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Mathematics 19 Online
OpenStudy (anonymous):

which categories does this fall in? -4/7 Natural, whole, integer, rational, irrational, and real?

OpenStudy (ghazi):

irrational

OpenStudy (zzr0ck3r):

rational, real

OpenStudy (anonymous):

rational

OpenStudy (anonymous):

Irrational numbers can't be expressed with a ratio. Rational and Real

OpenStudy (zzr0ck3r):

of course its not irational we can write is as a ratio, and of course its real...

OpenStudy (ghazi):

guys think of 22/7=pie

OpenStudy (anonymous):

ok so the final answer is rational and real?

OpenStudy (ghazi):

it is irrational

OpenStudy (zzr0ck3r):

your joking now? this might confuse people

OpenStudy (anonymous):

yes

OpenStudy (zzr0ck3r):

dude lol its not irrational. you cant write irational numbers and you can clearly write this one. as she did in the topic...

OpenStudy (ghazi):

yea real though

OpenStudy (ghazi):

think of 22/7

OpenStudy (zzr0ck3r):

yes 22/7 is rational just like -4/7

OpenStudy (zzr0ck3r):

anything you can write in a ratio is rational...the fact that we can write it as -4/7 means its rational

OpenStudy (zzr0ck3r):

and pi does not equal 22/7

OpenStudy (ghazi):

22/7 is irrational it never ends up with division

OpenStudy (anonymous):

ok. well i hope the correct answer is rational and real lol

OpenStudy (zzr0ck3r):

lol no, google rational numbers.

OpenStudy (ghazi):

yea go with it

OpenStudy (zzr0ck3r):

you are thinking about the decimel part. 22/7 has a repeating decemel where pi does not... and sqrt(2) does not.... but -4/7 does.

OpenStudy (zzr0ck3r):

if it repeats for ever it is rational

OpenStudy (anonymous):

rational numbers are numbers that can be written as a fraction correct?

OpenStudy (zzr0ck3r):

yes

OpenStudy (zzr0ck3r):

with two real numbers pi/7 can be written as a ratio but is not rational

OpenStudy (ghazi):

thank you

OpenStudy (ghazi):

that's why i mentioned your name..thanks for your suggestion

OpenStudy (zzr0ck3r):

o sorry:)

OpenStudy (ghazi):

:)

OpenStudy (anonymous):

ok wel now im going with irrational and real

OpenStudy (zzr0ck3r):

lol its not irrational

OpenStudy (anonymous):

im so confused lol

OpenStudy (zzr0ck3r):

can you write it with two real numbers as a ratio?

OpenStudy (anonymous):

no

OpenStudy (zzr0ck3r):

then its rational

OpenStudy (zzr0ck3r):

yes you can -4 and 7

OpenStudy (anonymous):

https://www.wolframalpha.com/input/?i=is+-4%2F7+irrational It's not irrational

OpenStudy (zzr0ck3r):

we have special symbols for irational numbers. like e, pi, sqrt(2)... notice we cant write any of those numbers as the ratio of two real numbers

OpenStudy (anonymous):

im confused, is there a way that you can explain it a little better, like break it down

OpenStudy (zzr0ck3r):

hence, e, pi, sqrt(2) , sqrt(5), sqrt(any prime number) is irrational

OpenStudy (zzr0ck3r):

can you write -4/7 as the ratio of two real numbers? the answer is yes we can write it with -4 on top and 7 on bottom. thus its rational

OpenStudy (anonymous):

will that always be that way. all prime numbers are irrational

OpenStudy (zzr0ck3r):

no, the square root of any prime number is irrational

OpenStudy (zzr0ck3r):

all prime numbers are natural numbers, any natural number N can be written as N/1 thus all prime numbers can be written as a ration number. but we are getting off a little bit.

OpenStudy (zzr0ck3r):

just know that if you can write a number as the ratio of two other numbers, where both numbers are not irrational, then that number is rational

OpenStudy (anonymous):

it is rational and real

OpenStudy (zzr0ck3r):

you can of course have a case where a irrational over a irrational is a rational..like pi/pi = 1 is rational but 1/pi and pi/1 is irrational

OpenStudy (anonymous):

omg yall are confusing this poor person lolz

OpenStudy (anonymous):

lol @courtneyfay ik im confused im trying to get the hang of it lol

OpenStudy (zzr0ck3r):

is 5/7 rational?

OpenStudy (anonymous):

haha lolz i dont blame u its rational and real

OpenStudy (zzr0ck3r):

we know its rational and real, im trying to get to the bottom of why.

OpenStudy (anonymous):

no i think

OpenStudy (anonymous):

wait yes

OpenStudy (anonymous):

well explain it easier lolz

OpenStudy (zzr0ck3r):

right it is

OpenStudy (zzr0ck3r):

@courtneyfay feel free....

OpenStudy (anonymous):

good job :)

OpenStudy (anonymous):

its rational because it repeats right

OpenStudy (zzr0ck3r):

correct, that is one way to look at it. what about 2/sqrt(2)

OpenStudy (anonymous):

ummm i wanna say rational

OpenStudy (zzr0ck3r):

sqrt(2) is irational and 2 is rational, so 2/sqrt(2) and sqrt(2)/2 are both irational.

OpenStudy (zzr0ck3r):

also any number that can be written as a/b with no symbols like sqrt(), pi, ln,e, will always be rational. so like 22/32, 67/3209, 56/76544, 100000000/3, 23454/909090909 all rational. any numbers that you can write like digit/digit will always be rational.

OpenStudy (zzr0ck3r):

the only time you need to worry about irrational is when you have sqrt(), of pi, or e, or ln, or log, or other things like this. The only way we can write irational numbers is with symbols. Think about this. we are saying that we cant write any irratioanl number with just digits, because if we could they would not be rational.

OpenStudy (zzr0ck3r):

because if we could they would not be irrational*

OpenStudy (zzr0ck3r):

so is 36/9 rational?

OpenStudy (anonymous):

i dont know why im not understanding this. im gonna go with yes

OpenStudy (zzr0ck3r):

yes because we know anything that can be written as a digit/digit is rational. so is 23/45 and 67/907, and -89898/32455 and 54/-2 all rational?

OpenStudy (anonymous):

yess

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