Please help me answer the following question on rational and irrational numbers.

Question

Which of these following numbers are rational and which are irrational?

 

a) 5.33.....

b) Pi

c) 6 and 1/3

d) 0.56

e) 2.32

f) square root of 16

g) 1.038120697

h) square root 3

i) 0.06666...

j) 9/20

 

Thanks so much!!

Answer 1

Hi Jack, the definition of a rational number is any number that can be expressed by the relationship p / q, where p and q are integers and q is not zero.

 

A: 5.333 is equal to 5 and 1/3. This is 16 / 3 and is rational.

 

B: Pi is not rational because it cannot be expressed as two integers.

 

C: 6 and 1/3, see answer A:

 

D: 0.56 is equal to 56 / 100. This is rational.

 

E: 2.32 is equal to 232 / 100. This is rational.

 

F: Square root of 16 is equal to 4 and can be expressed as 4 / 1. This is rational.

 

G: 1.038120697 is equal to 1038120697 / 1000000000. This is rational.

 

H: Square root of 3. Irrational, cannot be expressed as two integers.

 

I: 0.066666... is equal to 1 / 15. This is rational.

 

J: 9 / 20 is rational.

 

Questions?