Download Scientific Notation workshop

Catalyst – January
2
(6 -(2*5),
2010
Describe the pattern you see in the first 5. After, fill in the 6th answer.
1) 3,450,000.= 3.45 x 106

2) 1,240,000,000.= 1.24 x 109
3) 0.000072 = 7.2 x 10-5
4) 0.00000837 = 8.37 x 10-6
5) 8370000.= 8.37 x 106
6) 273000. = _________________________
Today’s Agenda





Catalyst
Scientific Notation Practice
Intro to Dimensional Analysis
Practice!
Exit Question
Today’s Objectives

SWBAT write numbers like a scientist/G.

SWBAT convert units like a scientist/G.
Problem


When scientists are talking about light
wavelengths, they are usually discussing
nanometers, which is 10-9 meters or
0.00000001 meters.
When scientists are talking about distances in
space, they are usually discussing
astronomical units (AU). 1 AU is 93,000,000
miles.
Problem


I don’t know about you, but I ain’t about to write all
them zeros.
SCIENTIFIC
If only there was a way to fix this…
NOTATION!!!!
Notes – Scientific Notation
Key Point #1 : Scientific notation is a way of
abbreviating very large or very small
numbers.
Exponent
3.03 x
Number
6
10
3 Parts!
Power of 10
Scientific Notation
Key Point #2: A number in correct scientific
notation has only one non-zero number to
the left of the decimal.
3.03 x
6
10
How to write numbers in scientific notation
Move it to the left or move it to the right
Add your exponent
Then it’s aaaaaalright!
Big Numbers  Scientific Notation
Let’s get rid of them zeroes at the end!
 To do this, move the decimal point to the
LEFT (to the left)
3 2 4 0 0 0 0 0.
Big Numbers  Scientific Notation
How many times do we move the decimal
to the LEFT (to the left)?
3 2 4 0 0 0 0 0.
Big Numbers  Scientific Notation
…the decimal moves SEVEN times
to the LEFT.
3.2 4 0 0 0 0 0
Big Numbers  Scientific Notation
So, how do we use that number 7???
3.2 4 x
0
7
10
00
00
Big Numbers  Scientific Notation
How many times do we move the decimal
to the LEFT (to the left)?
3 2 4 0 0 0 0 0.
Small Numbers  Scientific Notation
Let’s get rid of them zeroes at the front!
 To do this, move the decimal point to the
RIGHT (to the right)
0. 0 0 0 0 0 2 6
Small Numbers  Scientific Notation
How many times did we move the decimal
to the RIGHT (to the right)?
0. 0 0 0 0 0 2 6
Small Numbers  Scientific Notation
…the decimal moves SIX times to the
RIGHT (to the right).
0 0 0 0 0 0 2. 6
Small Numbers  Scientific Notation
So how do we use that number 6???
-6
10
x 0 0 0 2. 6
000
Positive and Negative Exponents

Key Point #3:
If
the number is BIG then the
exponent is
POSITIVE; if the
number is small then the exponent
is NEGATIVE.
Positive Exponent
Every time you move the decimal to the RIGHT,
exponent DECREASES by 1.
5. 6 x
2
3
10
Positive Exponent
5 6. 0
x 10
1
2
Positive Exponent
5 6 0. 0 x 10
Final answer: 5600
0
1
Negative Exponent
Every time you move the decimal to the LEFT,
exponent INCREASES by 1.
0
-1
3 .8 x 10
Final answer: 0.38
Scientific Notation
2250000
Scientific Notation
2.250000
2.25 x
6
10
Scientific Notation
10 300 000 000
Scientific Notation
1.0300000000
1.03 x
10
10
Scientific Notation
.000055
Scientific Notation
00005.5
5.5 x
-5
10
Scientific Notation
Think of a number-line:
-10 -5
0
5
10
Adding/taking 0’s on right is +
Adding/taking 0’s on left is -
Scientific Notation
9870000
.00000987
Scientific Notation
9870000
.00000987
9.87 x
6
10
9.87 x
-6
10
Scientific Notation
8.1 x
3
10
9.4 x
-2
10
Scientific Notation
8.1 x
3
10
8100
9.4 x
-2
10
.094
CONVERSIONS

GET READY FOR AWESOME!
Convert it like it’s hot

Key Point #1:
A
conversion factor shows the same value with two
different units.
 YOU
ALREADY KNOW THIS STUFF!
 Examples:
 10
dimes= 1 dollar
 20 nickels= 1 dollar
 4 quarters= 1 dollar
Dimensional Analysis

Key Point #2:
Dimensional
analysis is a tool
used to convert from one unit to
another.
Working on the Railroad

Step 1:
 What

Step 2:
 Write

to what?
conversion factor(s)
Step 3:
 Train
tracks
Practice! One-step problems.


How many meters are in 10
centimeters?
How many centimeters are in 327
meters?
Practice! On your own!
The distance from New
Orleans to Denver is 2258
kilometers. Convert this to
meters!

Always remember…

Key Point #3:
In
two step problems, always convert to
the unit without a prefix first.
Mass:
grams
Distance: meters
Volume: liters
Temperature: degrees Celsius
Practice…


Chris Paul has a mass of 79.4 kg,
convert this to mg.
*Bonus: If a standard basketball has a
mass of 620, 000 mg, how many
basketballs would equal the mass of
Chris Paul?
Practice


There are 1135 decaliters (daL)
in a pool. Convert to liters (cL).
10 L = 1 daL
Practice!
The average human eye
blink is 300 milliseconds.
Convert this to
hectoseconds.

Exit Question

In July 2008, it was estimated that the
world’s population is about
6,707,000,000. The United States’
population was estimated to be
304,060,000. The coldest temperature
ever created by man is .000000005°K.
Write these 3 numbers in scientific
notation.