Question

Classify each real number below as either rational or irrational. Select the number to see an explanation of the number’s classification.

21
7
π
√38
0.2
0.7
√100
9
5
−6

Answer 1

Hello!

21 is a whole number that can be written as a fraction, along with it being an integer and a whole number. Therefore, 21 is rational.

7 is a whole number that can be written as a fraction, along with it being an integer and a whole number. Therefore, 7 is rational.

$\pi$ continues on forever in no specified order, so therefore it cannot be written as a fraction and therefore $\pi$ is irrational.

√38 is like pi; it goes on forever in no specified order. √38 is irrational.

0.2 is a terminating decimal that can be written as a fraction. Therefore 0.2 is a rational number.

0.7 is a terminating decimal that can be written as a fraction. Therefore 0.7 is a rational number.

√100=10, which is a whole number and integer, therefore √100 is a rational number.

9 and 5 are both whole numbers and integers that can be written as fractions. 9 and 5 are both rational numbers.

-6 is an integer and can be written as a fraction. -6 is a rational number.


I hope this helps!