There is a potentially fatal flaw to entering exponential numbers on the TI-83/TI-84 calculator (and perhaps others too)

DO NOT use the 10^x key or the ^ key. EVER.

You can type in the numbers in what seems like the correct fashion, but the calculator won't interpret your keystrokes the way that you think that it will.

For example:

Let's say we want to calculate the frequency of sodium light which has a wavelength of 539 nanometers.

We know that the speed of light is related to the frequency and wavelength of light by:

c = νλ

So solving or frequency we have:

ν = c/λ

so

ν = (3.00 x 10⁸ m/s)/(539 x 10⁹ m)

if you type in:

3.00 * 10 ^ 8 / 539 * 10 ^ 9

the answer you get is

5.567862709 x 10¹⁴

WHICH IS CLEARLY NOT CORRECT (click here to see why)

So

From now on

YOU MUST

ABSOLUTELY

POSITIVELY

USE

THE

{EE} Key

3.00 {2nd} {EE} 8 / 539 {2nd} {EE} 9

which produces the much more meaningful (and accurate) answer:

5.57 E -4 (after sig figizing)

or

5.57 x 10^-4

Which is much, much more reasonable

TRY IT! (You'll like it or maybe not)

But USE IT

ALWAYS

========================================================

Here's why it gets weird:

Consider again our equation:

ν = (3.00 x 10⁸ m/s)/(539 x 10⁹ m)

and how we might incorrectly enter that into our calculator:

3.00 * 10 ^ 8 / 539 * 10 ^ 9

Here's how our calculator interprets that input:

1. 3 x 10⁸
2. / 539
3. x 10⁹
4. or in written words: the speed of light divided by 539 multiplied by a billion!

Which is clearly not what we want to do!