Question

How do I figure out if these are Rational and Irrational?

1. -101
2. 21.192
3. Square Root of 9
4. 8/17
5. Pie
6. Square Root of 2
7. 39.81 (there's a line over 81)

@Hero @mathslover @mathlover2014 @mathhelpwanted @mathstudent55 @jim_thompson5910

I need you to explain it really simple, because I really don't understand it. Well...I understand it to an extent. Don't worry this isn't a test or homework. Someone gave me some stuff to practice and I want to learn it to be ready for high school. :)

Answer 1

I'll be right back, I have to eat dinner.

Answer 2

A number is rational if it can be written in the form a/b, where a and b are integers. Otherwise it is irrational.

Answer 3

Like @Hero said, a number is rational if it can be written in the form a/b. In other words, if it can be written as a fraction. Numbers like pi are irrational because they are infinite and cannot be put into fractional form. It can be approximated to 22/7, but that is not exact.

Answer 4

OK, Can you walk me through each one?

Answer 5

@girlnotonfire Can you walk me through each one? :)

Answer 6

-101 would be.... -101/1?

Answer 7

Yes, so it is rational.

Answer 8

21.192 since the decimal expansion isn't made up of zeros or a single digit repeating is and irrational number?

Answer 9

21.192=21+192/1000=21+24/125=2649/125

Answer 10

21.192 = 21 + 192/1000
= 21000/1000 + 192/1000
= 21192/1000

Therefore 21.192 is rational

Answer 11

OK, so that means it's Rational?

Answer 12

Yes, it is rational.

Answer 13

Oh, I get it thanks! Hold On and let me see if I can figure out the answer for the next one. :)

Answer 14

The Square root of 9 is rational?

Answer 15

Yes! The square root of 9 is 3 or 3/1. Good job :)

Answer 16

Now 8/17 is already a fraction, so how do I work that? @girlnotonfire

Answer 17

If it is already a fraction, we automatically know it is rational, no work needed :)

Answer 18

OK, :) Now the next one look like pie, or n but it's completely straight on both side and straight on top. I don't know what that is. Do you? 0_0 @girlnotonfire

Answer 19

That's probably pi as well, I'm not sure what else it could be. If it looks like Π or π, it is definitely pi.

Answer 20

It looks like the first one, which if you said it was pie.. Then it's irrational. Right? :) @girlnotonfire

Answer 21

Yes, because it is an infinite decimal that cannot be made into an exact fraction.

Answer 22

I already know that #6 is irrational. :) So, that leaves #7. Since there is a line over the 81 in 39.81 it means it repeats like this.... 39.81818181 does that mean it's Rational?

Answer 23

Yes, all repeating decimals are classified as rational numbers. In this case, 39.81(repeating)=438/11, so it is rational.

Answer 24

Thanks! :)