This document discusses scientific notation, which is used to write very large and very small numbers in a shorter way. Numbers are written as the product of a number between 1 and 10 and a power of 10. This allows numbers like 602 quintillion to be written as 6.02 x 1023 or numbers as small as 0.000000000000000000000000000911 grams to be written as 9.11 x 10-28. The document provides instructions for converting numbers to and from scientific notation using exponents and the calculator. It also covers adding, subtracting, multiplying and dividing numbers in scientific notation.

1. Scientific Notation
Really large,
and really small
numbers

2. Why?
Chemistry often deals with very large and
very small numbers.
There are
602,000,000,000,000,000,000,000
molecules of water in 18 mL
one electron has a mass of
0.000000000000000000000000000911 g
We need a shorter way of writing these
numbers

3. Standard Exponential Form
another name for scientific notation.
consists of two parts
a number between 1 and 10
multiplied by 10, raised to some power
602,000,000,000,000,000,000,000 =
6.02 x 1023
0.000000000000000000000000000911 g =
9.11 x 10-28

4. Putting a number into scientific
notation
determine how many times you have to
move the decimal place to make it into a
number between 1 and 10
3240000
use that as the power of 10
3.24 x 106

5. What is the number is smaller?
if you make the number bigger by
moving the decimal point, make the
exponent smaller and visa-versa
0.00045
4.5 x 10-4

6. Getting back to original number
Move the decimal point the same
number of times as the exponent
If the exponent gets bigger the number
gets smaller
Change 2.99 x 108
Change 4.87 x 10-3

7. Using your calculator
EE and EXP button stand for x 10 to the
4.5 x 10-4
push 4.5
push either EXP or EE
push 4 +/- or -4
see what your display says.

8. Practice these problems
(4.8 x 10 5 ) x (6.7 x 10-6)
 (6.8 x 10 -6)
(3.2 x 10 4)
Remember when you multiply you add
exponents
106 x 10-4
When you divide you subtract
exponents.

9. Adding and Subtracting
You can’t add or subtract numbers until
they are to the same power of ten.
Your calculator does this automatically.
(4.8 x 10 5 ) + (6.7 x 106)
(6.8 x 10 -6) -(3.2 x 10-5)
Remember- standard form starts with a
number between 1 and 10 to start.

10. PEMDAS
  
 
3 3
4
2.4 10 4.8 10
1.2 10
 


 
  
3
4 3
4.8 10
1.2 10 2.4 10



 

11. PEMDAS
  
 
3 3
4
2.4 10 4.8 10
1.2 10
 


 
  
3
4 3
4.8 10
1.2 10 2.4 10



 