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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.

Calculator Screen Image Here

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.

Misha Lavrov
  • 142,276
Joy Nath
  • 31
  • rounding is why – terrace Nov 06 '17 at 03:58
  • You mean you want the calculator to show 0.00083521 instead of what it shows? Why? It requires virtually no thought to convert between these representations. The exponent tells you how many places to move the decimal to the left. So an exponent of $-4$ just means you have three zeros after the decimal point. – symplectomorphic Nov 06 '17 at 06:14
  • @simplectomorphic a lot of students struggling with math are utterly confused by scientific notation, and dealing with it is another difficulty they have to contend with. – Guillaume F. Jun 22 '23 at 20:04

2 Answers2

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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.

Misha Lavrov
  • 142,276
  • This works as long as the number is not too small. It will not work with $1E-20$ because it is below the machine epsilon. – Ross Millikan Nov 06 '17 at 05:04
  • It will "work" in the sense of telling you what the next few digits after the decimal are (all zeroes). I guess I'll edit to clarify. – Misha Lavrov Nov 06 '17 at 05:06
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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

Ross Millikan
  • 374,822
  • 1
    I checked with a debugger and in fact the digits stored in the calculator (as binary-coded decimals) are exactly 83521000000000. I assume this happens because the calculator uses 18 significant digits for intermediate calculations, but rounds to 14 significant digits at the end. – Misha Lavrov Nov 06 '17 at 05:02