Question

According to the Closure Property, which of these sums results in a rational
number? (1 point)
34
O 0.643892553... +
36 + 221
○ 0.6 +
9
10

Answer 1

To assess which of the given sums results in a rational number, we need to look at the sums provided.

1. **34**
2. **0.643892553... + 36 + 221**

- Here, we have \( 0.643892553...\), which is a repeating decimal. A repeating decimal is a rational number.
- When we add a set of rational numbers, the sum will also be rational. Therefore, \( 0.643892553... + 36 + 221\) is a rational number.

3. **0.6 + 9**

- The number \( 0.6\) is also a rational number (it can be expressed as \( \frac{6}{10} \) or \( \frac{3}{5} \)).
- Adding two rational numbers together (0.6 and 9) will yield a rational number. Thus, \( 0.6 + 9\) is a rational number.

Now, looking at these sums:

- \( 0.643892553... + 36 + 221\) is rational.
- \( 0.6 + 9\) is rational.

Since the Closure Property states that the sum of two rational numbers is also rational, both sums result in a rational number. Thus, both options lead to rational sums. However, both include different combinations leading to a sum.

Thus, we can conclude that both sums are rational as per the Closure Property.