S1T1 Number Line, Ordering , Simple Inequalities

The number line

Whole numbers, fractions and decimals can be represented on the number line.

The numbers are placed at their correct positions, equal distance apart.

Negative Numbers

We read -1 as negative one.

A negative number is any number less than zero. 

            Example: -1, -2.5, -4/7

Any pair of numbers  eg: 3 and -3 are same distance from the origin.

Using Number Line

Example 

What is the value of 3 - 5?

      3 - 5 = -2

Ascending and Descending Orders

Ascending : Increasing in value; Moving higher/becoming bigger 

[Tip to remember : A - side of A is going up, from small to big ]

Descending : Moving down in value/becoming smaller

[D => Down , from big to small]

Example

Arrange the following in ascending order

      5.3, 5.25, 5.205       

Step1: Arrange by the decimal point

          5.3

          5.25

          5.205

Step2: Ascending => small to big. 

           Compare the number values from left to right

          5.205 has the smallest hundredth value, 

          5.25 has the smaller tenth value

Step3: Arrange the numbers

          5.205, 5.25, 5.3

 

Comparing and Ordering Numbers

Symbols

                        >    greater than

                        <    less than

                        ≥    greater than or equal to

                        ≤    less than or equal to

                        =    equal

                        ≠  not equal to

Tip to remember

                                                   4  >  3

        greater = "open mouth"       >      “point” = less than

  

Similarly,

                                                   3  <  4

                  less than = “point”     <       greater = "open mouth"            

Using number line and Inequalities

Using the dot : o excluding the number  => < or > symbol

                        •  including the number   =>  ≤ or ≥ symbol

 

Using the symbol : > => right arrow  ------>

                                < => left arrow    <-------

Example ( > symbol)

Draw x > 2 on the number line.

Step1 : "stand" at 2, draw o (> symbol)

Step2 : > (greater than) symbol => Right arrow

[To check if arrow direction is correct, use a bigger number (eg 3), and move the arrow in that direction]

Example ( < symbol )

Draw x < 1 on the number line  

Steps : "stand" at 1, draw o (< symbol); then left arrow (<)

 

Example (≥ symbol )

     Draw x ≥ 2 on the number line.

                        

(Draw a solid circle at 2 and then right arrow direction) 

Example ( ≤ )

    Draw x ≤1 on the number line.

    

 (Draw a solid circle at 1 and left arrow direction)

  

Practice

1.  Arrange the following numbers in ascending order.

(a)  1.14, 1.106, 1.13, 1.1    

(b).  0.52, 0.543, 0.5, 0.506

2.  Arrange the following numbers in descending order.

(a)  6.07, 6.32,  6.3, 6.301

(b). 9.123, 9.09, 9.3, 9.15

3.  Round 965.27 km to 

a. 1 decimal place

b. the nearest 10 km

c. 3 significant figures

4.  The following are temperatures, in C, over 6 days in Iwate.

       -1.4, -2, 0, -3, -0.5

(a) List all the temperatures that are >= -1 C

(b) List all the temperatures that are < -0.5 C

5. Use <, > or = to complete each of these statements.            (1/14/2/4/T)

a.         1/3 ___ 0.3

b.         12 ½% ______ 1/8

c.         7/12 _______ 5/9

6. Complete the number line.

        <——|——|——|——|——|——|——|——|——|

               -6     ___ ___    3.      6.    ___  12    15    ____