What is a rational number

Question

Which of the following does notrepresent a rational number- 250 or 11/39

 

 

 

 

 

 

 

Answer 1

 

 They are both rational

 

    11/39 = 0.282051 = 282051/999999

 

 

If the decimal expansion can be written as a proper fraction, then it is rational.

 

Examples of irrationals:  pi=3.1416..., sqrt(3)=1.7173...,  square root of any non-perfect square, e=2.713...

The decimals do not stop and do not repeat in any organized pattern.

 

Do you understand the difference now between an irrational and a rational?

Answer 2

Answer: trick question! They're both rational. A rational number is anything that is or could be written as a fraction. That means every fraction is already rational. A mixed number could be written as an improper fraction, which means it's actually rational as well. All integers can be placed over 1,making them rational. Finally, decimals. That's where the trouble kicks in. A terminating decimal is still fine. That refers to something like 2.4, 3.07, 1.998, et cetera. Non-terminating decimals are fine IF they repeat, such as 2.1717171717...

Finally, if they do NOT terminate or repeat you have an irrational number. Only values like pi or imperfect square roots (square roots of 5, 6, 7 but not 4 or 9...) qualify.