Math CentralQuandaries & Queries


Question from angel, a student:

is 1.2731568 a natural number a whole number a irrational number or a inter

If "inter" is a typo for "integer", the answer is "none of the above." It is a non-integer rational number.

"Natural" and "whole" are synonyms. Both mean (depending on who is using them) either {1,2,3,4,5,...} or {0,1,2,3,4,...} and your number is clearly not in either set.

Integers include the negatives of these (and always 0) and your number is not in this set either.

However, because the decimal terminates, it is necessarily rational - specifically, rational with a denominator that is a power of 10. Thus 1.3 = 13/10, 0.5761 = 5761/10000, and

1.2731568 = 12731568/10000000.

A decimal represents a rational number if its digits loop forever or terminate; if they go on forever without repeating the number is irrational. Thus there are both rational numbers such as
1.273156801 = 1.2731568010101010...

and irrational numbers such as


starting with 1.2731568 . A calculator with an eight digit display would represent both by 1.2731568 .

Good Hunting!

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