## The Powers of Ten

Scientific notation is also known as powers-of-10 notation. Often in science large and very small numbers are used, and the concept of significant figures is applied so that the answer can be understood without every number actually being written out. However, sometimes just looking at these numbers can be quite confusing. Some examples of scientific notation are written below.

- 103
- 10-3

Scientific notation will always be used in relation to multiplying a number by ten. Here are some extended examples of this method

- 2.3 x 103
- 2.3 x 10-3

Read the next section to find out the specifics of scientific notation and how it helps you with significant figures.

## Use of Exponents

Scientific notation can either be used to express very large or very small numbers. The size of the number is expressed by the *power* of the number. Positive powers are used to express large numbers while negative powers are used to express small numbers. The power of the number tells you how many zeros are after or before the decimal point.

For example, 10^{4 }is actually 10 x 10 x 10 x 10= 10,000

In contrast, 10^{-4} is actually 1/10^{4} = 1/10,000 = 0.0001

In both instances, the power shows you how many zeros are involved in the number. The small number expressed to the right of the 10 is called an *exponent. *

To use scientific notation as a significant number, you first would have to know what the significant figure is. Below is an example of this process.

Express the answer to the following problem using significant terms and scientific notation.

3520 x 100

We know the significant amount of numbers in the answer is going to be 3 because 100 is the number with the smallest amount of significant numbers in it. Now we work the problem out.

3520 x 100 = 352000: Since we only need 3 significant numbers in our answer, we use scientific notation to reduce the amount of numbers in our answer. Therefore, the answer would be 352 x 10^{3}

Now let's try the problem using negative powers.

352 x .000001: Again, we can see that we need 3 significant numbers in our answer because the smallest amount of numbers in this equation is 3.

352 x .000001= 0.00352 Now we need to use powers of ten to reduce the amount of numbers in the answer.

352 x 10^{-5 }is the answer.

Notice that all you really did was move the decimal to the left 5 spaces. This is the easiest way to remember how to use the powers of ten. All you are actually doing is moving the decimal point however many places expressed by the power written. You know whether to move it left or right by whether or not the power is negative or positive. If the number is negative as in 10^{-2}, then you would move the decimal point over to the left 2 places. 10^{2} means that you would move the decimal point to the right 2 places.