What is 1.22323... as a Fraction?

1.223 equals 1211990 as a fraction.

How do you turn 1.223 repeating into a fraction?

Detailed Answer:

Step 1: To convert 1.223 repeating into a fraction, begin writing this simple equation:

n = 1.223 (equation 1)

Step 2: Notice that there are 2 digits in the repeating block (23) and 1 digit in the non-repeating part (2). Multiply both sides by 10³ = 1000.

1000 × n = 1223.23 (equation 2)

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

1000 × n = 1223.23
  10 × n = 1.223
 990 × n = 1211

n = 1211990 (answer)

1.223 = 1211990 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 1211990 is also equal to 1221990 when expressed as a mixed number.

The repeating decimal 1.223 (vinculum notation) has a repeated block length of 2. It is also represented as 1.2232323... (ellipsis notation) which equals approximately 1.22323232323 (decimal approximation)(*).

The recurring decimal 1.223 can be written as a ratio of two integers having 1211 as the numerator and 990 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.