What is a rational number?

Math Adda                     What is a rational number?

 

Any ordinary 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.

Q. Which of the following numbers are rational?

1

−6

3½

−

2 3

0

5.8

3.1415926535897932384626433

A rational number can always be written 

a b	, 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.

At this point, the student might wonder, What is a number that is not rational?

An example of such a number is  ("Square root of 2").  It is not possible to name any whole number, any fraction or any decimal whose

square is 2.

7 5

is close, because

7 5

·

7 5

=

49 25

-- which is almost 2.