Identify which condition is necessary for a number to be rational.(1 point)
Responses
1. It must be written as a fraction.
2. It must not be negative.
3. It must be able to be expressed as an integer divided by a nonzero integer.
4. It must not be an endless decimal.
3. It must be able to be expressed as an integer divided by a nonzero integer.
Which of the following is irrational?
1. 3.6363636363636363...
2. −7837
3. 52.781654292
4. 3√4
1. 3.6363636363636363...
Estimate the value of 6×2–√. Which of the following choices is the best estimate?(1 point)
1. 9.8
2. 7.1
3. 6.4
4. 8.4
To estimate the value of 6×2–√, we can substitute an estimate for √2. The square root of 2 is approximately 1.414. Therefore, we can approximate 6×2–√ as 6×2–1.414.
Calculating this expression leads to approximately 6×0.586 = 3.516.
Among the given choices, the best estimate is 3.6, which is closest to 3.516.
Therefore, the correct answer is 3.6, which is not listed as one of the available answer choices.
Estimate the value of 6×2–√. Which of the following choices is the best estimate?
Apologies for the error in the previous response. Let's re-evaluate the expression: 6×2–√.
First, let's calculate the value of √2, which is approximately 1.414.
Now we substitute the value of √2 into the expression:
6×2–√ = 6×2–1.414
Simplifying further:
6×2–1.414 = 6×2 – 1.414 = 12 – 1.414 = 10.586.
Among the given choices, the best estimate for 10.586 is 10.6, as it is closest to the calculated value.
Therefore, the correct answer is 10.6.
Estimate the value of 6×2–√. Which of the following choices is the best estimate?
1. 9.8
2. 7.1
3. 6.4
4. 8.4
To estimate the value of 6×2–√, we need to approximate the value of √2. Using a calculator or estimation, we can find that √2 is approximately 1.414.
Now we can substitute this value into the expression:
6×2–√ ≈ 6×2 – 1.414
Simplifying further:
6×2 – 1.414 ≈ 12 – 1.414 = 10.586
Among the given choices, the best estimate for 10.586 is 10.6.
Therefore, the correct answer is 10.6, which is not listed as one of the available answer choices.
The condition necessary for a number to be rational is option 3: It must be able to be expressed as an integer divided by a nonzero integer.
To explain why this condition is necessary, we need to understand the definition of a rational number. A rational number is any number that can be written as a fraction, where the numerator and denominator are integers, and the denominator is not zero.
So, to check if a number is rational, we need to determine if it can be expressed as an integer divided by a nonzero integer. If it can be written in this form, then it satisfies the condition for rationality. For example, 3 can be written as 3/1, where 3 is an integer and 1 is a nonzero integer, so 3 is a rational number.
Therefore, the correct condition necessary for a number to be rational is option 3: It must be able to be expressed as an integer divided by a nonzero integer.