Question

I want to know if these numbers rational or irrational and why?

Answer 1

Explanation:

2)
`(-3)/(10)`

This is a rational number because as a decimal, it is -0.3. It doesn't repeat, so it is a terminating decimal.

3)
`√(40)`

When you put this into a calculator, you get 6.324555... Since this decimal would go on forever, it is irrational.

4)
`√(81)`

When you put this into a calculator, you get 9. It is a whole number, so it is rational.

5) 2
`(1)/(3)`

As an improper fraction, this is 7/3. When you put this into a calculator, you would get 2.33333... Since this decimal would go on forever, it is irrational.

6) 0.35

This is a terminating decimal, just like number one. It doesn't repeat, so this is a rational number.

7) 0.33333 ....

This is an irrational number because it repeats.

8) -9

Since this is a whole number, it would be rational.

9) 3.4

This is a terminating decimal, just like number 6. It doesn't repeat, so this is a rational number.

10)
`√(2)`

When you put this into a calculator, you get 1.41421... Since this decimal would go on forever, it is irrational.