1. 5.1 - Scientific Notation & Units
Measurements & Calculations
5.1 - Scientific Notation & Units

2. Scientific Notation
Allows us to write very big and very small numbers

3. Scientific Notation
Every number written in scientific notation has two basic parts. 
The coefficient (first part) is always a decimal number between 1.00 and 9.99…
The second part is 10 times some exponent

4. Scientific Notation 3.42 x 106 or 8.005 x 10-3
Notice that in each of these, the coefficient is a decimal number between 1.00 and 9.99…

5. Scientific Notation 3.42 x 106 means
3.42 x (10 x 10 x 10 x 10 x 10 x 10)  
or 3,420,000

6. Scientific Notation 8.005 x 10-3 means 8.005 x (0.1 x 0.1 x 0.1)
 or

7. Scientific Notation
the exponent on the 10 tells you which direction to move the decimal and how many times it should be moved.
POSITIVE EXPONENT means > 1 (right)
NEGATIVE EXPONENT means < 1 (left)

8. Scientific Notation
Can I change standard notation to scientific notation?
Let's say you wanted to convert the following number to scientific notation:

9. Scientific Notation The first part has to be between 1.00 and 9.99...
Move your decimal until you have a number that qualifies
7.82

10. Scientific Notation
Remember that the exponent tells you the number of spaces that you moved it.  So the answer is either
7.82 X 106 or 7.82 X 10-6

11. Scientific Notation
A standard notation number LOWER than 1 means NEGATIVE exponent
A standard notation number GREATER than 1 means POSITIVE exponent

12. Scientific Notation
1) 3,400 2) ) 101,000 4) 0.010

13. Exponential Notation
A numerical system in which numbers are expressed in the form A × 10n where A is a number with a single nonzero digit to the left of the decimal place and n is a whole number.
A is the coefficient
n is a whole number 13

14. Converting from Decimal to Scientific Notation
The decimal point in the decimal number is moved to the position behind (to the right of) the first nonzero digit.
The exponent for the exponential term is equal to the number of places the decimal point has moved.
300. written as 3.00 × 102 (three sig figs)
written as × 10–3 (four sig figs) 14

15. Multiplication Using Scientific Notation
(2.5 x 104)(2.0 x 102) =
Multiply the coefficients
2.5 x 2.0 = 5.0
Add the exponents
= 106
Ans: x 106

16. Division Using Scientific Notation
(6.0 x 105) (2.0 x 102) =
Divide the coefficients
= 3.0
Subtract the exponents
105 ̶ 102 = 103
Ans: x 103 : :

17. Addition Using Scientific Notation
(2.0 x 103) + (2.0 x 102) =
Convert so that all exponents are the same
2.0 x 102 = 0.20 x 103
Add coefficients
x 103
x 103
Ans: x 103

18. Addition Using Scientific Notation
(4.0 x 107) ̶ (8.0 x 105) =
Convert so that all exponents are the same
8.0 x 105 = x 107
Subtract coefficients
x 107
̶ x 107
Ans: x 107

19. Scientific Notation
5) ) 1,000,000 7) ) 4.50

20. Homework Complete Scientific Notation Worksheet
Watch video on unit conversion