What is 71.30666... as a Fraction?

71.306 equals 534875 as a fraction.

How do you turn 71.306 repeating into a fraction?

Detailed Answer:

Step 1: To convert 71.306 repeating into a fraction, begin writing this simple equation:

n = 71.306 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 2 digits in the non-repeating part (30). Multiply both sides by 10³ = 1000.

1000 × n = 71306.6 (equation 2)

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

1000 × n = 71306.6
 100 × n = 71.306
 900 × n = 64176

64176900 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 12 (the GCF - greatest common factor).

n = 64176900 = 64176 ÷ 12900 ÷ 12 = 534875. So,

71.306 = 534875 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 534875 is also equal to 712375 when expressed as a mixed number.

The repeating decimal 71.306 (vinculum notation) has a repeated block length of 1. It is also represented as 71.30666... (ellipsis notation) which equals approximately 71.3066666 (decimal approximation)(*).

The recurring decimal 71.306 can be written as a ratio of two integers having 5348 as the numerator and 75 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.