Comparing and ordering rational and irrational number

Rational numbers are those which can be written in ‘p/q’ form where ‘p’ and ‘q’ belong to integers and ‘q’ is not equal to zero. The decimal numbers which are terminating and non- repeating fall under the category of rational numbers. On the other hand, irrational numbers can’t be written in ‘pq’ form because they are non- terminating and non- repeating decimals. We can easily make comparison between rational numbers by simply comparing numerators of the rational fractions (in case of like rational fractions), while by taking L.C.M. and then comparing the numerators (in case of unlike rational fractions).

In the previous topic, we have seen how to make comparison between irrational numbers. In this topic we will get to know about the comparison between rational and irrational numbers.

the function makes a strait line horizontally with no x intercept but a y intercept at 9.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c