Scientific Notation - the Math

When doing scientific notation work on your calculator, you must:

• find the appropriate keys on your calculator, 
• know how to enter the problems into your calculator, and
• understand what your calculator is saying when it uses scientific notation.

Finding the Keys

All scientific calculators have an exponent button and you must know where it is in order to use your calculator properly in chemistry. Unfortunately, not all calculators have these buttons in the same place. What you are looking for is a button that has one of the following abbreviations: EE, EEX, or EXP. These are used generally the only abbreviations used by manufacturers.

If the EE or EEX or EXP is not on the button itself (it may be above the button in another color), you will then need to hit an extra key to use it. In other words, if your calculator has the symbol EE above a key in yellow, then there is probably a yellow key that says 2nd. In this case you would hit the 2nd key and THEN the key with the EE above it to enter an exponent.

Entering Problems in Scientific Notation

Entering a problem that uses scientific notation is relatively straightforward as long as you remember that the exponent key means "times 10 to the." In other words you do NOT enter the 10.
In the examples below, EXP will be used to symbolize the exponent key. You may have a different key and you may need to hit 2 keys (2nd and the EE, for example) to use this function. Try these examples with the text. If you are getting different answers, you are entering the numbers incorrectly.
Example 1:

4.7*10⁹ * 3.2*10^-7

This should be entered into your calculator like this:

4.7 EXP 9 * 3.2 EXP -7

If you entered it correctly, you should get 1504.
Example 2:
8.7*10^-3 / 7.3*10¹⁷
This should be entered into your calculator like this:
8.7 EXP -3 / 7.3 EXP 17
If you entered it correctly, you should get the answer 1.1918*10^-20 which will look (on your calculator) like either 1.1918e-20 or 1.1918 ^-20.

What NOT to do

It may be tempting to use the ^ key (if you calculator has one) instead of the EXP key. In other words, you may be tempted to enter the number 7.3*10¹⁷ as 7.3*10^ 17. Although these numbers are equivalent, it is VERY easy to make mistakes when entering numbers in this way.

To be very concrete, if you enter the problem above ( 8.7*10^-3 / 7.3*10¹⁷) in the following way,  8.7*10^-3 / 7.3*10^17
you will get the WRONG answer. Specifically, you will get approximately 119,000,000,000,000. A VERY different value. The problem here is that the calculator treated 7.3*10^17 as two numbers not one. In other words it divided by 7.3 and then multiplied the answer by 10¹⁷.

Calculator Language

When a calculator shows a number in scientific notation it generally does it in one of two ways.
On a calculator with a graphics screen, the number 3.4*10⁷ would be shown as 3.4e7 or 3.4E7. In this case the e (or E) means "times 10 to the." So, 4.6e12 means 4.6*10 ¹² and 9.1E-5 means 9.1*10^-5.
If your calculator does not have a graphics screen the exponent is usually shown as a pair of smaller digits in the upper right hand corner of the screen. Thus 3.4*10⁷ would be written as 3.4 ⁰⁷. If your calculator shows numbers in this way, 4.6 ¹² would mean 4.6*10¹² and 9.15 ^-05 means 9,1*10^-5. You must understand that 4.5⁷ does NOT mean 4.5 raised to the seventh power.


Of course, you also need to understand what scientific notation means.