OBJECTIVE: Scientific Notation
the art of writing very large numbers
If it’s black, write it into your notes.
Get out some paper and a pencil or
pen NOW.
We can write numbers many ways.
For example the number one can be written as
100
200
2
100.0
2
All of these math
expressions means
This
last
one
is
called
that idea of
Scientific
Notation
“ONE”
1 x 10
We can write any number in scientific
notation, but it makes much more sense to
use it only for really, really big numbers (or
really small ones).
Let’s write these numbers in scientific notation
2,000,000 _________________________________
4,500,000,000 _______________________________
Let’s write these numbers in scientific notation
2,000,000 = 2 x 106
4,500,000,000 = 4.5 x 109
The rule is always write the numbers as a coefficient:
a decimal between 1.0 but less than 10.
Then, count how many places you moved the invisible
decimal and that’s how many times your power of ten
should be.
Let’s try three more big numbers to
scientific notation
55,000,000,000,000 ________________
3,450,000,000 ___________________
123,800,000 _____________________
Let’s try three more big numbers to
scientific notation
55,000,000,000,000 = 5.5 x 1013
3,450,000,000 = 3.45 x 109
123,800,000 = 1.238 x 108
We’ve discussed the crazy big numbers of measurements
like the distance of Neptune from the Sun.
That distance is 2,800,000,000 miles.
To say that number, we say: _________________________________________________
That number: 2,800,000,000 miles has an “INVISIBLE DECIMAL POINT” that I will add now
2,800,000,000. miles
Write this distance in scientific notation.
2,800,000,000. miles
is
2.8 x 109 miles
Now that we can, let’s
do a bunch of these
for practice. (ready?)
The distance between the Sun and the Earth is
93,000,000 miles ____________________
The distance between the Sun and Pluto is
4,800,000,000 miles ____________________
The diameter of the Sun is
870,000 miles _______________________
The number of water molecules in 1.0 liters of water is about
33,700,000,000,000,000,000,000,000
_____________________________
The distance between the Sun and the Earth is
93,000,000 miles 9.3 x 107 miles
The distance between the Sun and Pluto is
4,800,000,000 miles 4.8 x 109 miles
The diameter of the Sun is
870,000 miles 8.7 x 105 miles
The number of water molecules in 1.0 liters of water is about
33,700,000,000,000,000,000,000,000
3.37 x 1025 molecules
Change these to scientific notation as well…
4,560,000,000,000,000,000 ants in New York
____________________________________
3,400 pounds in a hippopotamus
______________________________
6,000,000,000 years the Earth has bee around
___________________________________
Change these to scientific notation as well…
4,560,000,000,000,000,000 ants in New York
4.56 x 1018 ants
3,400 pounds in a hippopotamus
3.4 x 103 pounds
6,000,000,000 years the Earth has bee around
6 x 109 years
Every Power of Ten is 10X bigger than the last one…
101 = 1 x 10 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10,000
105 = 10 x 10 x 10 x 10 x 10 = 100,000
106 =
10 x 10 x 10 x 10 x 10 x 10
107 =
10 x 10 x 10 x 10 x 10 x 10 x 10 =
= 1,000,000
10,000,000