Transcript Do now: Copy Homework A Tale Told by Tracks Due: Tomorrow

Note Pack #2
September 11, 2015
Aim: How to write very large
or very small numbers?
(Scientific Notation)
Do now: How many stars do you
think are in the universe?
About – 912,493,737,239,013,813
What is Scientific Notation?
1) Scientific notation is a simple way of writing very
large or very small numbers.
Example 1: There are 912493737239013813 stars in the
Universe or there are about 9.1 x 1017 stars
Example 2: There are about
7,000,000,000,000,000,000,000,000,000 atoms in
the human body or 7.0 x 1027 atoms in the human
body
Why do we use scientific notation?
1. Earth Science deals with a lot of large numbers.
•
It takes too long to write these numbers down
and too much space on paper to write.
•
Doing math problems with these numbers can
be very hard to do.
How do we convert large numbers
into scientific notation?
• Let’s use this number 93,000,000. The average distance
(in Miles) from the Earth to the Sun.
Step 1. – Move the decimal between the first and second
number. (count how many space you move it)
93000000
4
2
1
367
5
How do we convert numbers into
scientific notation? (cont)
Step 2. – drop all the number after the second
number. If there is a non zero number after the
second number then you must round up if the
number is 5 or higher.
93000000
4
2
1
367
5
How do we convert numbers into
scientific notation? (cont)
Step 3. – add “x 10” to the number
93 x 10
Step 4 – place the number of times you moved the
decimal to the power place next to the “10”
7
How do we convert small numbers
into scientific notation?
• When using very small numbers, the same steps
apply except, instead of a positive exponent we
use a negative exponent.
Example 1 – A grain of sand weighs 0.0000265
grams or 2.65 x 10-5 grams
Example 2 – A flea weighs .028 ounce or 2.8 x 10-2
ounce.
How do we convert small numbers
into scientific notation?
• Let’s use 0.000078125 ounce. – the weight of a
feather
Step 1 – move the decimal to the right until you
pass the first non zero number. (remember to
count the spaces)
0 000078125
4
2
1
5
3
How do we convert small numbers
into scientific notation?
Step 2 – Drop all the numbers before the first
whole number
0 000078125
4
2
1
5
3
How do we convert small numbers
into scientific notation?
Step 3 – add “x10” next to the number
78125 x 10
• Step 4 - place the number of times you moved the
decimal to the power place next to the “10”
• Step 5 – put a negative sign “-” in front of the
exponent
5
How do we convert scientific notation
into large numbers?
• Let’s use this number 2.4 x 105 miles. The average distance (in miles)
from the Earth to the Moon.
Step 1 – Drop the x10.
Step 2 – Move the decimal to the right the number of time the exponent
is.
Step 3 – Add the zero for each empty spot
5
24 0000
x 10
4
2
1
3
5
How do we convert scientific notation
into small numbers?
• Let’s use this number 3.1 x 10-4 grams. The average weight (in grams)
of an ant.
Step 1 – Drop the x10.
Step 2 – Move the decimal to the left the number of time the exponent
is.
Step 3 – Add the zero for each empty spot
00031 x
-4
10
4
2
1
3