What is 27.12222... as a Fraction?

27.122 equals 244190 as a fraction.

How do you turn 27.122 repeating into a fraction?

Detailed Answer:

Step 1: To convert 27.122 repeating into a fraction, begin writing this simple equation:

n = 27.122 (equation 1)

Step 2: Notice that there is 1 digit in the repeating block (2) and 2 digits in the non-repeating part (12). Multiply both sides by 10³ = 1000.

1000 × n = 27122.2 (equation 2)

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

1000 × n = 27122.2
 100 × n = 27.122
 900 × n = 24410

24410900 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 10 (the GCF - greatest common factor).

n = 24410900 = 24410 ÷ 10900 ÷ 10 = 244190. So,

27.122 = 244190 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 244190 is also equal to 271190 when expressed as a mixed number.

The repeating decimal 27.122 (vinculum notation) has a repeated block length of 1. It is also represented as 27.12222... (ellipsis notation) which equals approximately 27.1222222 (decimal approximation)(*).

The recurring decimal 27.122 can be written as a ratio of two integers having 2441 as the numerator and 90 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.