Real Numbers

A Rational number is any number that can be written in the form a/b where a and b are integers and b ≠ 0. a and b can be positive or negative.

 

Rational numbers may include fractions if the fraction can be expressed as a decimal that terminates, or as a decimal that repeats indefinitely.

 

Example: ½ can be expressed as 0.5 which is a decimal that terminates.

                14/11 can be expressed as 1.272727… which is a repeating decimal.    

 

Integers are all the rational numbers formed when b = plus or minus 1.

 

If a is positive and b = +1,  then the rational numbers are positive integers.

 

If a is positive and b = -1,  then the rational numbers are negative integers.

 

If a = 0, then the rational number is the integer 0.

 

Whole numbers are all the positive integers including 0.

 

Natural numbers are all the positive integers greater than 0.

 

An Irrational number cannot be expressed as a terminating or repeating decimal, or in the form of a/b. Examples include the square root of any number that is not a perfect square. On your calculator, take the square root of 3. The answer is 1.7320508... and is neither a terminating nor a repeating decimal.

 

A rational approximation of an irrational number is a rational number that is close to, but not equal to, the value of the irrational number. A rational approximation of the square root of 3 is 1.73.

 

1.73 is a rational number since it can be expressed in the form of a/b, or 173/100.