Lecture 2 1/9/2013 12:26:00 PM
A sense of scale
Size of the observable universe: 130,000,000,000,000,000,000,000 km.
(1.3 x 10 to the power of 23)
There are a couple of different ways to avoid writing so many zeros.
1. scientific notation
2. use different units.
Powers of 10 and scientific notation:
10, 100, 1000, etc. are all powers of 10: they can be though of as multiplied
by itself some number of times:
100=10x10=10 to the power of 2 (1 with 2 zeros)
1000-10x10x10= 10 to the power of 3 (1 with three zeros)
1,000,000= 10x10x10x10x10x10= 10 to the power of 6 (1 with six
zeros)
number of 0 = exponent
in this way, 6 million can be written as 6x1,000,000 = 6x10 to the power of
6.
6,500,000 = 6.5x10 to the power of 6.
Negative powers are fractions:
0.1= 1/10 = 10 to the power of -1
0.001 = 1/1000 = 10 to the power of -3
0.0065 = 6.5 x 1/1000 = 6.5 x 10 to the power of -3
Rules of expressing any number in scientific notation
Place the decimal after the first nonzero digit
Count the number of places that the decimal point moved. This
gives the power of 10 (the exponent)
If the decimal moved to the left, the power is positive. If the
decimal moved to the right, the power is negative.
Size of Jupiter: 143,000 km. =1.43x10^5 km.
Size of a large bacterium: 0.000002 m = 2x 10^-6 m. Suppose we need to multiply to numbers:
(3x10^5) x (2x10^3)
= 3 x 2 x 10^5 x 10^3
= 6 x 10^8
A complication:
(6 x 10^5) x (5 x 10^3)
= 30 x 10^8
… the number in

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