Posted by **christy** on Friday, January 20, 2012 at 3:27pm.

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?

- math -
**Steve**, Friday, January 20, 2012 at 10:36pm
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

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