Rational Number Systems

AMDG

Number Systems

LESSON 1

Real numbers.

Real numbers are split into two groups .

Natural Numbers

• Also known as counting numbers or positive integers.

• The set of natural numbers does not include zero.

Whole Numbers

The set of whole numbers includes all the elements of the natural numbers plus the number zero (0).

Integers

• This is an extension of the set of natural numbers.

• It includes all the numbers in the set of whole numbers and the “negatives” of all the numbers in the set of natural numbers.

Rational Numbers

• These numbers that can be written as a fraction or as a ratio of integers.

• However, the denominator cannot be equal to zero.

• All terminating and recurring decimals are considered to be rational numbers.

Terminating Decimals

FOR EXAMPLE :

 $0.2=\frac{1}{5}\ \ \ \ \ \ \ \ \ \ 0.12=\frac{12}{100}\ \ \ \ \ \ \ \ 1.53=\frac{153}{100}$  

Recurring Decimals

FOR EXAMPLE :

 $0.3333\ldots\ =\frac{1}{3}\ \ \ \ 0.6363636364\ldots=\frac{7}{11}$  

Irrational Numbers

• Numbers which cannot be expressed as a fraction.

• Numbers if written in decimal forms don’t terminate and don’t repeat.

Irrational Numbers

FOR EXAMPLE : Look at this right angled triangle. 

 $AC^2\ =\ 1^2+1^2$  
 $AC^2=2$  
 $AC=\sqrt{2}$  

 $\sqrt{2}=1.414213562......$  

Notice that the numbers don't repeat.

Irrational Numbers

Another example of an irrational number is $\pi$ .

Even though it is often rounded off to 3.142, the digits continue endlessly.

Multiple Choice

1. Is the statement is true or false. Every whole number is a natural number.

• True

• False

Multiple Choice

2. Is the statement is true or false. All integers are whole numbers.

• True

• False

Multiple Select

3. Select the set or sets of numbers to which the real number (7) belongs to.

• Natural

• Whole

• Integer

• Rational

Multiple Select

4. Select the set or sets of numbers to which the real number (0) belongs to.

• Natural

• Whole

• Integer

• Rational