Question

Explain Irrational numbers and give a few examples Thanks!

Answer 1

A rational number is a number that can be expressed as the ratio of two integers. For instance, 0.5 is a rational number, which is 1/2

Answer 2

0.394 repeating can be expressed as 394/999

Answer 3

ok so how many irrational numbers are from 1-10?

Answer 4

Im studying for my ACT test tomorrow

Answer 5

However, in the defined "real number set", not all numbers can be expressed as the division of two integers. Although historically it took a bit of time for us to accept this, a simple proof of the the fact that \(\sqrt{2}\) is irrational is suffice

Answer 6

There are an infinite number of rational AND irrational numbers between 1-10...

Answer 7

give me an example why please

Answer 8

Well, pick two numbers between 1 and 10.

Answer 9

2 and 7

Answer 10

Pick two numbers in between those two.

Answer 11

5, 6

Answer 12

Now do it again.

Answer 13

5.6, 5.7

Answer 14

an important property of the real numbers is that they are continuous - in a sense, there are an INFINITE "number" of numbers in between any two different numbers, no matter how small the difference

Answer 15

There are actually "far more" irrational numbers than rational numbers.

Answer 16

so in 1-3 there is many aswell?

Answer 17

Well, comparing the two expressions is indeterminant I believe

Answer 18

Great! Thanks a lot for your help it cleared my confusion. Hopefully I get this right on one of the biggest tests of my life!

Answer 19

@Marlins0412 , the key thing to know is that there are an infinite number of rational and irrational numbers

Answer 20

rational numbers can be expressed as the division of two integers, while irrational numbers cannot

Answer 21

I see

Answer 22

WEll off to more studying thanks again

Answer 23

yes - good luck!

Answer 24

Thanks so much!