Scientific Understanding

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: 10^{6 } 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 5^{4} 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**?

2^{2} = 2*2 |
4 |

5^{6} = 5*5*5*5*5*5 |
15625 |

6^{-3} = 1 / (6*6*6) |
1/216 |

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**?

10^{3} = 10*10*10 |
1,000 |

10^{-4} = 1 / (10*10*10*10) |
.0001 |

10^{5} = 10*10*10*10*10 |
100,000 |

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 10^{3}, 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.

10^{-2} |
.01 |

10^{6} |
1,000,000 |

10^{9} |
1,000,000,000 |

10^{-7} |
.0000001 |