Name:________________________________________________________________________________Date:_____/_____/__________
Brain blitz/ warm-up
Get Homework out FIRST! Then, begin warm-up.
Fill-in-the-table:
1)
245,000,000,000
2)
6,050,000
3)
5.6 x 106
4)
4.02 x 104
5) Order the following from least to great:
8.02 x 102
Answer:
3.9 x 105
9.1 x 105
2.05 x 106
Today’s lesson . . .
What:
Scientific Notation with
Negative exponents
Why:
To convert between numbers
written in scientific notation (w/
negative exponents) and numbers
written in standard form.
Who remembers what it is?
We use scientific notation to write very
LARGE
___________________
or very __________________
small
numbers.
Scientific notation is a # written as a
multiplication
____________________________________
sentence.
• The leading factor MUST be a
number greater than or equal to 1,
ten (10)
but less than _____________.
• The second factor must be a
power
_________________
of 10.
Example: 2.5 x 10-5
What does it mean when the
exponent is negative?
It means that the # will be
SUPER SMALL– a
DECIMAL!!
From scientific notation . . .
Guided practice:
#
Scientific
Notation
Standard
Form
We need 3 zeros in FRONT!
1.
2.8 x 10 -4
0.00028
Count digits to the LEFT of decimal point! How many
extra zeros do we need?
We need 6 zeros in FRONT!
2.
4.05 x 10 -7
0.000000405
On YOUR OWN:
#
Scientific
Notation
Standard
Form
3.
9 x 10 -6
0.000009
4.
7.02 x 10 -5
0.0000702
From standard form . . .
As soon as you see a DECIMAL
number, think NEGATIVE
EXPONENT!!!!
Guided practice:
#
1.
2.
Scientific
Notation
3.4 x
10-5
Notice the negative
exponent!
1.02 x 10-4
We still need to move
decimal so that we
make a number bigger
than 1, but less than 10.
Standard
Form
5 jumps!
0 000034
0 000102
4 jumps!
3.
7 x 10-6
6 jumps!
0 000007
ON YOUR OWN:
#
Scientific
Notation
Standard
Form
4.
2.1 x 10-6
0.0000021
5.
4.05 x 10-3
0.00405
Mixed practice:
When do we need a positive exponent and when
do we need a negative exponent???
#
Scientific Notation
Standard Form
1
2.5 x 108
250,000,000
2
7.5 x 10-7
0.00000075
3
2.09 x 10-3
0.00209
4
5.723 x 109
5,723,000,000
5
3.6 x 104
36,000
6
9.004 x 107
90,040,000
7
5.9 x 10-6
0.0000059
8
7.2 x 10-3
0.0072
IXL HOmework
A.8 - Scientific Notation
A.9 - Compare Numbers Written in Scientific
Notation
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then you are done!
(Spend at least 10 minutes practicing.)
END OF LESSON
The next slides are student copies of the notes for this
lesson. These notes were handed out in class and
filled-in as the lesson progressed.
Math-7 NOTES
NAME:
DATE: ______/_______/_______
What: Scientific Notation with Negative Exponents
Why:
To convert between #’s written in scientific notation and #’s written in standard form.
What is it?
We use scientific notation to write very ____________________________ or
very _________________________ numbers.
Scientific Notation: a # written as a _____________________________ sentence.
•
The leading factor MUST be a number greater than or
equal to 1, but less than ________________.
•
The second factor must be a ________________________ of 10.
Example: 2.5 x 10-5
From scientific notation . . .
Count digits to the LEFT of decimal point! How many extra zeros do we
need? Place zeros IN FRONT!
examples:
#
Scientific Notation
1.
2.8 x 10 -4
2.
4.05 x 10 -7
3.
9 x 10 -6
4.
7.02 x 10 -5
Standard Form
From standard form . . .
We still need to move decimal so that we make a number bigger than
1, but less than 10. Remember to use a NEGATIVE exponent!!
examples:
#
Scientific Notation
Standard Form
1.
0.000034
2.
0.000102
3.
0.000007
4.
0.0000021
5.
0.00405
Mixed practice:
When do we need a positive exponent and when do we need a
negative exponent???
#
Scientific Notation
Standard Form
1
250,000,000
2
0.00000075
3
0.00209
4
5,723,000,000
5
3.6 x 104
6
9.004 x 107
7
5.9 x 10-6
8
7.2 x 10-3
NAME:__________________________________________________________________________
DATE: ______/_______/____________
EXIT TICKET
“Scientific Notation”
Fill in the table:
1)
702,200,000
2)
0.000438
3)
8.91 x 107
4)
5.1 x 10-7
5) Order the following from least to greatest:
1.9 x 108
4.4 x 106
9.25 x 103
6.05 x 108
Answer:
NAME:__________________________________________________________________________
DATE: ______/_______/____________
EXIT TICKET
“Scientific Notation”
Fill in the table:
1)
702,200,000
2)
0.000438
3)
8.91 x 107
4)
5.1 x 10-7
5) Order the following from least to greatest:
1.9 x 108
Answer:
4.4 x 106
9.25 x 103
6.05 x 108
NAME:__________________________________________________________________________
DATE: ______/_______/____________
INDIVIDUAL practice
“Scientific Notation”
Remember: A
really BIG # needs a
positive exponent.
A # less than one
needs a negative
exponent!
4.5 x 100 --because the decimal pt. does not need to move.
Continued . . .
SOL PREP