Identify which condition is necessary for a number to be rational.
(1 point)
Responses
It must not be an endless decimal.
It must not be an endless decimal.
It must be written as a fraction.
It must be written as a fraction.
It must be able to be expressed an as integer divided by a nonzero integer.
It must be able to be expressed an as integer divided by a nonzero integer.
It must not be negative.
It must be written as a fraction.
Which of the following is irrational?(1 point)
Responses
3√4
the fraction with numerator square root of 3 and denominator 4
52.781654292
52.781654292
−7837
negative 7 and 8 over 37
3.6363636363636363..
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
Which statement is true about the square root of 28?(1 point)
Responses
It is between 5 and 6, probably closer to 5.
It is between 5 and 6, probably closer to 5.
It is between 5 and 6, probably closer to 6.
It is between 5 and 6, probably closer to 6.
It is between 6 and 7, probably closer to 6.
It is between 6 and 7, probably closer to 6.
It is between 4 and 5, probably closer to 5.
Which of the following is a rational number?(1 point)
Responses
11−−√
square root of 11
15−−√
square root of 15
16−−√
square root of 16
18−−√
The condition that is necessary for a number to be rational is that it must be able to be expressed as an integer divided by a nonzero integer. In other words, it can be written as a fraction. So, the correct answer is "It must be able to be expressed an as integer divided by a nonzero integer."
To understand why this condition is necessary, it is important to know that rational numbers are numbers that can be expressed as fractions. Fractions represent division, where the numerator (the top number) represents the dividend and the denominator (the bottom number) represents the divisor. As long as the denominator is not zero, any number can be expressed as a fraction.
For example, the number 2 can be written as 2/1, where the numerator is 2 and the denominator is 1. Similarly, the number -3 can be written as -3/1. Any whole number can be expressed as an integer divided by 1.
So, in order for a number to be rational, it must be able to be expressed as an integer divided by a nonzero integer. Any other condition, such as being an endless decimal or not being negative, is not sufficient for a number to be rational.