Real Number System

Real Number System

Objectives

• Identify the elements of each subset of the set of real numbers.

• Graph real numbers on the number line and compare the values.

• Identify or classify numbers as even or odd and prime or composite.

• Perform operations on whole numbers.

• Convert fractions to decimals and percent, and vice versa.

Open Ended

What is a real number?

Real Number

A real number is any number that can be mapped on the number line.

The Real Number Line

Multiple Select

In which subset/s of real numbers does 3 belong to? Select all that apply.

• Natural Numbers

• Whole Numbers

• Integers

• Rational Numbers

• Irrational Numbers

Multiple Select

In which subset/s of real numbers does  $\sqrt{5}$   belong to? Select all that apply.

• Natural Numbers

• Whole Numbers

• Integers

• Rational Numbers

• Irrational Numbers

Multiple Select

In which subset/s of real numbers does  $0.\overline{33}$  belong to? Select all that apply.

• Natural Numbers

• Whole Numbers

• Integers

• Rational Numbers

• Irrational Numbers

Multiple Select

In which subset/s of real numbers does  $-\frac{12}{4}$  belong to? Select all that apply.

• Natural Numbers

• Whole Numbers

• Integers

• Rational Numbers

• Irrational Numbers

Multiple Select

In which subset/s of real numbers does $1.327819023...$  belong to? Select all that apply.

• Natural Numbers

• Whole Numbers

• Integers

• Rational Numbers

• Irrational Numbers

The Real Number System

Natural or Counting Numbers  $\left(N\right)$ 
                $N=\left\{1,\ 2,\ 3,\ 4,\ ...\right\}$  

Whole Numbers  $\left(W\right)$ 
                $W=\left\{0,\ 1,\ 2,\ 3,\ ...\right\}$ 

Integers  $\left(Z\right)$ 
                $Z=\left\{...,\ -3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3,\ ...\right\}$  

The Real Number System

Rational Numbers  $\left(Q\right)$ 
           $Q=\left\{\frac{a}{b}:a\ and\ b\ are\ integers,\ with\ b\ne0\right\}$ 
           Examples:  $\frac{2}{3},\ -10,\ 1.25,\ \frac{11}{3},\ -9.\overline{125}$ 

Irrational Numbers  $\left(Q'\right)$ 

          Irrational numbers are numbers that cannot be expressed as a quotient (ratio) of two integers.

          Examples:  $\pi,\ e,\ \sqrt{7},\ 2.3187269114...$  

Multiple Choice

1 is an odd prime number.

• True

• False

Multiple Choice

2 is the smallest and the only even prime number.

• True

• False

Multiple Choice

-15 is an odd composite number.

• True

• False

Multiple Choice

-10 is an even number.

• True

• False

Even Number

An even number is a number that can be written in the form  $2k$ , where  $k$  is an integer.

Odd Number

An odd number is a number that can be written in the form  $2k+1$ , where  $k$  is an integer.

Prime Number

A prime number is a natural number greater than 1, which has no other natural number divisors other than 1 and itself.

Composite Number

A composite number is a natural number that has at least 3 natural number divisors.

Multiple Choice

Convert  $\frac{1}{3}$ in decimal form.

•  $0.3$  

•  $0.33$  

•  $0.\overline{33}$  

Multiple Choice

Convert  $\frac{5}{8}$ into percentage.

•  $62.5\%$  

•  $0.625\%$  

•  $6.25\%$  

Multiple Choice

Convert  $0.38$ into fraction.

•  $\frac{19}{50}$  

•  $\frac{19}{5}$  

•  $\frac{19}{500}$  

Multiple Choice

Convert  $0.785$ into percentage.

•  $78.5\%$  

•  $785\%$  

•  $7.85\%$  

Multiple Choice

Convert  $81\%$  into fraction.

•  $\frac{81}{100}$  

•  $\frac{100}{81}$  

•  $\frac{81}{10}$  

Multiple Choice

Convert $63.52\%$ into decimal.

•  $0.6352$  

•  $6.352$  

•  $6352$  

Multiple Choice

Convert $0.\overline{2}\$ 

into fraction.

•  $\frac{2}{9}$  

•  $\frac{1}{5}$  

Multiple Choice

Convert $0.\overline{15}$  

into fraction.

•  $\frac{5}{33}$  

•  $\frac{3}{20}$  

Multiple Choice

Convert $0.2\overline{4}$  

into fraction.

•  $\frac{11}{45}$  

•  $\frac{8}{33}$  

Open Ended

3-2-1 Chart

Identify

a. 3 things you've learned in this lesson;

b. 2 things you want to know more about; and

c. 1 question you still have.