Question

HELP PLEASE!!!!

Drag the values into the boxes to classify each number as rational or irrational.

(Check photo for the options)

Answer 1

Answer: Rational 11/3 6.25 0.01045 0.42line

16/81

Irrational 48 3/6

Explanation:

Answer 2

The rational numbers are
`(11)/(3), 6.25, 0.01045,\sqrt{(16)/(81)},0.\bar{42}` and the irrational functions are
`√(48),\sqrt{(3)/(16)}`.

Explanation:

A rational number can be expressed in the form of
`(p)/(q)`, where p and q are integers and q is not equal to 0. For example
`2,3.5,(2)/(5),...`.

An irrational function can not be expressed in the form of
`(p)/(q)`, where p and q are integers and q is not equal to 0. For example
`√(2),√(3),√(5),...`.

If any number is multiplied by a irrational number then the resultant number is an irrational number.

By the above definition we can conclude that:

The number
`(11)/(3)` is a rational number.

`√(48)=√(16* 3)=4√(3)`

Therefore
`√(48)` is an irrational number.

`6.25=(625)/(100)=(25)/(4)`

Therefore 6.25 is a rational number.

`0.01045=(1045)/(100000)=(209)/(20000)`

Therefore 0.01045 is a rational number.

`\sqrt{(16)/(81)}=(4)/(9)`

The number
`(16)/(81)` is a rational number.

`\sqrt{(3)/(16)}=(√(3))/(4)`

The number
`(3)/(14)` is an irrational number.

`0.\bar{42}=(42)/(99)`

Therefore
`0.\bar{42}` is an irrational number. The numbers with recursive bar are always rational numbers.