0.5, [tex]\frac{0}{100}[/tex] are rational. √24, 3.42859873 are irrational.
Solution:
Rational numbers can be expressed as [tex]\frac{p}{q} , \ q \neq 0[/tex] form.
Option A: 0.5
[tex]$0.5=\frac{1}{2}[/tex]
It is of the form [tex]\frac{p}{q} , \ q \neq 0[/tex].
Therefore 0.5 is a rational number.
Option B: [tex]\sqrt{24}[/tex]
[tex]\sqrt{24}=\sqrt{2^2\times 6}[/tex]
[tex]=2\sqrt{6}[/tex]
It cannot be simplified further. Roots are irrationals.
Therefore √24 is irrational.
Option C: 3.42859873
It cannot be written as [tex]\frac{p}{q} , \ q \neq 0[/tex] form.
Therefore 3.42859873 is irrational.
Option D: [tex]\frac{0}{100}[/tex]
It is of the form [tex]\frac{p}{q} , \ q \neq 0[/tex].
Therefore [tex]\frac{0}{100}[/tex] is rational.
