scientific notation the basics and some math.. take out your calculator. write these calculations...
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Scientific NotationThe basics and some math.
Take out your calculator. Write these calculations and the answer in
your notes:
12,922,341 / 0.011 435 7 =
1,130,000,000
0.05 / 20,111 =
0.000 002 486
Re-writing numbers in SCIENTIFIC NOTATION makes it so we don’t
have to deal with all of these “extra” zeros.
Scientific Notation(Exponential Notation)
Scientific Notation is used to express any number as: a number between 1 and 10
(called a coefficient) multiplied by 10
(the “base” as in “base 10”) raised to a power
(indicated by an exponent)
9.13x108
9.13E8
coefficient = 9.13
exponent = 8
What is it?
First, let’s review exponents
Count the “0”s
10 = 10 (x 1) = 101 1 100 = 10 x 10 = 102 2 1,000 = 10 x 10 x 10 = 103 3 10,000 = 10 x 10 x 10 x 10 = 104 4
The number in the exponent tells you how many times ten is multiplied by itself.
Reviewing Exponents
Any number raised to the 0 power – or has a 0 in the exponent = 1.
So, 100 = 1
Scientific NotationBase 10 cont.
109 would equal a 1 followed by how many zeros?
9 1,000,000,000
What would 1.13 x 109 be if written in “long form?”
Move the decimal place to the right 9 places. 1,130,000,000
What does this really mean?
When you have a positive exponent, move your decimal to the right
the same number of places that are in the
exponent.
Let’s rewrite the first number we calculated in scientific notation.
12,922,341 / 0.011 435 7 =
1,130,000,000
1.13 x 109
Scientific NotationBase 10 – negative exponents
If the exponent is negative, think division.
10-1 = 1/(10) = 0.1 10-2 = 1/(10 x 10) =1/(100) = 0.01 10-3 = 1/(10 x 10 x 10) = 1/(1,000) =
0.001 10-4 = 1/(10 x 10 x 10 x 10)= 1/(10,000) =
0.0001
What does this really mean?
Move the decimal point to the left if you have a
negative exponent.
Let’s rewrite our second number in scientific notation.
0.05 / 20,111 = 0.000 002 486
Coefficient = 2.486 The decimal would have to be moved to
the left 6 places, so our exponent will be -6.
2.486 x 10-6
Now give it a try with a partner. You have 5 minutes.
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