Why doesn't my TI-84 give me an exact value when calculating scientific notations?

Question

I was doing a statistics probability problem and I needed to find the value of (0.17)^4. When I entered the value into my calculator, I noticed that it gave me the answer in scientific notation (8.3521E-4). I figured let me try entering 8.3521 * 10^-4 hoping that it'd give me the decimal form I was looking for. However, it was the same exact issue.

I went to the 'mode' option of the calculator thinking that there was something wrong with the setting but everything was fine. I don't mind manually converting the scientific notation into decimal form but I'd really like for the value to be already in decimal form given the workload of these problems.

Thank you for reading!

Note: I have a TI-84 Plus Silver Edition.

Answer 1

Scientific notation can represent exact numbers if they are terminating decimals. In your case $0.17^4=0.00083521=8.3521E-04$ exactly. Did you drop the final $1$? I would expect the calculator to show it. The calculator probably does this calculation as $e^{4 \log 0.17}$ and $\log 0.17$ cannot be represented exactly, so there is a reasonable chance that the result is not exact. I wouldn't expect that to change anything as far forward as the fifth place, but seeing $8.35209999E-04$ would not surprise me

Answer 2

The calculator automatically uses scientific notation for numbers smaller than $0.001$ in absolute value, no matter what your mode settings are; this cannot be overridden.

The most straightforward way to get the calculator to immediately tell you how many zeroes there are after the decimal, in such a case, is to add $1$:

0.17^4
       8.3521e-4
Ans+1
      1.00083521

Just ignore the $1$ in front of the decimal point and you have the answer you want.

Note that in general, this will lose you precision:

0.17^8
  6.975757441e-7
Ans+1
     1.000000698

In this case, it's not too bad: we can use the second output to count zeroes and the first for more digits. Sometimes, it will lose you all of the precision:

0.17^16
  4.86611919e-13
Ans+1
               1

But in this last example, maybe you don't want the number as a decimal after all.