What is 72.666... as a Fraction?

72.6 equals 2183 as a fraction.

How do you turn 72.6 repeating into a fraction?

Detailed Answer:

Step 1: To convert 72.6 repeating into a fraction, begin writing this simple equation:

n = 72.6 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6), so multiply both sides by 10¹ = 10.

10 × n = 726.6 (equation 2)

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

10 × n = 726.6
 1 × n = 72.6
 9 × n = 654

6549 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 3 (the GCF - greatest common factor).

n = 6549 = 654 ÷ 39 ÷ 3 = 2183. So,

72.6 = 2183 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 2183 is also equal to 7223 when expressed as a mixed number.

The repeating decimal 72.6 (vinculum notation) has a repeated block length of 1. It is also represented as 72.666... (ellipsis notation) which equals approximately 72.66666 (decimal approximation)(*).

The recurring decimal 72.6 can be written as a ratio of two integers having 218 as the numerator and 3 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.