Question

Decide whether each number in this list is rational or irrational.

Answer 1

Step-by-step explanation

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero

`\begin{gathered} a=(p)/(q) \\ q\\e0 \\ a\text{ is rational } \end{gathered}`

and An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio

so,let's check every option

Step 1

a)-13/3

it is a fraction, so it is a rational number

b)

`\begin{gathered} 0.1234 \\ 0.1234*(10000)/(10000)=(1234)/(1000) \\ so,\text{ the number can be expressed as a ratio, hence} \end{gathered}`

it is a rational number

c)

`√(37)=6.0827625302...`

Square root of 37 is an irrational number, because the value of √37 is a non-teminating decimal

d)-77

The rational numbers include all the integers, and this is a integer, so this is a rational number

d)

`\begin{gathered} -√(100) \\ -√(100)=\text{ -10} \end{gathered}`

The rational numbers include all the integers, and this is a integer, so this is a rational number

e)

`\begin{gathered} -√(12) \\ -√(12)=-√(4*3) \\ -12=-√(4*3)\text{ = -}√(4)\sqrt{3\text{ }}=\text{ -2}√(3) \end{gathered}`

The sqrt of 3 is irrational. Specifically, it cannot be written as the ratio of two given numbers or be written as a simple fraction,so

this number is a irrational number

I hope this helps you