Scientific notation why

To translate 10,,,,,,, carbon atoms into scientific notation, we move the decimal point to the left 22 times. To convert numbers smaller than 1 into scientific notation, we have to move the decimal point to the right. The decimal point in 0. Converting 0. You can also enter numbers in e notation. Examples: 3. Order of magnitude will also be identified for the calculated standard form. The order of magnitude when written in standard form, is the nth power of Recall that any number or variable with an exponent of 0 is equal to 1, as in this example:.

We now have described the notation necessary to write all possible numbers on the number line in scientific notation. In the next video you will see how to convert a number written in scientific notation into decimal notation. Numbers that are written in scientific notation can be multiplied and divided rather simply by taking advantage of the properties of numbers and the rules of exponents that you may recall.

Then multiply the powers of ten by adding the exponents. This will produce a new number times a different power of All you have to do is check to make sure this new value is in scientific notation. Convert In the following video you will see an example of how to multiply tow numbers that are written in scientific notation.

In order to divide numbers in scientific notation, you once again apply the properties of numbers and the rules of exponents. Then you divide the powers of ten by subtracting the exponents. Convert 0. Notice that when you divide exponential terms, you subtract the exponent in the denominator from the exponent in the numerator. You will see another example of dividing numbers written in scientific notation in the following video.

Match each length in the table with the appropriate number of meters described in scientific notation below. Human cells come in a wide variety of shapes and sizes. Calculate the density of an average human cell. Read and Understand: We are given an average cellular mass and volume as well as the formula for density. We are looking for the density of an average human cell. The following video provides an example of how to find the number of operations a computer can perform in a very short amount of time.

Unlike the previous example, the distance between the earth and the sun is massive, so the numbers you will work with have positive exponents. If the sun is [latex]1. Write your answer in scientific notation. Think about the difference between 10 dollars and dollars. Any one who has balanced a checkbook knows that one zero can make a big difference in the value of the number. In the same way, 0. Though either one is probably more money than most of us will ever see in our checkbooks!

Negative exponents indicate negative powers of 10, which are expressed as fractions with 1 in the numerator on top and the power of 10 in the denominator on the bottom. Every number can be expressed in Scientific Notation. In our first example, ,,, should be written as 2. In theory, it can be written as 20 x 10 10 , but by convention the number is usually written as 2. It is easy to see that all the variations above are just different ways to represent the same number:. This illustrates another way to think about Scientific Notation: the exponent will tell you how the decimal point moves; a positive exponent moves the decimal point to the right, and a negative one moves it to the left.

So for example:. Note that Scientific Notation is also sometimes expressed as E for exponent , as in 4 E 2 meaning 4. This method of expression makes it easier to type in scientific notation.

Sometimes the advantage of scientific notation is not immediately obvious. A number like is much easier to read in decimal form than in scientific notation:.