Question

Classify each number as rational or irrational.

Drag the choices into the boxes to correctly complete the table.

Answer 1

√3 → irrational

-1/10 → rational

0 → rational

√2 → irrational

Answer 2

Answer: √3 and √2 are irrational numbers;

`-\fracP{1}{16}` and 0 are rational numbers.

Step-by-step explanation: We are given to classify the following numbers as rational or irrational:

`√(3),~~-(1)/(16),~~0,~~√(2).`

Rational number: The digits after the decimal are either repeating or terminating.

Irrational number: The digits after the decimal are non-terminating and non-terminating.

(a) We have

`√(3)=1.732050807568877~.~.~.`

Since the digits after the decimal are non-terminating and non-repeating, so √3 is an IRRATIONAL number.

(b) We have

`-(1)/(16)=-0.0625.`

Since the digits after the decimal are terminating, so
`-(1)/(16)` is a RATIONAL number.

(c) We have

`0=0.000.`

Since the digits after the decimal are terminating, so
`0` is a RATIONAL number.

(d) We have

`√(2)=1.414213562373095~.~.~.`

Since the digits after the decimal are non-terminating and non-repeating, so √2 is an IRRATIONAL number.