Hi my name is Will.I have a question about the calculator TI-83 Plus or the use of a scientific calculator. It is about using them to turn a cubed root to a decimal. When using that for a rational and irrational number. Rational numbers is a number that terminates or repeates. A irrational number goes on and on and uses ... (like pie). Like when you type the cube root of 8 it gives you 2, and that is a rational number. The squre root of 2 is 1.41421356... that is irrational. So why is it when you put the cube root of 16 in the calculator it says 2.5198421 that is rational it terminates at the ninth digit and my float is set for the tenth? But why when you do it by hand you get the 2 times the cube root of 2 and that is irrational? Why is that?

Can you please help me,

thanks, Will

Hi Will,

This is a nice question, and I'm glad you realized that the calculator answer does not match your hand calculations. If you cube 2.5198421 by hand, you will find that you do not get 16, but rather something a tiny bit larger. I tried taking the cube root of 16 with a TI-85 and at first it gave me 2.51984210. I then increased my float to 11 decimal places and got 2.15984209979. Let's examine the end of this decimal more carefully. When you round off at the ninth decimal place (giving you ten digits) you round 099 up to 100, thus you get two zeros at the end and it may appear that your decimal terminates when in actuality it does not. I'm curious if your calculator displayed the zeros at the end. Mine did.

Take care,

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