Question

question 5
which two numbers on the number line are rational?
√10 and 2
−√9 and −2.8
−2.8 and √10
all five numbers
question 6
name one irrational and one rational number from the number line:
irrational = , rational =
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Explanation:

Step1: Recall definition of rational numbers

Rational numbers can be written as a fraction $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. Also, integers, terminating decimals and repeating - decimals are rational.

Step2: Analyze $\sqrt{10}$

$\sqrt{10}$ is an irrational number because 10 is not a perfect - square. Its decimal expansion is non - terminating and non - repeating.

Step3: Analyze $2$

2 is an integer, and all integers are rational numbers. It can be written as $\frac{2}{1}$.

Step4: Analyze $-\sqrt{9}$

$-\sqrt{9}=- 3$. Since - 3 is an integer, it is a rational number. It can be written as $\frac{-3}{1}$.

Step5: Analyze $-2.8$

-2.8 is a terminating decimal. It can be written as $\frac{-28}{10}=-\frac{14}{5}$, so it is a rational number.

For question 5:
The pair of rational numbers is $-\sqrt{9}$ and $-2.8$. So the answer is the second option.

For question 6:
An irrational number could be $\sqrt{10}$ (since it cannot be written as a fraction of two integers). A rational number could be 2 (an integer and thus rational).

Answer:

Question 5: The second option ($-\sqrt{9}$ and $-2.8$)
Question 6: Irrational = $\sqrt{10}$, Rational = 2