Finite Decimal Approximations
Any real number can be approximated to any desired degree of accuracy by rational numbers with finite decimal representations.
Assume . Then for every integer there is a finite decimal such that
Proof:
Let, where . Then, and the result follows from dividing all sides by . (The fact that has a finite decimal representation is easily established.)
Read more about this topic: Decimal Representation
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—Blaise Pascal (1623–1662)
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