What is 71.666... as a Fraction?

71.6 equals 2153 as a fraction.

How do you turn 71.6 repeating into a fraction?

Detailed Answer:

Step 1: To convert 71.6 repeating into a fraction, begin writing this simple equation:

n = 71.6 (equation 1)

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

10 × n = 716.6 (equation 2)

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

10 × n = 716.6
 1 × n = 71.6
 9 × n = 645

6459 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 = 6459 = 645 ÷ 39 ÷ 3 = 2153. So,

71.6 = 2153 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 2153 is also equal to 7123 when expressed as a mixed number.

The repeating decimal 71.6 (vinculum notation) has a repeated block length of 1. It is also represented as 71.666... (ellipsis notation) which equals approximately 71.66666 (decimal approximation)(*).

The recurring decimal 71.6 can be written as a ratio of two integers having 215 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.