Please Explain the irrational numbers and rational numbers and differences between them and also
explain irrational functions.

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions.

- anonymous

- jamiebookeater

See more answers at brainly.com

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

A number is rational if it can be written as the quotient of two integers.

- anonymous

This is why the set of rational numbers is denoted \(\mathbb Q\) for quotient.

- anonymous

Please explain @nbouscal .

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- lgbasallote

other than the number itself over 1

- lgbasallote

example...2 is rational because i can express it as 4/2

- anonymous

For any rational number there is a \(p\) and \(q\) with \(p,q\in\mathbb Z\) such that the rational number can be written as \(\dfrac p q \)

- anonymous

Please mention differences between rational and irrational numbers also.

- anonymous

Irrational numbers are simply numbers that are not rational.

- lgbasallote

pi cannot be expressed as a quotient even though 22/7 is near therefore it is irrational

- anonymous

Some more examples ....@lgbasallote

- anonymous

The simplest proof of an irrational number is the one for \(\sqrt2\). http://www.homeschoolmath.net/teaching/proof_square_root_2_irrational.php shows the standard proof, due to the Greeks.

- lgbasallote

ALL integers are rational numbers

- lgbasallote

the integers are -1, -2, -3, 0, 1, 2, 3, etc

- anonymous

Decimal numbers that terminate are rational, because they can be written as a fraction. For example, 2.231 can just be written as 2231/1000. This is the case for any decimal that terminates.

- anonymous

- lgbasallote

some decimals that dont terminate can also be expressed as fractions...for example 0.333333 can be expressed as 1/3

- anonymous

1/3 is a quotient of two integers, so it is a rational number.

- lgbasallote

that is rational because 1 amd 3 are integers

- lgbasallote

do you get it now?

- anonymous

If you want to get even more fun you can look at the transcendental numbers, they are even more crazy than the irrational numbers. Irrational numbers that are not transcendental are called algebraic, they can be found as the roots of polynomials. There are all sorts of fun proofs to be read in this area of mathematics.

- lgbasallote

lol why make it confusing :p

- anonymous

Of coarse @lgbasallote is right.

- lgbasallote

the kid doesnt understand rational and irrational and you're suggesting "fun" :p

- anonymous

Also worth noting is that the union of the rational and irrational numbers forms the real numbers, \(\mathbb R\), which is the set that you usually work in. You can also go further to \(\mathbb C\), the complex numbers. And then even further than that :)

- anonymous

I'm giving him an idea of the cool stuff ahead, it doesn't just stop at rational and irrational :P

- lgbasallote

sometimes it's nicer to live in fantasies for some time

- ParthKohli

1/3 has recurring digits but is still expressed as a quotient of two integers, so it is rational.

- lgbasallote

i'd rather take the blue pill than the red

Looking for something else?

Not the answer you are looking for? Search for more explanations.