Download Scientific Notation

Scientific Notation
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MTH 4-06b
Standard form / Scientific Notation
Scientific Notation to Number Form
Scientific Notation very small numbers
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Starter Questions
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MTH 4-06b
1.
2.35 + 4  0.25
2.
Calculate (-14)+(-5)+8
3.
What fraction is x:
16
4. Simplify the fraction
80
5.
Calculate 20% of 210
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X
Scientific Notation
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MTH 4-06b
Learning Intention
Success Criteria
1. To show a very quick way
of putting a large number
in scientific notation very
quickly.
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1. To understand and use the
quick method to put large
numbers into scientific
notation.
Very large numbers!
MTH 4-06b
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BOOM!
How far?
92 000 000 miles
Very large numbers!
MTH 4-06b
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Happy 70th Birthday!
SPLAT!
Howyears
many= seconds
in 70
years?
70
2 200 000
000
seconds!
Very large numbers!
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MTH 4-06b
Dinosaurs roamed the earth
228 million years ago
Short hand !
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MTH 4-06b
10
= 10
1
100 = 10 x 10
= 10
1 000 = 10 x 10 x 10
2
= 10
10 000 = 10 x 10 x 10 x 10
3
= 10
100 000 = 10 x 10 x 10 x 10 x 10
4
= 10
1 000 000 = 10 x 10 x 10 x 10 x 10 x 10
5
= 10
6
Standard Form
MTH 4-06b
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200 = 2 x 100
= 2 x 10
2
4 000 = 4 x 1000
= 4 x 10
3
70 000 = 7 x 10 000
= 7 x 10
4
500 000 = 5 x 100 000
= 5 x 10
3 000 000 = 3 x 1 000 000
5
= 3 x 10
6
This is also known as
Scientific Notation.
Scale of
BIG Numbers
Standard Form
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MTH 4-06b
Exercise 1
(1) 2 000 = 2 x 1000 = 2 x 10
3
(2) 20 000 = 2 x 10 000 = 2 x 10
(3) 500 = 5 x 100 = 5 x 10
4
2
(4) 800 000 = 8 x 100 000 = 8 x 10
5
(5) 9 000 000 = 9 x 1 000 000 = 9 x 10
6
A short cut
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MTH 4-06b
Move the point to get a
number between 1 and 10
8. 000 000. = 8 x 10
Add the
decimal point
Between 1 and 10
6
The point
moved 6 places
A short cut
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MTH 4-06b
Move the point to get a
number between 1 and 10
92
. 000 000.= 9.2 x 10
7
Add the
decimal point
Between 1 and 10
9.2 x 10
7 miles
The point
moved 7
places
A short cut
MTH 4-06b
Move the point to get a
number between 1 and 10
2. 200 000 000 .= 2.2 x 10
9
The point
moved 9
places
Add the
decimal point
Between 1 and 10
Happy Birthday: =
2.2 x 10 9Seconds old!
A short cut
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MTH 4-06b
Move the point to get a
number between 1 and 10
228
. 000 000. = 2.28 x 10
Add the
decimal point
8
The point
moved 8
places
Between 1 and 10
= 2.28 x 10 8 years old
Standard Form
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MTH 4-06b
= 3 x 10 4
(1) 30 000
= 7 x 10 5
(2) 700 000
= 5.3 x 10 3
(3) 5 300
= 4.7 x 10 5
(4) 470 000
= 9.5 x 10 6
(5) 9 500 000
= 18.3 x 10 7
(6) 18 300 000
= 3.29 x 10 5
(7) 329 000
(8) 2 560 000
= 2.56 x 10 6
(9) 12 000 000 000 = 1.2 x 10 10
(10) 9 990 000
= 9.99 x 10 6
Starter Questions
MTH 4-06b
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1.
Find the highest number that divides into
8 and 18 without leaving a remainder.
2.
Simplify 2 y  3x  5 y  4 x  5xy
3.
Write 72% as a decimal
4.
Write in scientific notation 230000
5.
30% of £600
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Scientific Notation
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MTH 4-06b
Learning Intention
Success Criteria
1. To understand how to
change large numbers from
Scientific Notation to
number form.
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1. Know how to expand large
numbers in scientific
notation to number
format.
Changing back
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MTH 4-06b
The point
moves 7
places
8.6 x 10 7 =
8.60000000
. =86 000 000
Hint:
Add 7 zeros, although you
probably won’t need them all.
Zeros after the
point aren’t needed.
Changing back
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MTH 4-06b
The point
moves 5
places
3.46 x 10
5
= 3.4600000
. =346 000
Hint:
Add 5 zeros, although you
probably won’t need them all.
Zeros after the
point aren’t needed.
Changing back
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MTH 4-06b
(1) 6  105
(2) 8 103
(3) 6.5 105
(4) 1.2 108
(5) 3.71106
(6) 3.3 104
(7) 7.91106
(8) 5.55 107
(9) 1.05 104
(10) 3.033 109
= 600 000
= 8 000
= 650 000
= 120 000 000
= 3 710 000
= 33 000
= 7 910 000
= 55 500 000
= 10 500
= 3 033 000 000
Name that number!
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MTH 4-06b
= 1 x 10
= 1 x 10
1 000 000
1 000 000 000 = 1 x 10
1 000
3
one thousand
6
one million
9
one billion
10 000 000 000 000 000 000
000 000 000 000 000 000 000
one googol !!!
000 000 000 000 000 000 000
000 000 000 000 000 000 000
100
000 000 000 000 000 000
= 1 x 10
Starter Questions
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MTH 4-06b
1.
Find the highest number that divides into
28 and 14 without leaving a remainder.
2.
Simplify 6a  9b  15a  14b  5a
3.
Write 55% as a decimal
4.
Find the lowest number that both of 5 and 9
divide into without leaving a remainder.
5.
15% of £400
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Scientific Notation
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MTH 4-06b
Learning Intention
Success Criteria
1. To understand how to
change very small numbers
into Scientific Notation
and vice versa.
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1. Know how to change very
small numbers into
scientific notation and
how to do the reverse
process.
Very small numbers!
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MTH 4-06b
How wide is an atom?
0.000 000 000 1 metres wide!
Standard Form
for small numbers
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MTH 4-06b
Move the point to get a
number between 1 and 10
0.000 000 000 1 .
= 1 x 10
-10
The point moved 10
places. Negative sign
for small numbers.
1  10 metres wide
-10
Scale of
SMALL Numbers
Standard Form
for small numbers
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MTH 4-06b
Move the point to get a
number between 1 and 10
. = 7.6 x 10
0.000 000 76
-7
The point moved 7
places. Negative sign
for small numbers.
Standard Form
for small numbers
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MTH 4-06b
Move the point to get a
number between 1 and 10
0.000 001. 93 = 1.93 x 10
-6
The point moved 6
places. Negative sign
for small numbers.
Standard Form
for small numbers
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MTH 4-06b
4
(1) 0. 000 3
 3 10 5
(2) 0.000 07
 7 10
4
(3) 0.000 45
 4.5 103
(4) 0.003 4
 3.4 10
(5) 0. 000 724
 7.24 104
7
(6) 0.000 000 494
 4.94 10
5
(7) 0.000 095
 9.5 108
(8) 0.000 000 098
 9.8 10
4
(9) 0.000 1 03
 1.03 1010
(10) 0.000 000 000 66  6.6 10
Changing back small numbers
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MTH 4-06b
-3 so remember to
move point left for
small numbers.
Hint:
Add 3 zeros to the left of the
number.
2 x 10 -3 = 000
. 2.
= 0.002
Changing back small numbers
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MTH 4-06b
-5 so remember to
move point left for
small numbers.
8.6 x 10
-5
Hint:
Add 5 zeros to the left of the
number.
8. 6
= 00000
.
= 0.000086
Changing back small numbers
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MTH 4-06b
Hint:
-6 so remember to
move point left for Add 6 zeros to the left of the
number.
small numbers.
5.16 x 10 -6 = 000000
5.16
.
= 0.000 00516
Changing back small numbers
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MTH 4-06b
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
4
= 0.000 5
9 105 = 0.000 09
3
5.8 10 = 0.005 8
7
6.2 10 = 0.000 000 62
6.45 106 = 0.000 006 45
5.3 107 = 0.000 000 53
6 = 0.000 009 17
9.17 103
2.12 10 = 0.002 12
5
2.03 10 = 0.000 020 3
9
6.032 10 = 0.000 000 006 032
5 10