SCIENTIFIC NOTATION DAY 1
• Learn Vocabulary Terms
• Identify Vocabulary terms in problems
• Understand why Scientific Notation is used
• Identify numbers written in Scientific notation
& be able to explain why or why not
SCIENTIFIC NOTATION VOCABULARY
Scientific Notation: A way of expressing very large
or very small numbers more
easily using a power of 10
EX: 35,700 = 3.57 x 104
Standard Form:
EX: 35,700
The “normal” regular way
we write a number
SCIENTIFIC NOTATION VOCABULARY
Finite decimal: every whole number
EX: 5, 78, 90 (any number between 1 & 9)
Leading digit: the leftmost digit : single, NON-ZERO
number to the left of the decimal
EX: 6.5
9.0
Order of
magnitude:
2.34
The exponent used to
show the power (magnitude of 10)
It basically tells us how many times to move
the decimal left or right.
EX: 105 = 1.00000
http://www.mathsisfun.com/numbers/scientific-notation.html
HOW DO I KNOW IF IT’S SCIENTIFIC NOTATION?
1) Must be written as a PRODUCT (X’s)
EX: 3.6 x 103
2) The LEADING DIGIT must to the left of the decimal and
be a WHOLE number between 1 & 9
EX: 3.6 x 103
3) There must be a order of magnitude (power of 10)
EX: 3.6 x 103
EXIT TICKET
• IDENTIFY :
Leading digit
Order of magnitude
Product sign
7.8 x
6
10
SCIENTIFIC NOTATION DAY 2 & 3
• Identifying large vs. small numbers by the
placement of the zeros.
• Using zero placement to tell us which direction
the decimal is moved from the leading digit
• Identify if the power of 10 is positive or negative
by the zeros
• Know why we use it
DO NOW
WHICH NUMBER IS THE SMALLER NUMBER &
WHICH NUMBER IS THE LARGER NUMBER?
0.000000089
OR
8,000,000
BE PREPARED TO EXPLAIN/SHARE YOUR CHOICES.
SCIENTIFIC NOTATION BASICS
• Scientific Notation is a way of expressing very
large or very small numbers in an easier way.
Large numbers often have MANY zeros at the end.
EX: 450,000,000
Small numbers have the zeros at the beginning.
EX: 0.000000032
VERY SMALL OR VERY LARGE
• Identify each number as very small or very large:
1) 0.000015
SMALL LARGE
2) 6,000,000
SMALL LARGE
3) 0.00000901
SMALL LARGE
USE/THINK ABOUT
WHAT YOU ALREADY KNOW…
• What do you already know about the placement
of these zeros?
• What does the direction (left; before OR
right; after) they tell us about the numbers?
• HINT: Think about the number line or the
decimal place value chart
WE KNOW……
*ALL of these will help you understand
SCIENTIFIC NOTATION!!!
DO NOW
1) Please write HW in your planners
2) With the people at your tables, complete
the review sheet on your desks.
REVIEW
Vocabulary: Match the term with its definition.
____large numbers
A) have zeros at the beginning
____ leading digit
B) exponent that shows power of 10
____ order of
magnitude
C) have zeros at the end
____ small number
D) leftmost digit : single, NON-ZERO
number to the left of the decimal
Use the expression below to answer the questions:
7.98 x 10 6
The 7 is called the _________________
10 6 is the ______________
The “x” is the _____________
PRODUCT
WORD BANK
ORDER OF MAGNITUDE
leading digit
IDENTIFY which is NOT written in scientific
notation and give a reason why
06.9 x 103
9.7 x 52
7.89 x 104
Identify each number as very small or very large:
1) 0.000025
SMALL LARGE
2) 9,000,000
SMALL LARGE
3) 0.00000745
SMALL LARGE
Writing numbers in Scientific Notation
• Identifying large vs. small numbers by the
placement of the zeros.
• Using zero placement to tell us which direction
the decimal is moved from the leading digit
• Identify if the power of 10 is positive or negative
by the zeros
How to Do it:
Writing large numbers in Scientific Notation
• To figure out the power of 10, think "how many
places do I move the decimal point?“
• If the number is 10 or greater, the decimal point
has to move to the left, and the power of 10 will
be positive; large number
VIDEO
http://learnzillion.com/lessons/1177-write-large-numbers-in-scientific-notation
EXAMPLE:
Write 4,250,000,000 in scientific notation
4.250000000.
4.250000000.
9 places
4.25 x
109
Move the decimal so that only 1 digit is
to the left of the decimal
Count the number of spaces that
the decimal has to be moved to the
RIGHT.
Write the number WITHOUT ending
the zeros, & multiply by the correct
power of 10
Let’s PRACTICE
Write each number in scientific notation:
1) 68,000
2) 73,280,000
How to Do it:
Writing Small numbers in Scientific Notation
• To figure out the power of 10, think "how many
places do I move the decimal point?“
• If the number is smaller than 1, the decimal point
has to move to the right, so the power of 10 will
be negative; small number
VIDEO
http://learnzillion.com/lessons/1255-write-small-numbers-in-scientific-notation
EXAMPLE:
Write 0.0000000425 in scientific notation
0.00000004.25
Move the decimal so that only 1
NON ZERO digit is to the left of the decimal
0.00000004.25
Count the number of spaces that
the decimal has to be moved to the
LEFT.
8 places
4.25 x
10-8
Write the number WITHOUT beginning
the zeros, & multiply by the correct
power of 10 AND use a NEGATIVE
exponent to move the decimal to the left.
Let’s PRACTICE
Write each number in scientific notation:
1) 0.0038
2) 0.0000004
Check!
After putting the number in Scientific Notation,
just check that:
• The "digits" part is between 1 and 10 (it can
be 1, but never 10)
• The "power" part shows exactly how many
places to move the decimal point
EXIT TICKET
Write the following in scientific notation:
1) 53,000
_______________
2) 0.0082
_______________
Name:_______________________
Date:_____________________
CLASSWORK M1L9 BASIC SCIENTIFIC NOTATION
LEFT
NEGATIVE
RIGHT
POSITIVE
Write each number in scientific notation:
ORIGINAL NUMBER
PLACE DECIMAL & MOVE IN CORRECT DIRECTION
FINAL ANSWER
420,000
0.002
4.2 0 0 0 0
4.2 x 105
2 x 10-3
30,000,000
0.00037
804,000,000
13,060,000,000,000
0.0000506
0.000000005507
45,000,000
5,840,000
0 .0 0 2 .
SCIENTIFIC NOTATION DAY 4 & 5
• Use knowledge of decimal movement &
scientific notation to convert
:
• Convert FROM scientific notation TO
standard form with positive & negative
exponents
HOW TO USE THE CALCULATOR
1) On
2) Clear
3) Enter the standard form number
4) Press blue “2nd “ key
5) Press “DRG” ( SCI/ENG)
6) Using the right/left arrow keys choose:
“FLO” for standard form
“ SCI” for scientific notation
*if you want to go back to choose another form
repeat steps 5 and 6 and then press enter twice
http://www.youtube.com/watch?v=BW55IniDb2g&list=PL698BE8091CA9C622
SCIENTIFIC NOTATION VOCABULARY
Scientific Notation: A way of expressing very large
or very small numbers more
easily using a power of 10
EX: 35,700 = 3.57 x 104
Standard Form:
EX: 35,700
The “normal” regular way
we write a number
CONVERTING FROM SCIENTIFIC
NOTATION TO STANDARD FORM
It’s EASY!!!!
ALL you do is work BACKWARDS…
SMARTEXCHANGE
EXAMPLE: WITH A POSITIVE EXPONENT
Write 7.035 X 106 in STANDARD FORM
The exponent is a 6 and
it is positive
Move the decimal 6
places to the RIGHT
7.035000.
6 places
7,035,000
• Study the exponent
• Move the decimal point
the Correct number of
places to the right
• Add any necessary zeros at
the END of the number as
place holders
• Write the number in
standard form
http://www.youtube.com/watch?v=8bUvkPYXjco
LETS PRACTICE
SCIENTIFIC
NOTATION
5.3 x 104
9.24 x 108
1.205 x 105
DECIMAL
MOVEMENT
STANDARD FORM
EXAMPLE: WITH A NEGATIVE EXPONENT
Write 4.16 x 10-5 In STANDARD FORM
The exponent is a -5
and it is negative
Move the decimal 5
places to the LEFT
0.00004.16.
5 places
0.0000416
• Study the exponent
• Move the decimal point
the correct number of
places to the left
• Add any necessary zeros at
the BEGINNING to fill up
to the decimal point
• Write the number in
standard form
http://www.youtube.com/watch?v=8bUvkPYXjco
LETS PRACTICE
SCIENTIFIC
NOTATION
7.1 x 10-4
5.704 x 10-6
8.65 x 10-2
DECIMAL
MOVEMENT
STANDARD FORM
EXIT TICKET
Suppose the table below displays data for the
Top prime-time television shows for a given week
the year. Complete the empty columns in table by
converting the number of households into either
scientific notation OR standard form.
NAME OF SHOW
The Voice
NUMBER OF HOUSEHOLDS
STANDARD FORM
15,553,000
Duck Dynasty
The Simpsons
NUMBER OF HOUSEHOLDS
SCIENTIFIC NOTATION
1.4623 x 107
0.0865
HOMEWORK
• SCIENTIFIC NOTATION PUZZLE
http://www.youtube.com/watch?v=QarMTT5YweQ&list=PL698BE8091CA9C622