1. Scientific Notation

2. What is Scientific Notation?
Scientific notation is a way of expressing really big numbers or really small numbers.
It is most often used in “scientific” calculations where the analysis must be very precise.

3. Why use scientific notation?
For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form.

4. Scientific notation consists of two parts:
n x 10x
n: A number between 1 and 10
x: A power of 10
Are the following in scientific notation?

5. Changing standard form to scientific notation.

6. To change standard form to scientific notation…
Step 1: Place the decimal point so that there is one non-zero digit to the left of the decimal point.
Step 2: Count the number of decimal places the decimal point has ‘moved’ from the original number. This will be the power on the 10.

7. Step 3: If the original number was less than 1, then the power is negative. If the original number was greater than 1, then the power is positive.

8. Eg1) Write the following in scientific notation:
23,000,000,000
Step 1: Place the decimal point so that there is one non-zero digit to the left of the decimal point
Step 2: The decimal has moved 10 places to get a number between 1 and 10.
2.3  1010
Step 3: The original number is greater than 1, so power is positive.

9. Q1) Write the following in scientific notation:
5800
= 5.8  103

10. Eg 2) Write the following in scientific notation:
Step 1: Place the decimal point so that there is one non-zero digit to the left of the decimal point
8.11  10 -4
Step 2: The decimal has moved 4 places to get a number between 1 and 10.
Step 3: The original number was less than 1, so the power is negative.

11. Q2) Write the following in scientific notation:
=  10-4

12. Changing scientific notation to standard form.

13. To change scientific notation to standard form…
POSITIVE POWER
Move the decimal point to the RIGHT by the same number of places as the value of the index.
NEGATIVE POWER
Move the decimal point to the LEFT by the same number of places as the value of the index.
(Use zeros to fill in places.)

14. Insert zeros as the values for any places not filled by other digits

15. Example
Given: 8.6 x 107

16. Q3) Change the following to standard form
Given: 4.35 x 106 =

17. Example
Given: 2 x 10-3

18. Q3) Change the following to standard form
Given: 1.78 x 10-3 =