Final answer:
To write the recurring decimal 0.1 recurring 2 recurring as a fraction, we can use a geometric series formula. The fraction form of the decimal is 1.1/9.
Step-by-step explanation:
To write the recurring decimal 0.1 recurring 2 recurring as a fraction, we can use a geometric series formula. Let's call the recurring decimal x. First, multiply x by 10 to get rid of the decimal point. This gives us 10x = 1.2232323... Next, subtract x from 10x to eliminate the recurring part. We get 10x - x = 1.2232323... - 0.1232..., which simplifies to 9x = 1.1. Finally, divide both sides by 9 to solve for x. We get x = 1.1/9. Therefore, the recurring decimal 0.1 recurring 2 recurring can be written as the fraction 1.1/9.