What is 71.36666... as a Fraction?

71.366 equals 214130 as a fraction.

How do you turn 71.366 repeating into a fraction?

Detailed Answer:

Step 1: To convert 71.366 repeating into a fraction, begin writing this simple equation:

n = 71.366 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (6) and 2 digits in the non-repeating part (36). Multiply both sides by 10³ = 1000.

1000 × n = 71366.6 (equation 2)

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

1000 × n = 71366.6
 100 × n = 71.366
 900 × n = 64230

64230900 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 30 (the GCF - greatest common factor).

n = 64230900 = 64230 ÷ 30900 ÷ 30 = 214130. So,

71.366 = 214130 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 214130 is also equal to 711130 when expressed as a mixed number.

The repeating decimal 71.366 (vinculum notation) has a repeated block length of 1. It is also represented as 71.36666... (ellipsis notation) which equals approximately 71.3666666 (decimal approximation)(*).

The recurring decimal 71.366 can be written as a ratio of two integers having 2141 as the numerator and 30 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.