Scientific Tutor

One representation or function that a lot of people can be unfamiliar with is the exponent. Simply put, exponents are causing a chain of multiplication events. For example, 10 with an exponent of 6 (looks like this: 10⁶ or 10^6) means that you take 10 and multiply it by 10, 6 times in a row. The formula is: 10*10*10*10*10*10. Exponents can also appear with a negative in front of them, like 10^-4. The formula for this one is: 10 / 10 / 10 / 10. So they are the opposite of each other. If you have a positive exponent, you multiply, and if you have a negative exponent, you divide. If you are unsure how to input exponents into a calculator, then go to this page: VIDEO How do I put exponents into my calculator? The link in previous sentence includes demonstrations of the examples below.

Numerical exponents should only be shown as a number in the upper position next to other numbers. Exponents will not be shown next to letters of elements (this is a charge which we will discuss in a later lesson). So for an example of what I mean, you can write 5⁴ and that is an exponent. However, if I write out S^-2, that is not an exponent.

Examples: Provide the answers for these exponent problems.  VIDEO How do I put exponents into my calculator?

Exponents will be used throughout chemistry, but they are usually very common when it comes to a concept called scientific notation, which will be discussed in the next lesson. In scientific notation, the focus is on exponents of 10, as illustrated in the examples below.

Examples: Provide the answers for these exponent problems.  VIDEO How do I put exponents into my calculator?

You can input these problems into your calculator and work them out that way, but as you get further into chemistry, you might want to use a trick to make finding exponents of 10 faster and easier for you. This trick involves moving the decimal to the right or left, depending on if it is a positive or negative exponent. If it is a positive exponent of 10, then you move the decimal to the right however many spaces the exponent number is. In the previous example of 10³, You start off with 1.0 : if you move the decimal to the right once, you get 10 : if you move the decimal to the right again, you get 100 : and if you move the decimal to the right yet again, you get 1000. How many times did we move the decimal? Answer: 3. That is because the exponent was 3.

PRACTICE PROBLEMS: Give the regular (non-exponent number) for the exponent problems below problems.