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    ____   

D2 Decimals : Ordering and Comparing Decimals, Using Number Lines

ORDERING AND COMPARING DECIMALS

Comparing Decimals

Example

Which number is bigger: 0.43 or 0.403?

Looking at the digits, 403 seems bigger than 43. But, it is not!

Method

Step1: Draw the place_Value_tables and put the numbers

th	h	o	.	t	h	th
		0	.	4	3
		0	.	4	0	2

Step2: Put 0 into the empty square

th	h	o	.	t	h	th
		0	.	4	3	0
		0	.	4	0	2

                             =    3 bigger

Step3: Compare the first column on the left. If the digits are equal, move to next number until the bigger number

            0.43 is bigger than 0.402

Example

Which number is smaller: 8.003 or 8.01?

Method

Step1: Draw the placeValuetable and put the numbers

th	h	o	.	t	h	th
		8	.	0	0	3
		8	.	0	1

Step2: Put 0 into the empty square

th	h	o	.	t	h	th
		8	.	0	0	3
		8	.	0	1	0

             =      =    0 is smaller

Step3: Compare the first column on the left. If the digits are equal, move to next number until the required smaller number.

             8.003 is smaller than 8.01

Ordering Decimals

Ascending order is arranging the numbers from the Smallest to the Biggest numbers

Ascending order:     1.01, 2.01, 3.01, 4.01

Descending order is arranging the numbers from the Biggest to the Smallest numbers.

                                    5.2, 4,2 , 3.2, 1.2

            Descending -> Down => from big to small

Example

Put the 1.517, 1.57, 1.08 and 0.8 in ascending order

Method

Step1: Draw the placeValueTable and put the numbers

th	h	o	.	t	h	th
		1	.	5	1	7
		1	.	5	7
		1	.	0	8
		0	.	8

Step2: Put 0 into the empty square

th	h	o	.	t	h	th
		1	.	5	0	7	3
		1	.	5	7	0	4
		1	.	0	8	0	2
		0	.	8	0	0	1

            (1)    (2) (3) (4) number

Step3: Compare the first column on the left. If the digits are equal, move to next number until the required smallest number (for Ascending), write number

                        0.8 , 1.08, 1.517, 1.57

Example

Put the 0.402, 1.2, 0.41, 0.375 in descending order.

Method

Step1: Draw the placeValueTable and put the numbers

th	h	o	.	t	h	th
		0	.	4	0	2
		1	.	2
		0	.	4	1
		0	.	3	7	5

Step2: Put 0 into the empty square

th	h	o	.	t	h	th
		0	.	4	3	2	3
		1	.	2	0	0	4
		0	.	4	1	0	2
		0	.	3	7	5	1

Step3: Compare the first column on the left. If the digits are equal, move to next number until the required biggest number (for descending), write number

                        1.2, 1.432, 0.410, 0.375

Using Number Line

Example

What are the values A, B and C?

Method(count blank spaces)

Step1: Find the interval value between 2 known number (1.0 and 1.5).

           Count number of blanks: 5 blanks / ‘spaces’ between 1.0 and 1.5  

Each marker = 1.5 -1.0 / 5 = 0.5/5 = 0.1

 => 1.0 + 0.1 = 1.1 for first marker

Step2: Put in the marker

             1.0 + 0.1=1.1, 1.1+0.1 = 1.2, …

Step3: Answer

            A = 1.2 , B = 1.8 and C = 2.4

Example

What are the values of A and B?

Method (marker + 1)

Step1: Find the interval value between 2 known number (1.0 and 2.0).

           - Count number of marker I between the 2 numbers, and ADD 1

            - 4 marker + 1 = 5

Each marker = 2.0 -2.0 / 5 = 1.0/5 = 0.2

=> 1.0 + 0.2 = 1.2 for first marker

Step2: Put in the marker

             1.0 + 0.2, 1.2+0.2, …

Step3: Answer

            A = 1.6, B = 1.2

~~ the end ~~~ :)