Ti-83 giving inconsistent answers

allyourbass2212 · #1 $Old$ June 28th, 2009, 02:19 PM

What I have been doing is just taking a fraction and raising it to ^(1/2) to find the difference of squares and it has worked for every problem except this one, and it seems to be a fault with the calculator.
For instance
$\frac{16}{81}x^4-16=(\frac{4}{9}x^2-4)(\frac{4}{9}x^2+4)=(\frac{2}{3}x-2)(\frac{2}{3}x+2)(\frac{4}{9}x^2+4)$

For some reason in my TI-83 if I just enter $\frac{16}{81}^{1/2}$ it will yield $\frac{16}{9}$

but if I do $\frac{16}{81} = .1975308642$ , turn it back into the fraction $\frac{16}{81}$ and then raise that to $^{1/2}$ it will give me the correct fraction $\frac{4}{9}$

Very strange indeed, anyone know why the calculator might be doing this?

Same thing for $\frac{4}{9}$ if I just try to raise this to ^(1/2) in the calculator it will yield 1.333 repeating, which equals $\frac{4}{3}$ when converted back to a fraction. But if I do $\frac{4}{9}$ it will yield .444 repeating, turn it back into the fraction $\frac{4}{9}$ and then I can raise that to ^(1/2) to get the correct answer which is $\frac{2}{3}$

earboth · #2 $Old$ June 28th, 2009, 02:26 PM

Quote:

Originally Posted by allyourbass2212 $View Post$

What I have been doing is just taking the number or fraction and raising it to ^(1/2) to find the difference of squares and it has worked for every problem except this one, and it seems to be a fault with the calculator.
For instance
$\frac{16}{81}x^4-16=(\frac{4}{9}x^2-4)(\frac{4}{9}x^2+4)=(\frac{2}{3}x-2)(\frac{2}{3}x+2)(\frac{4}{9}x^2+4)$

For some reason in my TI-83 if I just enter $\frac{16}{81}^{1/2}$ it will yield $\frac{16}{9}$

but if I do $\frac{16}{81} = .1975308642$ , turn it back into the fraction $\frac{16}{81}$ and then raise that to $^{1/2}$ it will give me the correct fraction $\frac{4}{9}$

Very strange indeed, anyone know why the calculator might be doing this?

Same thing for $\frac{4}{9}$ if I just try to raise this to ^(1/2) in the calculator it will yield 1.333 repeating, which equals $\frac{4}{3}$ when converted back to a fraction. But if I do $\frac{4}{9}$ it will yield .444 repeating, turn it back into the fraction $\frac{4}{9}$ and then I can raise that to ^(1/2) to get the correct answer which is $\frac{2}{3}$

If you type 16/81^(1/2) then only the square-root of 81 will becalculated.

With a TI83 you better write fractions in brackets. Type (16/81)^(1/2) and afterwards MATH ENTER ENTER

allyourbass2212 · #3 $Old$ June 28th, 2009, 02:28 PM

Ah, many thanks Earboth!