According to the Closure Property, which of these sums results in a rational number?(1 point)
Responses
0.643892553…+34
0.643892553 dot dot dot plus Start Fraction 3 over 4 End Fraction
0.6¯¯¯¯+910
0 point Modifying above 6 with bar plus Start Fraction 9 over 10 End Fraction
π+4–√
pi plus Start Root 4 End Root
36−−√+221−−−√
36 plus Start Root 221 End Root
According to the Closure Property, in order for a sum to result in a rational number, both operands must be rational numbers, and the operation performed (addition, subtraction, multiplication, or division) must also result in a rational number.
Let's analyze each of the given sums to determine if they result in a rational number:
1. 0.643892553... + 34: The first operand, 0.643892553..., is a decimal, so it is not a rational number. However, 34 is a whole number, which is a rational number. Therefore, the sum of these two numbers does not meet the Closure Property.
2. 0.643892553 + (3/4): The first operand, 0.643892553, is a decimal and is not a rational number. The second operand, 3/4, is a fraction and is a rational number. Adding a rational number with a non-rational number does not meet the Closure Property.
3. 0.6¯¯¯¯ + (9/10): The first operand, 0.6¯¯¯¯, represents a repeating decimal, but it can be expressed as a fraction. Similarly, the second operand, 9/10, is a fraction and is a rational number. Adding two rational numbers meets the Closure Property, so this sum results in a rational number.
4. π + 4 – √: The first operand, π (pi), is an irrational number. The second operand, 4, is a whole number and is a rational number. Taking the square root (√) of a non-rational number also results in an irrational number. Therefore, the sum of these three numbers does not meet the Closure Property.
5. 36 – √ + 221 – √: The first operand, 36, is a whole number and is a rational number. Taking the square root (√) of a non-rational number results in an irrational number. Therefore, the sum of these two numbers does not meet the Closure Property.
Based on the analysis above, the sum that results in a rational number is:
0.6¯¯¯¯ + (9/10)