Transcript Scientific Notation

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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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