Transcript Scientific Notation

Astronomy has really big
numbers
Distance between Earth and Sun
150000000000 meters
1500000000 kilometers
This is the closest star.
Distance To Next Closest Star
Alpha Centauri
41295206500000 kilometers
Or
41295206500000000 meters
Too big. Mind explosion.
What’s a better way?
4.12952065 × 1013 km
Or
4.365 light years
Scientific Notation
Turning a really big or really small
number into a number that is >1 but
<10
Scientific Notation
A number is written in two parts:
1. Just the digits (with the decimal point placed after
the first digit),
2. × 10 to a power
Example:
MX
N
10
2.75 x 103
3
x 10 = ????????
× 10 to a power puts the decimal point back where
it should be
(it shows how many places to move the
decimal point)
Examples:
3
2.75 x 10 = 2750.0
Another Example
How to do it
Step 1
• To figure out the power of 10, think
– "how many places do I move the decimal
point?"
How to do it
Step 2
• If the number is 1 or greater
– the decimal place has to move to the left
– the power of 10 will be positive.
• If the number is smaller than 1
– then decimal place has to move to the right
– the power of 10 will be negative:
Example
0.0055 would be written as
-3
5.5 × 10
Because
0.0055 = 5.5 × 0.001 = 5.5 × 10-3
Why not just write the number?
Scientific Notation is used for numbers that are
HUGE or
tiny
For example it is easier to write (and read)
• 1.3 × 10-9
Than
0.0000000013
So what do you think?
The distance from the earth to the sun
150000000000 meters
1500000000 kilometers
or
1.50 x 1011 m
Which one is easier to read?
Practice Problems
700 into Scientific Notation
= 7.0 × 102
•
• Both 700 and 7.0 × 102 have the same value, just shown
in different ways.