Question

How can you tell if a number is rational or irrational?

a) 3.215 (there is a line drawn over the 15)
b.) square root 10
c) 0.143639854024
d)4.312

can you please explain what i need to look at to tell which is which?

Answer 1

any number whose decimal expression terminates or ends in a repeating group of digits is rational. Otherwise, probably not.

(a) 3.21515151515...
3 + 2/10 + 15/990 is rational

To find out what .0151515... is, let it be x

x = .015151515...
10x = .151515
1000x = 15.15151515...
subtract 10x from 1000x:
990x = 15
x = 15/990

(b)the square root of any number which is not a perfect square is irrational

(c) If that's exact, it terminates and is rational
(d) same