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PHY183-Lecture04 - F e w P o in t s M o v i e P o w e r s o...

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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 3.2e-12 or 3.2*10^-12 number = mantissa ! 10 exponent August 29, 2006 Physics for Scientists&Engineers 1 4 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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August 29, 2006 Physics for Scientists&Engineers 1 5 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 3-digit precision, then we cannot claim that we know the circumference of the same circle to better than 3 digits.
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