Question
According to the Closure Property, which of these sums results in a rational number? (1 point)
• 0.643892553 . . . + 3/4
● π+ √4
• 0.6(not ending) + 9/10
• √36 + √221
• 0.643892553 . . . + 3/4
● π+ √4
• 0.6(not ending) + 9/10
• √36 + √221
Answers
Answered by
GPT-4o mini
To determine which of these sums results in a rational number, we need to evaluate each option:
1. **0.643892553... + 3/4**: The number 0.643892553... (which appears to be a non-repeating decimal) is not rational. The fraction 3/4 is rational. The sum of a rational and an irrational number is irrational. Therefore, this option does not result in a rational number.
2. **π + √4**: π is an irrational number, and √4 is equal to 2, which is rational. The sum of an irrational number (π) and a rational number (2) is irrational. Therefore, this option does not result in a rational number.
3. **0.6 (not ending) + 9/10**: The notation "0.6 (not ending)" suggests a repeating decimal, specifically 0.6666... which is equal to 2/3 (a rational number). The fraction 9/10 is also rational. The sum of two rational numbers is rational. Therefore, this option results in a rational number.
4. **√36 + √221**: √36 is equal to 6 (a rational number), while √221 is irrational. The sum of a rational number (6) and an irrational number (√221) is irrational. Therefore, this option does not result in a rational number.
Based on this analysis, the only option that results in a rational number is:
**0.6 (not ending) + 9/10**.
1. **0.643892553... + 3/4**: The number 0.643892553... (which appears to be a non-repeating decimal) is not rational. The fraction 3/4 is rational. The sum of a rational and an irrational number is irrational. Therefore, this option does not result in a rational number.
2. **π + √4**: π is an irrational number, and √4 is equal to 2, which is rational. The sum of an irrational number (π) and a rational number (2) is irrational. Therefore, this option does not result in a rational number.
3. **0.6 (not ending) + 9/10**: The notation "0.6 (not ending)" suggests a repeating decimal, specifically 0.6666... which is equal to 2/3 (a rational number). The fraction 9/10 is also rational. The sum of two rational numbers is rational. Therefore, this option results in a rational number.
4. **√36 + √221**: √36 is equal to 6 (a rational number), while √221 is irrational. The sum of a rational number (6) and an irrational number (√221) is irrational. Therefore, this option does not result in a rational number.
Based on this analysis, the only option that results in a rational number is:
**0.6 (not ending) + 9/10**.