
Large and Small Numbers

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 
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

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

These powers of ten can now
be used to express large and small number efficiently.
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

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^(CF)

