Scientific Notation

         Last week’s subject was about scientific notation. It is funny how memory works because I remembered everything that I learned 12 years ago, and I felt confident with the subject. Today, I will show you guys how large or small numbers can be written in a simpler format.

IN SCIENTIFIC NOTATION, you move the decimal place until you have a number between 1 and 10. Then you add a power of ten that tells how many places you moved the decimal.

If the number is 10 or greater, the decimal point has to move to the left, and the power of 10 will be positive.

1. Example

Lets say you have a number 145, this is not a very large number, but it will work nicely for an example.

 145 you can write as 1.45 x 100=145 or 1.45 × 10²  =145 because 10² =100

In scientific notation 145 is written as 1.45 × 10²

2. Example

Write 9800000 in scientific notation

9800000 = 9.8 x 1000000 or 9.8 x 10⁶ because 10 x10 x10 x10 x10 x10=1000000

How did I know that the number 9.8 x 1 0 0 0 0 0 0 will give me 9800000?

                                                                6   5  4   3   2   1           

9  8  0  0  0  0  0     

    6    5    4     3     2     1    I moved the decimal point six places to the left until I had a number between 1 and 10 (in this case I get 9.8)

If the number is smaller than 1, the decimal point has to move to the right, so the power of 10 will be negative

3. Example

Write 0.010 in scientific notation (the number is smaller than 1)

•    First, move the decimal place until you have a number between 1 and 10. If you keep moving the decimal point to the right in 0.010 you will get 1.0

•    Next, count how many places you moved the decimal point. You had to move it 2 places to the right to change 0.010 to 1.0; you can show that you moved it 2 places to the right by noting that the number should be multiplied by 10^-2.

0 . 0 1 0   so 1.0 x10^-2 = 0.010

        1   2

Summarizing

•  The "digits" part is between 1 and 10 (it can be 1, but never 10)

•  The "power" part shows exactly how many places to move the decimal point

•  Left Is Positive and Right Is Negative; remember LIP or RIN