# Phys Scientific Notation

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SCIENTIFIC NOTATION
Machart Physics
Why do we use Scientific Notation
Mass of the Earth is :
5,972,000,000,000,000,
000,000,000 kg
Mass of a Proton is:
0.00000000000000000
00000000016726219 kg
It is called Scientific Notation because:
■ Our numbers
are based on
units of 10.
■ Our Standard
Units are based
on units of 10
Example: 5.4 x 10^7
What are we really saying?
8 x 10^5
8 x 10 ^-5
■ 8 x 10 x 10 x 10 x 10 x 10
■
8
______________________________
10 x 10 x 10 x 10 x 10
But we can also look at it as a decimal
point mover.
3.25 x 10 ^ 2
68.5 x 10 ^-2
When the
exponent is
Positive the
number is getting
bigger.
When it is negative
the number is
getting smaller.
Zeros can always be place holders.
5.2 x 10 ^ -3
3.25 x 10 ^3
Convert 61,425 to Scientific Notation
REVERSE!
Step
1. Note where the
decimal is now.
61,425
Step 2 Note where you want
the decimal to be (You want a
number between 1 and 9
Step 3 If you have made the
number smaller, it will be the
exponents job to make it
bigger so you need a positive
number.
If you have made the number
bigger then the exponents job
is to make it smaller so you
need a negative exponent.
0.2134
What if I’m adding or subtracting two
numbers in Scientific Notation?
■ 1. Use a calculator. (It’s funny…. But I’m serious) Then the exponents don’t matter.
■ 2. If you must do it by hand: Your exponents must match.
– 3.2 x 10^3 + 4.7 x 10^3 = YES This is okay. You just add the base numbers
and then put the same x10^3 on them.
– 4.5 x 10^2 + 3.5 x 10 ^3 = NO This is NOT okay. You must convert one of
them to match the other
– Here’s how you do that….
You can always just write
out the number and convert
it back.
OR
If you are making the
exponent smaller then the
decimal moves to the right.
If you are making the
exponent bigger then the
decimal moves to the left
■ 4.5 x 10^2 + 3.5 x 10 ^3
But Multiplication and
Division are way easier.
■ 3 x 10^4 * 2 x 10^6
Multiplication: Just multiply