### Scientific Notation and Significant Figures

```2.2
Scientific Notation and Significant Figures
Scientific Notation:
In science, we deal with some very LARGE
numbers:
1 mole = 602000000000000000000000
In science, we deal with some very SMALL
numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
Imagine the difficulty of calculating the mass of
1 mole of electrons!
0.000000000000000000000000000000091 kg
x 602000000000000000000000
???????????????????????????????????
Scientific Notation:
A method of representing very large or very small
numbers in the form:
M x 10n


M is a number between 1 and 10
n is an integer
 300,000,000 = 3.0 x 108
 .000034 = 3.4 x 10-5
Scientific Notation Rules
• Only one number should be to the left of the
decimal
• This is wrong: 34.0 x 10-4
• This is wrong: .56 x 10-4
• This is correct: 7.2 x 10-4
• If the number goes down, the exponent goes up
• If the number goes up, the exponent goes down
.
2 500 000 000
9 8 7
6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end up so that one
number is to its left
Step #3: Count how many places you bounce the decimal
point (This is equal to n)
Step #4: Re-write in the form M x 10n
2.5 x
9
10
The exponent is the
number of places we
moved the decimal.
0.0000579
1
2
3
4
5
Step #1: Insert an understood decimal point (Decimal point is
given in this problem)
Step #2: Decide where the decimal must end up so that one number
is to its left
Step #3: Count how many places you bounce the decimal point
Step #4: Re-write in the form M x 10n
5.79 x
-5
10
The exponent is negative because
the number we started with was less
than 1.
Example:
The Distance From the Sun to the Earth is 93,000,000 miles
Step #1: 93,000,000.
Step #2: 93,000,000 = 9.3000000
Write numbers without zeros: 9.3000000 = 9.3
Step 3: Count how many places you moved your decimal and
make that your power of ten. (7 places)
Step 4: 9.3 X 107
Example
The Distance From the Sun to the Earth is 93,000,000 miles
93,000,000 - Decimal or Standard Form
9.3 X 107 - Scientific Notion
Practice Problems:

98,500,000 = 9.85 x 10?
9.85 x 107

64,100,000,000 = 6.41 x 10?
6.41 x 1010

279,000,000 = 2.79 x 10?
2.79 x 108
Practice Problems
Convert to scientific notation:
5400000
5.4 x 106
.000045
4.5 x 10-5
Scientific Notation to Standard Form
Move the decimal to the right - The number to the power
of 10.
Example:



3.4 x 105 in scientific notation
3.4 = 340000 (Move the decimal right five places)
340,000 in standard form
Practice Problems:

6.27 x 106
6,270,000

9.01 x 104
90,100

4.56 x 10-3
.00456
Significant Figures
The measurable units of a measuring device plus
one estimated digit.
Significant Figures

.Pacific -----------------------Atlantic
Practice Problems
•
•
•
•
•
•
34.007
.0078
234000
6700.100
4000.00
1.005
Pie Graph and Table
A pie chart is a circular chart divided into sectors, each
sector shows the relative size of each value.
Bar Graphs
A bar graph is a graph drawn using rectangular bars to
show how large each value is. (The bars can be horizontal
or vertical)
Line Graphs
A line graph is a graph that uses points connected by lines to
show how something changes in value (as time goes by, or
as something else happens).
```