Transcript Scientific Notation

Test on Numbers
th
7
Thursday
October
Surds
Index laws
Cubes and Squares
Scientific Notation
Quick Revisit- Surds
72
6 2
144
12
200
10 2

2 25
4 200

10
40 2
Quick check Index Laws
a


b
3
a
6
3b
4


7
3
Order each set of numbers from least to greatest (
ascending order)
Order each set of numbers from least to greatest ( ascending
order)- solutions
POWERS of 10
10  10
1
10  1010  100
2
10  1010  100
2
10 
1010101000
10 
1010101010000
3
4
 5
10 
 6
1010101010100000
10  1010101010101000000
10  10 10  100
2
100  10 10  10
2
200  2 100  2 10
2
2000  2  2101010 
 


2 10
3
Write 6 million as power of 10
Write 20000 as power of 10

Write 15000 as power of 10



 6000000  6 10
 2 10
 15 10
4
3
 1.5 10 10
 1.5 10
4
3
6
An ordinary penny contains about
20,000,000,000,000,000,000,000 atoms.
The average size of an atom is about 0.00000003
centimeters across.
The length of these numbers in
standard notation makes them awkward
to work with.
Scientific notation is a shorthand way of writing such
numbers.
An ordinary penny contains about
20,000,000,000,000,000,000,000
atoms.
In scientific notation the
number of atoms in a penny is
2.0  1022,
The average size of an atom is
about 0.00000003 centimeters
across.
and the size of each atom is
3.0  10–8 centimeters across.
Helpful Hint
The sign of the exponent tells which direction to
move the decimal. A positive exponent means move
the decimal to the right, and a negative exponent
means move the decimal to the left.
Translating Standard Notation to Scientific Notation
Write 0.00709 in scientific notation.
0.00709
7.09
Move the decimal to get a number between 1
and 10.
7.09  10
Set up scientific notation.
Think: The decimal needs to move left to change 7.09 to 0.00709, so
the exponent will be negative.
Think: The decimal needs to move 3 places.
So 0.00709 written in scientific notation is 7.09  10–3.
Check 7.09  10–3 = 7.09  0.001 = 0.00709
Try This: Example 2
Write 0.000811 in scientific notation.
0.000811
8.11
Move the decimal to get a number between 1
and 10.
Set up scientific notation.
8.11  10
Think: The decimal needs to move left to change 8.11 to
0.000811, so the exponent will be negative.
Think: The decimal needs to move 4 places.
So 0.000811 written in scientific notation is 8.11  10–4.
–4
Check 8.11  10 = 8.11
 0.0001 = 0.000811
Additional Example 3: Application
A pencil is 18.7 cm long. If you were to lay 10,000 pencils end to
end, how many millimeters long would they be? Write the
answer in scientific notation.
1 centimeter = 10 millimeters, so 18.7
centimeters = 187 millimeters
187 mm  10,000
1,870,000 mm
Find the total length.
Additional Example 3 Continued
1,870,000 mm
Set up scientific notation.
1.87  10
Think: The decimal needs to move right to
change 1.87 to 1,870,000, so the exponent
will be positive.
Think: The decimal needs to move 6
places.
The 10,000 pencils would be 1.87  106 mm long, laid end to end.
This is about one mile long.
Try This: Example 3
An oil rig can hoist 2,400,000 pounds with its main
derrick. It distributes the weight evenly between 8 wire
cables. What is the weight that each wire cable can
hold? Write the answer in scientific notation.
Find the weight each cable is expected to hold by dividing the
total weight by the number of cables.
2,400,000 pounds ÷ 8 cables = 300,000 pounds
per cable
Each cable can hold 300,000 pounds.
Now write 300,000 pounds in scientific notation.
Try This: Example 3 Continued
3.0  10
Set up scientific notation.
Think: The decimal needs to move
right to change 3.0 to 300,000, so
the exponent will be positive.
Think: The decimal needs to move 5
places.
5
Each cable can hold 3.0  10 pounds.
Multiplying and Dividing numbers in Scientific Notation form
What is the product of:
2.15 10
3
And
3.0 10
(use index laws) and express answer in SN

8
2.15 10
3
X
3.0 10
8
Same base, different exponent or index
Write them out so that same base
numbers are next to each 
other
If same base number, add the index

Multiply the whole numbers

2.15  3.0 10 10
3
2.15  3.0 10
6.45 10
11
11
8
Dividing numbers in SN form
6.45 10  3.15 10
11
6
6.45 10
3.15 10 6
11
1. Rewrite it as one over the other
Use index laws: if dividing
 2.same
base numbers, subtract the
indices
3. Complete operation with
index numbers
6.45 10
3.15


4. Divide whole numbers

116
6.45 10 5
3.15
2.05 10
5
Lesson Quiz
Write in standard notation.
1. 1.72  104
17,200
2. 6.9  10–3
0.0069
Write in scientific notation.
3. 0.0053
5.3  10–3
4. 57,000,000
5.7  107
5. A human body contains about 5.6 x 106 microliters
of blood. Write this number in
standard notation.
5,600,000
6. Evaluate and express in SN
7. Evaluate and express in SN




8 10  2 10
6
4 10
12
6
310  2.310
17
6.9 10
20
3
Additional Example 1A: Translating Scientific
Notation to Standard Notation
Write the number in standard notation.
A. 1.35  105
1.35  10
5
10 5= 100,000
1.35  100,000
135,000
Think: Move the decimal right 5
places.
Try This: Example 1A
Write the number in standard notation.
A. 2.87  109
2.87  10
9
10 9= 1,000,000,000
2.87  1,000,000,000
2,870,000,000
Think: Move the decimal right 9
places.
Additional Example 1B: Translating Scientific
Notation to Standard Notation Continued
Write the number in standard notation.
B. 2.7  10
2.7  10
2.7 
–3
–3
1
100
10
–3
=
1
100
2.7  100
Divide by the reciprocal.
0.0027
Think: Move the decimal left 3
places.
Additional Example 1C: Translating Scientific
Notation to Standard Notation Continued
Write the number in standard notation.
C. –2.01  104
–2.01  10
4
4
10 =
10,000
–2.01  10,000
–20,100
Think: Move the decimal right 4
places.
Try This
Write the number in standard notation.
B. 1.9  10–5
1.9  10
1.9 
–5
1
10,000
10
–5
=
1
10,000
1.9  10,000
Divide by the reciprocal.
0.000019
Think: Move the decimal left 5
places.
Try This
Write the number in standard notation.
C. –5.09  108
–5.09  10
8
8
10 =
100,000,000
–5.09  100,000,000
–509,000,000
Think: Move the decimal right 8
places.
Write 28750.9 in scientific
notation.
1. 2.87509 x 10-5
2. 2.87509 x 10-4
3. 2.87509 x 104
4. 2.87509 x 105
Write (2.8 x 103)(5.1 x 10-7) in
scientific notation.
1. 14.28 x 10-4
2. 1.428 x 10-3
3. 14.28 x 1010
4. 1.428 x 1011
Write 531.42 x 105 in scientific
notation.
1. .53142 x 102
2. 5.3142 x 103
3. 53.142 x 104
4. 531.42 x 105
5. 53.142 x 106
6. 5.3142 x 107
7. .53142 x 108