945 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 346945 is also equal to 77445 when expressed as a mixed number.

The repeating decimal 77.8 (vinculum notation) has a repeated block length of 1. It is also represented as 77.888... (ellipsis notation) which equals approximately 77.88888 (decimal approximation)(*).

The recurring decimal 77.8 can be written as a ratio of two integers having 3469 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.