August 29, 2006
Physics for Scientists&Engineers 1
1
Physics for Scientists &
Engineers 1
Engineers 1
Fall Semester 2006
Lecture 4
August 29, 2006
Physics for Scientists&Engineers 1
2
Few Points
Few Points
!
Movie “Powers of ten” at the end of the lecture (if time)
!
No class on Monday: Labor day
!
Homework
•
First set opened
•
Due by Wednesday 23:59
!
Helproom starts on Tuesday
!
Honors option: last chance to enroll or change the hours in the helproom
August 29, 2006
Physics for Scientists&Engineers 1
3
Scientific Notation
!
Physical quantities consist of a number that
specifies its magnitude AND its unit
•
Example: this lecture lasts
50
minutes
(number)
(unit)
!
For very large or very small numbers, we use
scientific notation
•
Example:
3.2·10
12
(or
3.2x10
12
)
•
Product easy: (4.8x10
17
)x(7.21x10
7
)=34.6x10
10
=3.46x10
9
•
You can enter number in scientific notation into the LON
CAPA homework system as 3.2e12 or 3.2*10^12
number = mantissa
!
10
exponent
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Physics for Scientists&Engineers 1
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Significant Figures
!
Two statements:
•
The population of the USA is 294,109,799
•
The population of the USA is 294,000,000=2.94·10
8
•
First statement implies precision that is simply not warranted
•
Second statement claims that the population is somewhere
between 293M and 295M.
This is justified!
!
General Rule:
•
The number of digits we write down in a number specifies
the precision with which we claim to know that number.
US Census Bureau
August 2004
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Physics for Scientists&Engineers 1
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Example: Significant Figures
•
Suppose we are told that the radius of a circle is 2.66 feet;
what is its circumference?
•
Formula:
•
Type
into your pocket calculator and get:
16.7132729170977
•
But if we only know that the radius of the circle is between
2.65 and 2.67 feet, i.e. to 3digit precision, then we cannot
claim that we know the circumference of the same circle to
better than 3 digits.
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 Spring '08
 Wolf
 Physics, International System of Units, Kilogram, Litre, Scientists&Engineers

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