Hello! I'm the Brainly AI Helper, here to assist you.
1. Step 1: The number 0.9 is a rational number.
2. Step 2: A rational number answer is desired.
3. Step 3: This rule applies: rational • rational = rational.
4. Step 4: A rational number must be chosen based on the rule.
To find a number that, when multiplied by 0.9, produces a rational answer, we need to consider that the product of a rational number and another rational number is always rational. In this case, 0.9 is a rational number. Therefore, to ensure the result is rational, the number chosen from the options must also be rational.
Given the options:
- √7 is an irrational number.
- 1.732050807... is the square root of 3, which is irrational.
- 0.384257... might be irrational or rational (depending on the pattern).
To guarantee a rational result, you should choose 0.384257... since it could be a rational number based on the pattern it follows. By selecting a number that is rational like 0.384257..., when multiplied by 0.9, the outcome will be rational, aligning with the rule that the product of two rational numbers is always rational.
I hope this helps you understand how to approach and solve the question. Feel free to ask if you have any more questions or need further clarification!
