S1T1 - Numbers, Power, Place Value

NUMBERS                                                                              

Integers

Whole numbers including negative whole number

            Example:          …,-4, -3, -2, -1, 0, 1, 2, 3, 4,…

A positive number is any number greater than zero. 

            Example: 1, 2, ½, 6.4

Negative Numbers

We read -1 as negative one.

A negative number is any number less than zero. 

            Example: -1, -2.5, -4/7

Large Numbers

One Million : 1 000 000 [6 zeros, 1000 times of thousands]

One Billion: 1000 000 000 [9 zeros, 1000 times of millions] 

Place Values

Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used to form numbers.

The value the digit is the position of the digit in the number

            487

          7 è Value of the digit 7 is 7

        80 è Value of 8 is 80

      400 è Value of 8 is 400

Example: 

Give the value of the digit 6 in the following numbers.

a.   234.60

Digit 6 is in the tenth place. The value is 0.6

b.  620912

The digit 6 is in the hundred thousands place. Its value is 600000

 Index/Power

The small, raised number next to a normal letter or number, to be multiplied by itself

Example

b²= b x b

4³ = 4 x 4 x 4

 

Square power 2 : ²

- multiplying by itself

Example

(1)        Square of 4 = 4² = 4 x 4 = 16                    

(2)        3² = 3 x 3 = 9

(3)        Square of (-5)² = (-5) x (-5) = 25

Perfect Square are the squares of whole numbers: 

             (2 x 2) 4, (3 x 3) 9, (4 x 4) 16, …

Square Root - the Opposite of Square

            A number that when multiplied by itself, gives the number

                                    Symbol: √ 

        

5 -->         square 5²       --> 25

                        5 <--    Square root √25  <-- 25

Example

(1) 16 = 4 x 4

     √16 = 4

(2) a² = 25        

      a = + √5 x 5 =    = +5             

Why +5 when a number is square-root?

   (-5) x (-5) = 25 ( -ve x -ve = + ve)

    5 x 5 = 25

  => 25 = (-5)² = 5² = 25

       a2 =  + √a x a = -a or a

Cube - Power of 3 : ³

- Multiplying the number by 3 times

Example:

(1)        Cube of 3 = 33 = 3 x 3 x 3 = 27                                

(2)        4³ = 4 x 4 x 4 = 64

(3)        cube of (-5) ³ = (-5) x (-5) x (-5) = = -125                            

Cube Root

            A value that when ‘cubed’ gives the original number

                        Symbol: ³√

4 -->        cube 4³         --> 64

                4 <--  cube root ³√64    <-- 64

Example: 

                  3√8 = 3√2 x 2 x 2 = 2

             ³√216 = ³√6 x 6 x 6 = 6

Prime Number

 Greater than 1 that cannot be formed by multiplying 2 smaller natural number. 

            Example: 2, 3, 5, 7, …

            2 = 1 x 2, 13 = 1 x 13

* 1 is not a prime number because prime numbers are greater than 1

* All even numbers are not prime number except 2.

Example

List all the prime number that are greater than 10 and less than 20

Step 1: List all the numbers 

 11, 12 , 13 , 14, 15, 16, 17, 18, 19

Step 2: Strike out the non-prime number

            11, 12 , 13 , 14, 15, 16, 17, 18, 19

Step 3: List out the prime number

  11, 13, 17, 19

Practice:

1. Write the following in numerals

(a) 7.18 billion.   (b) 19.05 million

Refresh and Revise

Conversion of Unit of Measurement

Length

(mm = millimeter cm = centimeter   m = metre)

1 cm = 10 mm

1 m = 100 cm                           

1km = 1000 m  

1km = 1000m = 100000cm (1000 x 100)             

Area

1 cm² = 1cm x 1cm = 10mm x 10mm = 100mm²

1 m² = 1m x 1m = 100 cm x 100 cm = 10000 cm²

1km² = 1000m x 1000m = 1 000 000 m²

Mass

1 g = 1000mg

1kg = 1000g

1 ton = 1000kg

TIME

1 min = 60 seconds (s)                         

1 hour (h) = 60 min (m)                         

1h = 60 x 60 = 3600s

1 s = 1/60   x 1/60   = 1/3600 h

            1 s = 1/3600 h

            1 h = 3600 s

            0.5 or ½ hr = 30 mins

Volume

1 litre = 1000ml = 1000cm³

            1cm³ = 1ml

Practice:

1.  Convert 125 km to m

2.  Convert 299 m to km

3.  Convert 700 g to kg

4.  Convert 2 ton to g

5.  Convert 2 hrs to seconds

6.  Convert 1260 seconds to minutes 

7.  Convert 100 kilometres per hour into metres per second.  (2/13/1/2/T)