To determine which number produces a rational number when added to 0.3, we will evaluate each option to see the result of their sum with 0.3 and discuss their properties.
1. Option A: [tex]\(\sqrt{7}\)[/tex]
- [tex]\(\sqrt{7}\)[/tex] is an irrational number.
- When you add an irrational number to a rational number (0.3), the result is always irrational.
- Therefore, [tex]\(0.3 + \sqrt{7}\)[/tex] is irrational.
2. Option B: [tex]\(\pi\)[/tex]
- [tex]\(\pi\)[/tex] (pi) is also an irrational number.
- Adding an irrational number to a rational number gives an irrational result.
- Thus, [tex]\(0.3 + \(\pi\)[/tex]\) is irrational.
3. Option C: [tex]\(0.5050050005 \ldots\)[/tex]
- This number appears to be an infinite non-repeating decimal, which classifies it as an irrational number.
- Adding an irrational number to a rational number results in an irrational number.
- So, [tex]\(0.3 + 0.5050050005 \ldots\)[/tex] is irrational.
4. Option D: [tex]\(\frac{2}{4}\)[/tex]
- [tex]\(\frac{2}{4}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex], which is 0.5.
- 0.5 is a rational number.
- Adding two rational numbers results in another rational number.
- Hence, [tex]\(0.3 + 0.5\)[/tex] equals 0.8, which is a rational number.
In conclusion, option D ([tex]\(\frac{2}{4}\)[/tex]) produces a rational number when added to 0.3. So the answer is:
D. [tex]\(\frac{2}{4}\)[/tex]
