What is 66.777... as a Fraction?

66.7 equals 6019 as a fraction.

How do you turn 66.7 repeating into a fraction?

Detailed Answer:

Step 1: To convert 66.7 repeating into a fraction, begin writing this simple equation:

n = 66.7 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (7), so multiply both sides by 10¹ = 10.

10 × n = 667.7 (equation 2)

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

10 × n = 667.7
 1 × n = 66.7
 9 × n = 601

n = 6019 (answer)

66.7 = 6019 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 6019 is also equal to 6679 when expressed as a mixed number.

The repeating decimal 66.7 (vinculum notation) has a repeated block length of 1. It is also represented as 66.777... (ellipsis notation) which equals approximately 66.77777 (decimal approximation)(*).

The recurring decimal 66.7 can be written as a ratio of two integers having 601 as the numerator and 9 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.