Question

Could someone explain to me what a rational and irrational number is?

Answer 1

a rational number is any value that can be defined as a fraction such that the top and bottom numbers are integers, and the bottom not 0

Answer 2

irrational numbers are everything else

Answer 3

Amistre to save the day!

Answer 4

can you go into depth what a rational number is?

Answer 5

I've looked at some things online but couldn't quite understand

Answer 6

back in the day, they formed ratios of things, a:b these developed into ratioed numbers of the form a/b, but b not equal 0

Answer 7

a and b tend to be restricted to integer values for safety even tho:\[\frac{1.3}{3/4}\]has a rational value ... it can be expressed in terms of an integer divided by an integer

Answer 8

right, how does b not equal zero, and how can it be identified as equaling zero?

Answer 9

recall that division and multiplication are inverse operation
\[3*x = 15\]\[x=\frac {15}3\]
they undo each other

Answer 10

the restriction of the bottom not 0 is of the effect that\[0*x=5\]\[x = \frac50\]makes no sense

Answer 11

hmmmm i'm beginnnng to see what you mean.

Answer 12

but if you are given two decimals how could you tell which is irrational?

Answer 13

the only way it might remotely make sense is in\[0*x=0\]\[x=\frac{0}{0}\]
but we know that anything times 0 = 0, so the value of x in this case is still undeterminable

Answer 14

all rational numbers a/b are simply decimalized by dividing a by b

these decimal values terminate (zero out) or start repeating a pattern after a given decimal position

3/4 = .75000000000.....

1/2 = .50000000000....

12398623/1234987679052 might be a very long decimal construction, but will eventually either zero out, or start to repeat

1/3 is a classic example of a repeater: .333333......

Answer 15

irrational number: never zero out, and never repeat a given pattern

Answer 16

now I see!

Answer 17

one question that comes up is; how do we know a pattern never develops as opposed to us never getting to a point at which it starts to develop?

Answer 18

like if a decimal was so long you'd not know when it zeroed out?

Answer 19

spose "a" is a given string of number that is 183540121750702475 digits long

the decimal pattern: .aaaaaaaaaaaa.... is still a repeater, and therefore representative of some rational value

but determing a pattern that is 183540121750702475 in length is nigh impossible

Answer 20

correct

Answer 21

there are higher mathing skills that develop proofs for why an irrational number is irrational

and most have to do with assuming that you can form some a/b construction and then show that assumption to be false

Answer 22

I suppose that would come up..

Answer 23

hopefully that doesn't show up on this test I am fixing to take.

Answer 24

:) prolly not. im not that good at proving the irrationality of irrational numbers

Answer 25

well thanks! Until next time!

Answer 26

good luck ;)