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Large and Small Numbers
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| In chemistry we often
have to deal with very large or very small numbers. since atoms
are so small it takes a large collection of them before we can
see a substance or weigh it. It thus becomes necessary to have
a simple way to express large and small numbers - scientific
notation. |
Scientific notation is a way
to express powers of 10 and 1/10 e.g.,
| powers of 10 |
powers of 1/10 |
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1 = 10^0
10 = 10^+1
100 = 10^+2
1000 = 10^+3
10,000 = 10^+4
100,000 = 10^+5
1,000,000 = 10^+6
10,000,000 = 10^+7
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0.1 = 10^-1
0.01 = 10^-2
0.001 = 10^-3
0.0001 = 10^-4
0.00001 = 10^-5
0.000001 = 10^-6
0.0000001 = 10^-7
0.00000001 = 10^-8
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These powers of ten can now
be used to express large and small number efficiently.
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12,000,000 = 1.2x10^+7
546,000,000,000,000 = 5.46x10^+14
0.000013 = 1.3x10^-5
0.000000000000234 = 2.34 x10^-13
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It is important to remember
how to multiply and divide numbers expressed in scientific notation
Let A = Bx10^C
and D = Ex10^F
Then
AxD = (BxE)x10^(C+F)
and
A/D = (B/E)x10^(C-F)
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