Math1003 1.14 - Scientific Notation
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MATH1003 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 1.14 Scientific Notation
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Transcript of Math1003 1.14 - Scientific Notation
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
1.14Scientific Notation
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Goal
To be able to write in and understand the difference between decimal notation and scientific notation.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Big numbers
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Big numbers
“The distance from the earth to the moon is approximately 46,000,000,000 centimeters.”
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Big numbers
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Big numbers
“There are roughly 100,000,000,000,000,000,000 stars in the universe.”
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Small numbers
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Small numbers
“It takes approximately 0.00000000008 seconds for light to travel 1 inch.”
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Small numbers
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Small numbers
Intel has moved their chip manufacturing to 0.000000032 (32nm) technology.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Writing Big and Small Numbers
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Writing Big and Small Numbers
Instead of writing
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Writing Big and Small Numbers
Instead of writing
46,000,000,000
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Writing Big and Small Numbers
Instead of writing
46,000,000,000100,000,000,000,000,000,000
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Writing Big and Small Numbers
Instead of writing
46,000,000,000100,000,000,000,000,000,000
0.00000000008
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Writing Big and Small Numbers
Instead of writing
46,000,000,000100,000,000,000,000,000,000
0.000000000080.000000032
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Writing Big and Small Numbers
Instead of writing
46,000,000,000100,000,000,000,000,000,000
0.000000000080.000000032
we’ve developed scientific notation to deal with these types of numbers.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Writing Big and Small Numbers
Instead of writing
4.6 x 109
100,000,000,000,000,000,0000.000000000080.000000032
we’ve developed scientific notation to deal with these types of numbers.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Writing Big and Small Numbers
Instead of writing
4.6 x 109
1020
0.000000000080.000000032
we’ve developed scientific notation to deal with these types of numbers.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Writing Big and Small Numbers
Instead of writing
4.6 x 109
1020
8.0 x 10-11
0.000000032
we’ve developed scientific notation to deal with these types of numbers.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Writing Big and Small Numbers
Instead of writing
4.6 x 109
1020
8.0 x 10-11
3.2 x 10-8
we’ve developed scientific notation to deal with these types of numbers.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3476
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3476
this number is in decimal notation
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3476 x 100
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3476 x 100
remember that 100 is equal to 1
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 100.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 100.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 100.
as we move the point to the left, we add 1 to the exponent
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 101.
as we move the point to the left, we add 1 to the exponent
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 101.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 101.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 101.
we add 1 to the exponent
everytime we move the point to the
left
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 102.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 102.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 103.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 103.
there has to be one non-zero
significant digit to the left of the point
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
34760 x 103.
trailing zeroes are omitted
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3476 x 103.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3476 = 3476 x 103.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023.
this number is in decimal notation
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 100.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 100.
as we move the point to the right, we subtract 1 from the exponent
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 10-1.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 10-1.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 10-2.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 10-2.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 10-3.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 10-3.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 10-4.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 10-4.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 10-4.
there has to be one non-zero
significant digit to the left of the point
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 10-4.
leading zeroes are omitted
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 x 10-4.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
000023 = 23 x 10-4..
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437.
Where do we want the point - between which two numbers?
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437.
Where do we want the point - between which two numbers?
.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437.
Where do we want the point - between which two numbers?
.1
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437.
Where do we want the point - between which two numbers?
.1 2
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437.
Where do we want the point - between which two numbers?
.1 2 3 4 5 6 7
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437.
Where do we want the point - between which two numbers?
.1 2 3 4 5 6 7
we had to move the point seven places
to the right
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437.
Where do we want the point - between which two numbers?
.1 2 3 4 5 6 7
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437.
Where do we want the point - between which two numbers?
.1 2 3 4 5 6 7
since we moved the point 7 spaces to the right, our exponent will
be -7
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437 x 10-7.
since we moved the point 7 spaces to the right, our exponent will
be -7
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437 x 10-7.
since we moved the point 7 spaces to the right, our exponent will
be -7
we don’t need to write the leading
zeroes
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437 x 10-7.
we don’t need to write the leading
zeroes
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
00000001437 =1437 x 10-7.
.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000
This Google’s net income in US dollars in 2006.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000
Where do we want the point - between which two numbers?
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000
Where do we want the point - between which two numbers?
.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000
Where do we want the point - between which two numbers?
.1
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000
Where do we want the point - between which two numbers?
.123456789
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000
Where do we want the point - between which two numbers?
.1
we had to move the point nine places
to the left
23456789
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000
Where do we want the point - between which two numbers?
.1
since we moved the point to the left, our exponent will be
9
23456789
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000 x 109
Where do we want the point - between which two numbers?
.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000 x 109
Where do we want the point - between which two numbers?
.
we don’t need to write the trailing
zeroes
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000 x 109
Where do we want the point - between which two numbers?
.
we don’t need to write the trailing
zeroes
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000 x 109
Where do we want the point - between which two numbers?
.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077 x 109.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
3077000000 =3077 x 109.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
2.3 x 106.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
2.3 x 106.
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
2.3 x 106.
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
2.3 x 106.
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
2.3 x 106.
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
23 x 105.
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
230 x 105.
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
2300 x 104.
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
23000 x 103.
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
230000 x 102.
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
2300000 x 101.
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
23000000 x 100.
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
2300000
This represents an estimate of the number of servers in Google’s server farms around the world.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
12 x 10-5.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
12 x 10-5
This represents the size of an influenza virus (in centimeters).
.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
12 x 10-5
This represents the size of an influenza virus (in centimeters).
.
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
0000012 x 10-5
And back to Decimal Notation...
.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
0000012 x 10-5
And back to Decimal Notation...
.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
0000012 x 10-4
And back to Decimal Notation...
.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
0000012 x 10-4
And back to Decimal Notation...
.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
0000012 x 10-3
And back to Decimal Notation...
.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
0000012 x 10-3
And back to Decimal Notation...
.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
0000012 x 10-2
And back to Decimal Notation...
.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
0000012 x 10-2
And back to Decimal Notation...
.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
0000012 x 10-1
And back to Decimal Notation...
.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
0000012 x 10-1
And back to Decimal Notation...
.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
0000012 x 100.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
And back to Decimal Notation...
0000012.
This represents the size of an influenza virus (in centimeters).
MATH1003
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Scientific Notation
An understanding of scientific notation is necessary to understand computers because this is the way real
numbers are stored.
