Final answer:
The correct answer to which number produces a rational number when added to 1/3 is Option A: 0.22, as it is the only option given that represents a rational number and thus will result in a rational number when added to 1/3.
Step-by-step explanation:
The student asks which number produces a rational number when added to 1/3. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. When adding a rational number to 1/3, we must also get a rational number as the result. Now let's evaluate the options given:
- Option A: 0.22 - This is a rational number because it can be written as 22/100. Adding 1/3 to 0.22 gives us a numerical value that can be expressed as a fraction, thus resulting in another rational number.
- Option B: π (Pi) - π is an irrational number. It cannot be precisely expressed as a fraction, thus adding π to 1/3 would not result in a rational number.
- Option C: √10 (Square root of 10) - Like π, the square root of 10 is irrational and adding it to 1/3 would not yield a rational number.
- Option D: 5.38516480... - This appears to be an infinite non-repeating decimal, which would suggest it is an irrational number. However, if this is meant to be a terminating decimal or has a recurring pattern, it would be rational. Without additional context or precision, it cannot be definitively classified from the information given.
Therefore, Option A: 0.22 is the correct answer since it is the only number provided that is guaranteed to be rational and, when added to 1/3, will produce another rational number.