A warning about calculators

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Let's enter this number:

2.45 x 10¯9

into the calculator.

Here is the RIGHT way:

1) Press "2," the decimal button, then "4" and then "5"
2) Press a key marked either "EXP" or "EE"
3) Press "9," then the sign change key (usually marked "+/-").

Here is the typical wrong way:

1) Press "2," the decimal button, then "4" and then "5"
***2) Press the times button ("x") and then enter "10" (by pressing "1" then "0")***
3) Press a key marked either "EXP" or "EE"
4) Press "9," then the sign change key (usually marked "+/-").

***That step #2 is WRONG!!*** Don't do it. Pressing "EXP" means "times ten to the power of." The step #2 (where you enter "times 10") means you entered 2.45 x 10 x 10¯9. This equals 2.45 x 10¯8. Try entering it the wrong way and then pressing the "equals" button. See?

The ChemTeam has had this happen in the classroom:

"Mr. ChemTeam, you did that problem wrong. See, when I do it, I get <some answer> and yours is too small by a factor of ten."

You can imagine the ChemTeam's unmitigated glee when this happens!!

Let's use 2.45 x 10¯9 to highlight another problem.

Some (usually older, with small screens) calculators puts the number into shorthand on the screen.

2.45 x 10¯9 is written in scientific notation. Here is how it is displayed on the calculator screen:


However, do not, DO NOT write it that way on paper. DON'T DO IT. 2.45 x 10¯9 and 2.45¯9 are different numbers!!

2.45¯9 is calculator shorthand for 2.45 x 10¯9.

Make sure you include the "x 10" when you make the transfer from screen to paper.

Some students are lazy. They get in the habit of writing 2.45¯8 when they do a calculation at home during study. Then, they do it the same way (after being warned not to) on the test and write the answer that way. The ChemTeam marked off full points in that situation. Pretty mean, huh?

There is another way to show 2.45 x 10¯9. This is it:


The use of this format is widespread among calculators. The ChemTeam uses a MacBook Pro and the calculator uses the above format. Here is an article from 1999. It uses the x 10exponent format throughout the article, but switches to the E format in an appendix that is nearly 10 pages long.

If you do not know what the E means, you will make a mistake. Like these:

(a) Ignore the E and "round off" the answer to 2.45.

(b) Ignore the E, write 2.45 − 9 to get −6.55.

(c) Think that ā€œEā€ is the irrational number e (Euler's Number) and then calculate 2.45e−9 as 0.000302. The interesting thing here is that the student uses −9 as an exponent, but doesn't realize what the E stands for.

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