Scientific Notation

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Scientific Notation
A method for re-writing really, really big and
really, really small numbers as a power of ten.
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Really BIG numbers and really small numbers have
too many digits to fit on a calculator.
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• A number that is written in scientific notation
  must
• have . . .
• a decimal point after the first non-zero digit
  ex) 7.08
• a number in the tenths position ex)
  2.0
• be written as a product of a power of 10 ex)
  3.45x109

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BIG Numbers
1,000,000,000,000,000
To change this number to scientific notation,
the decimal point has to move to the right of the
first non-zero number.
The decimal point of any whole number is at the
end of the number.
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BIG Numbers
1,000,000,000,000,000
To get the decimal point to the new position
required for scientific notation, the decimal has
to travel 15 place values to reach the position
immediately to the right of the first non-zero
number. That means it has moved 15 multiples of
10 or . . .
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BIG Numbers
1 000000000000000
To get the decimal point to the new position
required for scientific notation, the decimal has
to travel 15 place values to reach the position
immediately to the right of the first non-zero
number. That means it has moved 15 multiples of
10 or . . .
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BIG Numbers
1,000,000,000,000,000
Disappear

• the decimal point is after the first non-zero
  digit
• a number is in the tenths position
• it is written as a product of a power of 10

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BIG Numbers
Convert to scientific notation.
Where is the decimal point in this number?
After the last zero.
Where does the decimal point need to move to?
Between the 1 and the 2.
How many place values will the decimal point move?
11
What is the answer?
9
BIG Numbers
Convert to scientific notation.

• the decimal point is after the first non-zero
  digit
• a number is in the tenths position
• it is written as a product of a power of 10

10
BIG Numbers
Convert to scientific notation.
Where does the decimal place need to move to?
Between the 6 and the 0.
How many place values will the decimal point move?
13
What is the answer?
11
BIG Numbers
Convert to standard form.
The exponent (8) tells you how many place values
needs to be put back into the number.
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BIG Numbers
Convert to standard form.
The exponent (11) tells you how many place values
needs to be put back into the number.
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SMALL Numbers
Convert to scientific notation.
Where does the decimal point need to move to?
Between the 1 and 2.
How many place values does the decimal need
to move? (Notice the decimal has to move to the
right)
-9
What is the answer?
14
SMALL Numbers
Convert to scientific notation.

• the decimal point is after the first non-zero
  digit
• a number is in the tenths position
• it is written as a product of a power of 10

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SMALL Numbers
Convert to scientific notation.
Where does the decimal point need to move to?
Between the 9 and the 0.
How many place values does the decimal point need
to move?
-5
What is the answer?
16
SMALL Numbers
Convert to standard form.
How many place values need to be put back
into the number?
-9
Notice that there is an extra zero for the ones
place value.
What is the answer?
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SMALL Numbers
Convert to standard form.
How many place values need to be put back
into the number?
-7
What is the answer?
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Adding Numbers in Scientific Notation
Remember - Whenever you add or subtract in math,
things must be the same.
To add or subtract decimal numbers, place values
must be the same. To insure this one must
convert both numbers to standard form first.
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Multiplying Numbers in Scientific Notation
Remember - When multiplying powers with the same
base you can add the exponents.
Reorder and regroup using the Commutative and
Associative properties of multiplication.
Follow PEMDAS.
What is the answer?
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Multiplying Numbers in Scientific Notation
Reorder and regroup using the Commutative and
Associative properties of multiplication.
Follow PEMDAS
What is the answer?
But wait, is this answer in scientific notation
form?
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Multiplying Numbers in Scientific Notation
Why is this not considered in the correct form?
The decimal point is not after the first non-zero
number.
If the decimal point has to move one more place
value to the right, what will happen to the
exponent on the power?
The exponent has to decrease one to move one
place value to the right.
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Multiplying Numbers in Scientific Notation
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Dividing Numbers in Scientific Notation
Remember - When dividing powers with the same
base just subtract exponents on those like bases.
Separate into two separate fractions.
Divide.
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Dividing Numbers in Scientific Notation
The result is . . .
But this in not in the correct form for
scientific notation. What needs to happen?
The answer is . . .
Decrease the exponent by 1