Identify which condition is necessary for a number to be rational.(1 point)
Responses
It must be able to be expressed as an integer divided by a nonzero integer.
It must be able to be expressed as an integer divided by a nonzero integer.
It must not be negative.
It must not be negative.
It must not be an endless decimal.
It must not be an endless decimal.
It must be written as a fraction.
It must not be an endless decimal.
Which of the following is irrational?(1 point)
Responses
3√4
Start Fraction Start Root 3 End Root over 4 End Fraction
52.781654292
52.781654292
3.6363636363636363...
3.6363636363636363...
−7837
negative 7 Start Fraction 8 over 37 End Fraction
3√4
Rational and Irrational Numbers Quick Check
3 of 53 of 5 Items
Question
Estimate the value of 6×2–√. Which of the following choices is the best estimate?(1 point)
Responses
7.1
7.1
9.8
9.8
8.4
8.4
6.4
The best estimate for 6×2–√ is 6.4.
Which statement is true about the square root of 28?(1 point)
Responses
It is between 6 and 7, probably closer to 6.
It is between 6 and 7, probably closer to 6.
It is between 5 and 6, probably closer to 6.
It is between 5 and 6, probably closer to 6.
It is between 5 and 6, probably closer to 5.
It is between 5 and 6, probably closer to 5.
It is between 4 and 5, probably closer to 5.
The statement "It is between 5 and 6, probably closer to 6" is true about the square root of 28.
Which statement is true about the integer fraction that equals the square root of 2?(1 point)
Responses
It is equal to 1.
It is equal to 1.
It involves large numbers.
It involves large numbers.
It requires a computer to find it.
It requires a computer to find it.
It does not exist.
It does not exist.
The statement "It does not exist" is true about the integer fraction that equals the square root of 2.
The correct answer is: "It must be able to be expressed as an integer divided by a nonzero integer."
To understand why this condition is necessary for a number to be rational, let's break it down:
A rational number is any number that can be written as a fraction, where the numerator and denominator are both integers. In other words, it can be expressed as a ratio of two integers.
The condition of being able to be expressed as an integer divided by a nonzero integer ensures that the result is a fraction, which is a key characteristic of rational numbers. If the denominator is zero, the fraction would be undefined.
For example, let's take the number 3. This number can be expressed as the fraction 3/1, where the numerator is an integer (3) and the denominator is a nonzero integer (1). Therefore, 3 is a rational number.
On the other hand, a number like π (pi) or √2 (square root of 2) cannot be expressed as a fraction of two integers. These types of numbers are called irrational numbers, as they cannot satisfy the condition of being able to be expressed as an integer divided by a nonzero integer.
So, in summary, for a number to be rational, it must be able to be expressed as an integer divided by a nonzero integer.