What is a rational number?
Any number of arithmetic: Any whole number, fraction, mixed number or decimal; together with its negative image.
A rational number is a nameable number, in the sense that we can name it according to the standard way of naming whole numbers, fractions, and mixed numbers. "Five," "Six thousand eight hundred nine," "Nine hundred twelve millionths," "Three and one-quarter," and so on.
A rational number can always be written in what form?
As a fraction
, where a and b are integers (b 0).
An integer itself can be written as a fraction: b = 1. And from arithmetic, we know that we can write a decimal as a fraction.
When a and b are positive, that is, when they are natural numbers, then we can always name their ratio.
Hence the term, rational number. N
ow a fraction can always be expressed as a decimal.
Either the decimal will terminate -- as 1/4 = .25;
or the decimal will have a predictable pattern -- as 1/11 = .090909. . .
A rational number, then, can always be expressed as such a decimal. -->