The Sørensen pH scale and strong acids diltution from pH 1 to pH 4 by 1000 times?

I am reading a chemistry book that makes the following point about Sørensen's pH discovery regarding [H+] being in negative powers of 10: 



> 
> To dilute a solution from a pH 1 to a pH 4 (just 3 pH units) would require dilution by 10 x 10 x 10 = 1000 times.
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> 
> 


I don't understand how this calculation is derived, nor is there any proof available in the book. 


Can someone explain how this is the case?




The confusion here probably comes from your statement that Sørensen *discovered* the pH scale for expressing [$\ce{H+}$]. The pH scale is something that he *created* or *defined* for convenience. The definition of pH is basically: 


$$\mathrm{pH} = -\log[\ce{H^+}]$$ 


Since this is a (negative) log scale, a pH of 4 has 10 times the $[\ce{H+}]$ as does a pH of 5, and so on. In other words each pH unit represents a factor of 10 change in $[\ce{H+}]$.


The purpose behind such a scale is simply to avoid having to write out a bunch of zeros, and having to read a bunch of zeros!


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