Monday, December 21, 2009

What are real numbers and what are rational numbers?

In my book it says real numbers can be placed on the number line. What does that mean? what is not a real number then? and what about rational numbers? many thanks!What are real numbers and what are rational numbers?
real numbers: the set of all rational and irrational numbers (3, pi, square root of 3)





rational numbers: ratio of two integers; a number that can be written as a fraction where the numerator and denominator are both integers (-2, 2/3, 1.21)


:can be expressed as whole numbers, fractions, and decimals (all repeating and finite decimals)What are real numbers and what are rational numbers?
Real Numbers:


The real numbers are the numbers that can be written in decimal notation, including those that require an infinite decimal expansion.





Rational Numbers:


A rational number is a number that can be expressed as a fraction or ratio (rational). The numerator and the denominator of the fraction are both integers.
there are also imaginary numbers, they are a negative number that it rationalized. you will know if it is because it would have an ';i'; in front of the number. and a rational number it anything that can be made into a fraction. for example 1/2 or 1/1 or 5/1 and example of an irrational number is 3.333 repeating or pi.
A number line looks kind of like this


________________________


...-3...-2...-1...0...1...2...3...4...


All real numbers can be found at some point on this line.





Examples of not real (imaginary) numbers : i=sqrt-1 , 3i , sqrt -9


Examples of rational numbers (can be expressed as fractions with integers) :


10 = 10/1 , 5/2 , 4/3
Rational numbers are the numbers made from dividing one integer by another. The numbers that fill the infinitesimally small gaps between the rational numbers are called irrational numbers. Together they make up the set of real numbers.
real numbers are basically any number that isnt the square root of a negative number. (because thats not possible)





rational numbers are numbers that do not go on and on forever. (like pi. its NOT a rational number))

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