What is 12.227272... as a Fraction?

12.2272 equals 26922 as a fraction.

How do you turn 12.2272 repeating into a fraction?

Detailed Answer:

Step 1: To convert 12.2272 repeating into a fraction, begin writing this simple equation:

n = 12.2272 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (72) and 2 digits in the non-repeating part (22). Multiply both sides by 10⁴ = 10000.

10000 × n = 122272.72 (equation 2)

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

10000 × n = 122272.72
  100 × n = 12.2272
 9900 × n = 121050

1210509900 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 450 (the GCF - greatest common factor).

n = 1210509900 = 121050 ÷ 4509900 ÷ 450 = 26922. So,

12.2272 = 26922 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 26922 is also equal to 12522 when expressed as a mixed number.

The repeating decimal 12.2272 (vinculum notation) has a repeated block length of 2. It is also represented as 12.22727272... (ellipsis notation) which equals approximately 12.227272727272 (decimal approximation)(*).

The recurring decimal 12.2272 can be written as a ratio of two integers having 269 as the numerator and 22 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.