N1 Number Notation, Place Value

NUMBERS

 – why do we need to know them well

Numbers are usually written using: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. 

(1) To count: 1, 2, 3 strawberries    

Number Notation

PLACE VALUES

Value is the positional value of the digit in the number or where the digit is in the number. 

Stands for is another term used to describe ‘value’ in math.

What is a digit?

Digits are symbols or characters to represent a number in writing. 

Method to find the Value in a number

Step1: Underline the digit in the number given

Step2: Replace the numbers after the digit with zeros

Step3: Write the answer in numeric form

Example:

What is the value of the digit 4 in 854013?

Step1: Underline 4                                             854 013

Step2: Replace number to right of 4 to 0            4000

  Step3: Write : Answer: 4000

Practice:

What is the value of digit 3 in 

           (a) 89300,          (b) 55293,         (c) 30984

More practices: Whole-number-revision-practice

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N2 Number-Word-Number Conversion

Expressing Numbers in Words

(1) Numbers can be expressed in words using hundreds, thousands and millions.

(2) The last number to be written must be preceded by an ‘and’.

Example       

                        2 7 8 is two hundred and seventy-eight

 5 6 0 8 is five thousand six hundred and eight

4 5 6 70 is forty-five thousand six hundred and seventy

Method 1 – Grouping 

Example: Write 8765432 in words

Step 1: Separate numbers from right to left, 3 numbers in one group

Step2: Fill From left to right:

-         first underline is for hundred,

-         second underline is for thousand

-         third underline is for million

Step3: Write the word

Method 2: Place-Value-Table 

A place-value table can be drawn to teach placement of values and word notations. 

There are 4 main blocks to the place-value table:

(1) millions, 

(2) thousands

(3) hundreds and 

(4) decimals.

Within each block, it is further divided into hundreds, tens and ones. 

A given number is to be written onto the place value table from the right to left. 

Example: 

Write 930527 in words

Step1: Draw/Fill ‘9’,’3’,’0’,’5’,’3’,’7’ from the right to the left. 

Step2: READ the number from left to right, and including the word at every end of 

Method 3 : Writing 'Place Value Table' Title

Method 3 : Writing 'Place Value Table - PVT' Title

h t o (M)    h t o (T)      h t o

                     ^                ^       ^ ^ ^

  (millions  thousands  hundreds tens ones)

Example

Write 1459 in words

h t o (M)    h t o (T)      h t o          
       1      4 5  9                            Step 1: Write and fill in number                    

One thousand four hundred and fifty-nine    Step 2 : Write from left to right

Example: Write 1498012 in words
h t o (M)    h t o (T)      h t o            
      1          4 9 8          0 1 2                       Step 1: Write and fill in number   

Step 2: Write from left to right

  One million four hundred nine eight thousand and twelve  

Practice: 

Write the following in words : (a) 2930     (b) 47084     (c) 106507

{Ensure that the spellings are correct}

FROM WORDS TO NUMBER

METHOD1 (PVT)

Convert eight million seven hundred and sixty-five thousand four hundred and thirty-two to numbers

Step1: Underline hundred, thousand and million and write PVT in line with words 

            h t o (M)                                               h t o (T)             h t o

           eight million seven hundred and sixty-five thousand four hundred and thirty-two

Step 2: Convert words to number Fill in numbers from right to left

            h t o (M)                                               h t o (T)             h t o

         eight million seven hundred and sixty-five thousand four hundred and thirty-two

                8 (3rd)                                            765 (2nd )          432 (1st to convert)

Step 3: Answer : 8,765,432

METHOD2

Example           

Write Eight million, seven hundred and sixty-five thousand, four hundred and      thirty-two in number form.

 Step 1: Underline keywords – “Million’ (if any), ‘thousand’ 

 Step 2: Circle words before keywords ‘Million’, ‘thousand’ and the last group.

      8           ,                                 765                              ,                         432

Step 3: Write numbers below the circle, and put a comma for the underline words. 

Answer: 8,765,432

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N3. Whole Numbers : Comparing and Ordering Numbers (more than/less than)

MORE THAN

 

       OOOO△△△

                    4 is more than 3

The number of circles is MORE THAN the number of triangles

LESS THAN

              OOOO△△△

                     3 is less than 4

The number of triangles is LESS THAN the number of circles

SMALLEST, LARGEST 

Smallest: of the least value as compared to others

Largest: of the biggest value as compared to others

Example: 

            (a)    0 ,1 4, 7, 8

            (b)    2, 4, 6, 8, 0

            (c)    9, 8, 6, 4, 0

            (d)    3, 5, 4, 6, 9

Which number-set is arranged in order, beginning with the smallest number? (a)

Which number-set is arranged in order, beginning with the largest number? (c)

ODD NUMBER

Numbers ending with 1, 3, 5, 7, 9

Example

       19   ,    23,     835,    47,    1259,     361

EVEN NUMBER

Numbers ending with 0, 2, 4, 6, 8

ORDERING

Example

Arrange the following in decreasing order (big to small)

            23 642,          22 893,          25147

Method

Step1: Arrange numbers in rows

                        2 2  6 4 2

                        2 3  6 9 3

                        2 5 1 4 7

Step 2: Compare from left to right, until the column with different values, label from big (1) to small 

                        2 3  6 4 2   (2)

                        2 2  8 9 3   (3)

                        2 5  1 4 7   (1)

              same ↑    go next right number

                          ↑  5 is the largest number(1), then 3(2) , 2(1) <- label (1), (2) ,(3)

Step3: Write the answer with label (1), (2), (3) 

                      25147, 23693, 22642

Example

Arrange the following in increasing order (small to big)

            43642,          43193,          54147

Method

Step1: Arrange numbers in rows

                        4 3  6 4 2

                        4 3  1 9 3

                        5 4  1 4 7

Step 2: Compare from left to right, until the column with different values, label 3 (for 3 numbers comparison) for the largest number, and continue to next column

                        4 3  6 4 2   2

                        4 3  1 9 3   1

                        5 4  1 4 7   3             

                       ^           5 is biggest, strike, label 3(3 numbers), go next right number

                           ^       both are 3, go next right number

                                ^  6 and 1, label 2 for the bigger number, and 1 for the smaller number

Step3: Write the answer - label 1, 2, 3

                        43193, 43642, 54147

Solving 'More than' and 'Less than' questions

More than question (big - small)

Method

=> Big number - small number

Example: 102 is ______ more than 77.

Step1: Circle/Underline 102, 77, More than (-)  => [big - small]

Step2: Write in equal form 

     => 102 -  77 =  ___    [Arrange  big number - small number = _____ ]

           102 - 77 = 25    

Step3: Solve 

        102 is 25 more than 77.

Example: 523 is 100 more than ____

Step 1 : Circle/Underline 523, 100, More than  => [big - small]

Step 2 Write in equal form

       => 523 - 100 = ____  [Arrange  big number - small number = _____ ]

             523 - 100 = 423  

Step 3 : Solve

              523 is 100 more than 423

Less than questions

(1) The first number is smaller than the second number

First number is smaller than the second number, big number subtract(-) the small number  

            First number smaller :  big number - small number 

Example

    68 is ______ less than 89.

Step1: Circle/Underline 68(1st), 89(2nd) , Less than => 1st number(68) is smaller (-)

Step 2: Write in equal form (big number - small number)

           89 - 68 =  _____

       => 89 - 68 = 21

Step 3: Solve

              68 is 21 less than 89

(2) The first number is bigger than the second number

If the first number is bigger than the second number, ADD + both numbers

      First number bigger :  big number + small number 

Example: 523 is 100 less than ____

Step 1 : Circle/Underline 523(1st), 100 (2nd), less than: 1st number bigger (+)

Step 2 : Write in equal form

             523 + 100 =  _____ (Add both numbers)

             523 + 100 = 623

Step 3 : Solve

              523 is 100 less than 623

Example (more than / Less than)

Eric has 5 yellow balls. Rahul has 3 blue stickers.

           

(a) How many more sticker does Eric have?

Step 1: Underline, (method - more than => - )

Step 2:  Write in equal form

              5 - 3 = 2

Step 3: Solve

Eric has 2 more stickers than Bala

(b) How many stickers must Rahul has to have the same number of sticker as Eric?

Step 1: Underline and method to use

      [Rahul has less sticker than Eric ]

       3 is ___ less than 5 [1st number is smaller, big - small

Step 2 : Write in equal form

5 - 3 =. 

5 - 3 = 2

Step 3 : Solve

       Rahul has 2 fewer than Eric

COMPARE and ORDER Terms

(1)   Great/greater/greatest; as great as, greater than

(2)   Small/smaller/smallest; as small as, smaller than

(3)   Many/More/Most; as many as, more than       

(4)   Little/Less/Least; as little as, less than

(5)   Few/Fewer/Fewest; as few as, fewer than

(6)   Long/Longer/Longest; as long as, longer than                     

(7)   Short/Shorter/Shortest; as short as, shorter than

(8)   Tall/Taller/Tallest, taller than, as tall as  

(9)   Heavy/Heavier/Heaviest; as heavy as, heavier than                               

(10) Light/Lighter/Lightest; as light as; lighter than

(11) Decreasing / Increasing

Link to : Mathematics Resource Content Page

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