Transcript Scientific Notation PowerPoint

BIG
NUMBERS
and
SMALL NUMBERS
(Scientific Notation)
In science, you sometimes have to deal
with very LARGE numbers
How far is the
sun from
the earth?
150,000,000,000
meters
Or there may be times that you’ll use very
small numbers…
How wide is
one atom of
gold?
0. 000 000 000 274
meters
Scientific notation is a
system used to avoid
dealing with all the ZEROS
in very big and very small
numbers
In scientific notation, numbers
have TWO parts
n
{ a number
between 1-10
that may be
followed by
decimals}
X
10 x
a power
of 10
How do you write numbers in
scientific notation?
Problem
Write 150,000,000,000 in
scientific notation:
Step 1 Move the decimal point from its
original position until it is behind first
nonzero digit (1) . This gives you a number
between 1 and 10.
150 000 000 000.
From here
To here
The number becomes 1.5
Step 2
Count the number of places that the
decimal point moves to the left; this
becomes the positive exponent
150 000 000 000.
(The decimal pt. moves 11 places;
the exponent of 10 must be 11)
Answer: 1.5 x 1011
As you can see, there are two
ways to write the SAME number
150 000 000 000
(standard notation)
or
1.5 x 1011
(scientific notation)
Problem: Write 0.000 000 000 274
in scientific notation
Step 1 Move the decimal point from its original
position until it is behind first nonzero digit (2).
This gives you a number between 1 and 10.
0.000 000 000 274
From here
To here
The number becomes 2.74
Step 2
Count the number of places that the decimal
point moves to the right ; this becomes the
negative exponent
0.000 000 000 274
(The decimal pt. moves 10 places; the
exponent of 10 must be 10)
Answer: 2.74 x 10-10
Again, there are obviously two
ways to write this small number.
0.000 000 000 274
(standard notation)
or
2.74 x 10 -10
(scientific notation)
Remember
Big numbers have
positive exponents
Small numbers have
negative exponents
Now let’s practice !
Write 45 880 000 in
scientific notation.
Correct answer is:
4.588 x 107
Let’s try another one…
Write 0.000 005 397 in
scientific notation.
Correct answer is:
5.397 x 10-6
You’re on your own…
Write these numbers in scientific notation:
(1) 6,700
(2) 123,000
(3) 0.0089
(4) 9,362,000
(5) 0.000 008 75
One more thing
Be sure you also know how to change a
number in scientific notation back to
standard form.
For example:
Scientific notation: 8.32 x 10 4
How do you write this number in
standard form?
Answer: Standard form: 83 200
How do you change numbers in
scientific notation to standard form?
Big numbers
For numbers with positive exponents
Move the decimal point from its current
position to the right. The number of decimal
places moved must be the same as the
exponent. Fill the spaces with zeros.
6.33 x 10 5
From here
…. move decimal point 5 places to
the right (you need to write 3 zeros)
Answer: 633 000
Shall we give it a try?
Change 5.02 x 106 to standard form
5.02 x 106
Move the decimal point 6 places to the right
You will need to write in 4 more zeros
Answer: 5020000 or 5 020 000
Small numbers
For numbers with negative exponents
Move the decimal point from its current
position to the left. The number of decimal
places moved must be the same as the
exponent. Fill the spaces with zeros.
7.88 x 10-4
From here …. move decimal point 4
places to the left (you need to write 3 zeros)
Answer: .000788
Let’s try this problem…
Change 9.12 x 10-3 to standard form
9.12 x 10-3
Move the decimal point 3 places to the left
You will need to write 2 more zeros
Answer: .00912 or .009 12
Arrange these numbers from
the largest to the smallest.
6.5 x 104
5.8 x 10-3
9.2 x 10-2
4.17 x 108
- 3.4 x 105
7.01 x 10-1
2.2 x 106
Multiplying Numbers in
Scientific Notation
(4.2 x 103 ) ( 6.01 x 104 )
1) Multiply the first factors :
(4.2 x 6.01)
2) Add the powers of 10:
103+4
ANSWER: 25.2 x 107
Dividing Numbers in
Scientific Notation
(3.0 x 105 ) / (6.0 x 102 )
1) Divide the first factors:
3.0 / 6.0
2)
Subtract the powers of 10
10 5 – 2
ANSWER: 0.5 x 103 = 5.0 x 102
Adding and Subtracting
Numbers in Scientific Notation
If you are adding and subtracting numbers in
scientific notation without a calculator:
first,adjust the numbers so that the exponents
are the same
( 5.4 x 103 ) + ( 8.0 x 102 )
1) Adjust second number
8.0 x 102 = 0.8 x 103
2) Add the two numbers
(5.4 x 103 ) + (0.8 x 103 )
ANSWER: 6.2 x 103