1. Scientific Notation

2. Scientific Notation In science, we deal with some very LARGE numbers:
1 mole =
In science, we deal with some very
SMALL numbers:
Mass of an electron = kg

3. M x 10n Scientific Notation
Scientific Notation is a method of representing very large or very small numbers in the following form:
M x 10n
Where M represents a number between 1 and 10
Where n is an integer

4. Scientific Notation: Very Large Numbers
Step 1: Insert an understood decimal point
Step 2: Decide where the decimal point must end so there is one number to its left

5. Scientific Notation: Large Numbers
Step 3: Count how many places you move the decimal point
Step 4: Re-write in the form M x 10n
2.5 x 109

6. Scientific Notation: Very Small Numbers
Step 2: Decide where the decimal must end so there is one number to the left

7. Scientific Notation: Very Small Numbers
Step 2: Decide where the decimal must end so there is one number to the left

8. Scientific Notation: Very Small Numbers
Step 3: Count how many places you want to move the decimal point

9. Scientific Notation: Very Small Numbers
Step 3: Count how many places you want to move the decimal point

10. Scientific Notation: Very Small Numbers
Step 4: Re-write in the form M x 10n
5.79 x 10-5
The exponent is negative because we started with a number less than 1

11. Scientific Notation: Adding and Subtracting
If the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.
4 x 106
+ 3 x 106
7 x 106

12. Scientific Notation: Adding and Subtracting
If the exponents are not the same, we must move a decimal to make them the same.
4 x 106
+ 3 x 105

13. Scientific Notation: Adding and Subtracting
Move the decimal on the smaller number
4.0 x x 106
x x 106
4.3 x 106

14. Scientific Notation: Adding and Subtracting
A problem for you to try:
2.37 x 10-6
x 10-4

15. Scientific Notation: Adding and Subtracting
Here’s the answer:
x 10-4
x x 10-4

16. Scientific Notation: Multiplying and Dividing
Here’s how we multiply scientific notation:
(2 x 106) x (7 x 103)
Step 1: Multiply the base numbers
2 x 7 = 14

17. Scientific Notation: Multiplying and Dividing
Here’s how we multiply scientific notation:
(2 x 106) x (7 x 103)
Step 2: Add the exponents
106+3 = 109

18. Scientific Notation: Multiplying and Dividing
Here’s how we multiply scientific notation:
(2 x 106) x (7 x 103)
Step 3: Put the numbers back together
(2 x 106) x (7 x 103) = 14 x 109

19. Scientific Notation: Multiplying and Dividing
Here’s how we divide scientific notation:
(12 x 106) ÷ (4 x 103)
Step 1: Multiply the base numbers
12 ÷ 4 = 3

20. Scientific Notation: Multiplying and Dividing
Here’s how we divide scientific notation:
(12 x 106) ÷ (4 x 103)
Step 2: Subtract the exponents
106-3 = 103

21. Scientific Notation: Multiplying and Dividing
Here’s how we divide scientific notation:
(12 x 106) ÷ (4 x 103)
Step 3: Put the numbers back together
(12 x 106) ÷ (4 x 103) = 3 x 103