Identify which condition is necessary for a number to be rational
A. It must not be an endless decimal
B. It must not be negative
C. it must be written as a fraction
D. It must be able to be expressed as an integer divided by a nonzero integer
C. it must be written as a fraction
D. It must be able to be expressed as an integer divided by a nonzero integer
Which of the following is irrational?
A. 3.63636363636363636363.....
B. -7 8/37
C. √3/4
D. 52.781654292
Estimate the value of 6x√2. Which of the following choices is the best estimate?
A. 7.1
B. 9.8
C. 6.4
D. 8.4
To estimate the value of 6√2, we need to approximate the value of √2. The square root of 2 is approximately 1.41. Multiplying 6 by 1.41 gives us an estimate of 8.46.
Based on the given choices, the best estimate is D. 8.4.
Which statement is true about the square root of 28?
A. It is between 6 and 7, probably closer to 6.
B. It is between 4 and 5, probably closer to 5.
C. It is between 5 and 6, probably closer to 5.
D. It is between 5 and 6, probably closer to 6.
To determine which statement is true about the square root of 28, we can estimate the value.
The square root of 28 is approximately 5.29.
Based on the given choices, the true statement is C. It is between 5 and 6, probably closer to 5.
Which statement is true about the integer fraction that equals the square root or 2?
A. It does not exist
B. It requires a computer to find it
C. It is equal to 1
D. It involves large numbers
The statement that is true about the integer fraction that equals the square root of 2 is:
A. It does not exist
The square root of 2 is an irrational number, which means it cannot be expressed as a fraction of two integers. Therefore, there is no integer fraction that equals the square root of 2.
The correct answer is C. A number is considered rational if it can be written as a fraction, where both the numerator and denominator are integers and the denominator is not zero.
To understand this concept, we need to know the definition of a rational number. A rational number is any number that can be expressed as a fraction of two integers, such as 2/3, -1/4, or 5/1. These numbers can be positive, negative, or zero.
Now, let's go through the other options and see why they are not necessary conditions for a number to be rational:
A. It must not be an endless decimal: This condition doesn't guarantee that a number is rational. For example, the number 0.333... (repeating decimal) is rational because it can be written as the fraction 1/3.
B. It must not be negative: Negative numbers can still be rational. For example, -2/3 is a rational number because it can be expressed as a fraction.
D. It must be able to be expressed as an integer divided by a nonzero integer: This option is incorrect because it is actually the definition of a rational number. Therefore, it is not a necessary condition but the definition itself.
Therefore, the only condition necessary for a number to be rational is that it can be written as a fraction (option C).