Final answer:
A number cannot simultaneously be the reciprocal of 9 multiplied by 2 (which is 2/9) and the product of 9 times 9 (which is 81). There appears to be a misunderstanding in the question, as the properties described are mutually exclusive.
Step-by-step explanation:
To find the number described in the question, we need to consider it in two parts and remember the basic rules of multiplication and reciprocals. The first part of the phrase 'I am the reciprocal of 9 multiplied by 2', requires us to calculate the reciprocal of 9, which is 1/9, and then multiply that by 2. The reciprocal of a number is simply dividing 1 by that number, making this step relatively easy to execute.
The second part 'and the product of 9 times 9' asks us to multiply 9 by itself, which yields 81. With both parts computed, we can now express the complete answer. The reciprocal of 9 multiplied by 2 is 2/9, and the product of 9 times 9 is 81. Our number is thus both 2/9 and 81 at the same time, which is impossible. It seems there might be a typo in the question, or potentially a misunderstanding, as a number cannot be both a fraction and a whole number simultaneously.
In normal circumstances, without conflicting information, to find a number accurately, follow these steps of calculation, considering the correct mathematical rules such as those regarding reciprocals, multiplication, and management of exponents as necessary.