Final answer:
The number that produces a rational number when added to 0.49 is 1/7, which is a fraction and thus a rational number. Adding 1/7 to 0.49, which is 49/100 in fraction form, results in another rational number.
Step-by-step explanation:
When we are asked Which number produces a rational number when added to 0.49?, we are essentially looking for a value that, when combined with 0.49, results in a number that can be expressed as the ratio of two integers. A rational number is any number that can be written as a fraction, where the numerator and the denominator are both integers, and the denominator is not zero.
The options provided are:
- π (Pi), which is known to be an irrational number.
- 1/7, which is a fraction and therefore a rational number.
- √3 (the square root of 3), which is an irrational number.
- 0.62030548..., which appears to be a non-repeating and non-terminating decimal, suggesting it's an irrational number.
So, when 1/7 is added to 0.49, we get a rational result. This is because 0.49 can be expressed as 49/100, which is already in a fraction form, and adding another fraction (1/7) to it will result in a fraction as well. Therefore, the correct answer to the question is b. 1/7.