What is 27.1333... as a Fraction?

27.13 equals 40715 as a fraction.

How do you turn 27.13 repeating into a fraction?

Detailed Answer:

Step 1: To convert 27.13 repeating into a fraction, begin writing this simple equation:

n = 27.13 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (3) and 1 digit in the non-repeating part (1). Multiply both sides by 10² = 100.

100 × n = 2713.3 (equation 2)

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

100 × n = 2713.3
 10 × n = 27.13
 90 × n = 2442

244290 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 6 (the GCF - greatest common factor).

n = 244290 = 2442 ÷ 690 ÷ 6 = 40715. So,

27.13 = 40715 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 40715 is also equal to 27215 when expressed as a mixed number.

The repeating decimal 27.13 (vinculum notation) has a repeated block length of 1. It is also represented as 27.1333... (ellipsis notation) which equals approximately 27.133333 (decimal approximation)(*).

The recurring decimal 27.13 can be written as a ratio of two integers having 407 as the numerator and 15 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.