 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^(C-F)

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C101 Class Notes
Prof. N. De Leon   