Comparision of Numbers

COMPARISION OF NUMBERS:

We compare two numbers to find out which is greater or smaller or equal by using >,<, = signs.

(i)  We use Equal to ( = )  sign, if the digits places in the given two numbers are Equal.

(ii) In the given numbers, if one of the number is greater than the other number, then we will use Greater than symbol (>).

(iii) In the given number, if one of the number is lesser than the other number, then we will use Lesser than symbol (<).    

In comparision of two numbers, we have to check two cases:

Case(i)  Numbers with Different number of Digits.

Case(ii) Numbers with the Same number of Digits.

 

Case (i) Numbers with Different number of Digits:

If  two numbers have different number of digits, the number with more digits is greater.

1) Compare 8349 and 937

Answer:

In the number 8349,the number of digits are : 4

The number 937, the number of digits are : 3

The number 8349 has more digits than the number 937,therefore

Th	H	T	O
8	3	4	9

H	T	O
9	3	7

 

        

  Number of digits = 4               >   Number of digits = 3                                       

   8349 > 937  

 

 

2) Compare 659 and 5094

Answer:

The number of digits in 659 are: 3

The number 5094,the number of digits are 4,which is greater than 3.Therefore;

H	T	O
6	5	9

Th	H	T	O
5	0	9	4

 

  

Number of digits = 3     <     Number of digits = 4

659 < 5094

    (or)

5094 >  659 .

 

3) Compare 126 and 78

Answer:

H	T	O
1	2	6

T	O
7	8

                                   

           

Number of digits = 3   >   Number of digits = 2

126 > 78

 

4) Compare 90000 and 9523

Answer:

TTh	Th	H	T	O
9	0	0	0	0

Th	H	T	O
9	5	2	3

 

 

Number of digits = 5                       >         Number of digits = 4

90000 > 9523

 

5) Compare 36 and 387

Answer : 36 < 387.

                    (or)

                387 > 36 .  

 

 

  Case(ii) Numbers with Same number of Digits:

If two numbers have the same number of digits, then compare the digits at the greatest place.We have to continue comparing the digits place until we find different digits at the same place.The number with the greater digit at its place is greater.

 

1) Compare 5764 and 5839

Answer:             

The two numbers have same number of digits i.e; 4. So, we have to compare the digits in greatest place of the two numbers. The greatest place of the two numbers are Thousands place.

The Thousands Place digit in two numbers are same = 5. So, we have to compare the next digit place i.e; Hundreds place. The digits in the Hundreds place are 7 and 8 ( 7 < 8 ).In Hundreds place we found different digits. Therefore, we stop comparing the next digit places.

    

5764 < 5839  

      (or)  

  5839  >  5764 .

  

2) Compare 4987 and 2376

Answer:

The greatest place value of the digits are Thousands place.So, we have to compare the digits in Thousands place,which are different.The number with the greater digit at its place is the greater number.

4987 > 2376

 

3) Compare 3584 and 3588

Answer:

 In this problem, the digits in Thousands , Hundreds ,Tens place have Same values. So, we have to compare the digits in the Ones place.

3584 < 3588 

      (or)

 3588 > 3584

 

4) Compare   6820 and 6873

Answer:

Here, the digits have the same values at Thousands, Hundreds places. So, we have to compare the digits at Tens place.

6820 < 6873 

    ( or ) 

 6873 > 6820.

Decimal Number- Expanded Form and Standard Form

Decimal Number- Expanded Form and Standard Form

Expanded Form:

1) 6.87

In the number 6.87, the whole part is 6 and the decimal part is 87.

The whole part has only one digit,i.e; 6 which is in Ones Place.

The decimal part has two digits,i.e; 87.

The digit 8 is in Tenths place(1/10) ,so the place value of digit 8 is

 8* 1/10 = 8/10 = 0.8  

The digit 7 is in Hundredths place(1/100) ,so the place value of digit 7 is

 7 * 1/100 = 7/100 = 0.07

Therefore, the Expansion form of the number

 6.87 =  6 + 8/10 + 7/100

         =  6 + 0.8 + 0.07               

 

2)  644.219

   The whole part of the number is 644, and its expansion is

    644 = 600 + 40 + 4

  The decimal part of the number is 219

  The digit 2 is in Tenths place(1/10),its place value is :2* 1/10 = 2/10 = 0.2

  The digit 1 is in Hundredths place(1/100),its place value is :

   1 * 1/100 = 1/100 = 0.01

  The digit 9 is in Thousandths place(1/1000), its place value is: 

    9 * 1/1000 = 9/1000 = 0.009

 Therefore, the Expansion form of the number 644.219  is

 644.219 = 600 + 40 + 4 + 2/10 + 1/100 + 9/1000

              = 600 + 40 + 4 + 0.2 + 0.01 + 0.009

 

3) 0.705

The whole part of the number is 0

The decimal part of the number is 75.

The digit 7 is in Tenths place(1/10) ,the place value of digit 7 is 

 7 * 1/10 = 7/10 = 0.7

The digit 0 is in Hundredths place(1/100), its place value is

 0 * 1/100 = 0/100 = 0    

The digit 5 is in Thousandths place(1/1000),its place value is 

5* 1/1000 = 5/1000 = 0.05

Note: If  digit Zero is in either Whole part or in Decimal part,then no need to write its digit place value in the expansion form.

0.705 = 7/10 + 5/1000

          = 0.7 + 0.05

 

4)  7025.004 = 7000 + 20 + 5 + 4/1000

                      = 7000 + 20 + 5 + 0.004

        

 5) 65.709 = 60 + 5 + 7/10 + 9/1000

                 = 60 + 5 + 0.7 + 0.009

 

Standard Form:

1)   300 + 5/10 + 8/100 + 9/1000

 The whole part in the given expansion is 300.The digit in the Hundreds place value is 3.There are no digits in Tens and Ones place value(as the digits in Tens,Ones place value are Zeroes.).

The decimal part digits in the expansion are 5/10 + 8/100 + 9/1000.

The digits of the decimal part occupies three places values: Tenths, Hundredths , Thousandths.

The digit in the Tenths place (1/10) is 5

The digit in the Hundredths place (1/100) is 8

The digit in the Thousandths place (1/1000) is 9

Therefore , the standard form is

300 + 5/10 + 8/100 + 9/1000 = 300.589

 

2) 100 + 3 + 4/100

There are three place values for the digits in the whole part ,i.e; Hundreds,Tens,Ones.

The digit in the Hundred place is 1. The digit in Tens place is 0 . 

The digit in Ones place is 3.

The number of digits in the decimal part are two.Tenths,Hundredths.

The digit in the Tenths place is 0.

The digit in the Hundredths place (1/100) is 4

Therefore,the standard form is

100 + 3 + 4/100 = 103.04

 

3)  7/10 + 9/1000

There are no digits in the whole part,so we can put Zero in the whole part.

The number of digits in the decimal part are Three.

The digit in the Tenths place (1/10 ) is 7

The digit in the Hundredths place ( 1/100 ) is 0

The digit in the Thousandths place is(1/1000) is 9

Therefore,the standard form  is

7/10 + 9/1000 = 0.709

 

4) 1000 + 70 + 9/100

In the number, the greatest place value for the whole part is Thousands,the digit is 1.

There are no digits in Hundreds and Ones place value ,so we have to put Zeroes in their place value.The digit in the Tens place is 7.

The decimal digits place value in the number two: Tenths and Hundredths.

The digit in Tenths place is 0.The digit in the Hundredths place (1/100) is 9

Therefore, the standard form is

1000 + 70 + 9/100 = 1070.09

 

5) 7 + 8/10 + 5/100 = 7.85

Expanded Form and Standard Form of a Number

EXPANDED FORM AND STANDARD FORM OF A NUMBER:

Expanded Form:

The expanded form of a number is written as the sum of the place values of each digit.

Standard Form :

In writing the standard form of a number ,we have to write the face value of each digit at its correct place.

 Expanded Form:

1) 5736 :

Answer:

There are 4 digits in the number  5736. The digits occupies four place values .i.e; Ones(O),Tens(T),Hundreds(H),Thousands(Th).

The place values for the digits are given from right to left in the number.

5736 = 5000 + 700 + 30 + 6.

 

2)  9406:

 In this number  9406, zero is in tens place.If digit zero is in any place in the number,then we need not write the digit zero place value in the expansion of that number.

9406 = 9000 + 400 + 0 + 6

         = 9000 + 400 + 6.

3)  68927 = 60,000 + 8,000 + 900 + 20 + 7.

4)  5040 =  5000 + 40.

 

Standard Form:

1)  7000 + 200 + 1 =

  In the expanded form , the greatest place value is Thousands and the digit is 7. The next greatest place value is Hundreds,the digit  is 2.The next is Tens place, and then  it is Ones place,the digit is 1.

In the given problem,there is no digit in the tens place.If there is no place value for a digit in the expansion,we have to put zero in its place value while writing the number.

So, in writing the number we have to put zero in Tens place value of the number.

7000 + 200 + 1 = 7201 .

 

2)  6000 + 40 + 5 =

Here, the greatest place value is Thousands and the digit is 6, next greatest is Hundreds: in Hundreds place no digit is there i.e; 0.so we have to put 0 in Hundreds Place value.The next place value is Tens,the digit is 4. The next place value is Ones,the digit is 5.

Therefore; 6000 + 40 + 5 = 6045.

 

3) 40000 + 900 + 50 =

The greatest Place value is TenThousands,the digit is 4.The next greatest place value is Thousand,no digit is there so the digit is 0 .The next is Hundreds place value,the digit is 9.The next place value is Tens,the digit is 5.The next place value is Ones, no digit is there in Ones place,so the digit is 0.

 Therefore, 40000 + 900 + 50 = 40950.

 

4) 8000 + 200 + 50 + 7 = 8257.

5) 900 + 80 + 3 = 983.

Decimal Number - Place Value

PLACE VALUE CHART FOR DECIMAL NUMBERS

1)  36.524

Answer:

In the number 36.524, the whole part digits are 36 and the decimal part digits are 524.

The place values of the whole part digit 36  are Tens ( T ), Ones (O).

Digit 3 is in Tens(T) place ,so place value of 3 becomes = 3*10 = 30

 Digit 6 is in Ones(O) place,so the place value of 6 becomes = 6*1 = 6.

 The place values of the Decimal part digit 524 are Tenths(t) ,Hundredths(h), Thousandths(th).

Digit 5 is in Tenths(t) place,so place value of 5 becomes = 5* 1/10 = 5/10 = 0.5

Digit 2 is in Hundredths(h) place,so the place value of 2 becomes = 2 * 1/100 = 2/100 = 0.02

Digit 4 is in Thousandths(th) place,so the place value of 4 becomes = 4 * 1/1000 = 4/1000

     = 0.004

Place value Chart of the number 36.524:

Place value	Tens  (T)	Ones   (O)	Tenths   (t)	Hundredths    (h)	Thousandths      (th)
Number	3	6	5	2	4
	Whole part		Decimal Part

Place Value for the number : 36.524

Expanded Form: 

 36.524 = 30 + 2 + 0.5 + 0.02 + 0.004.

2)  571.872

Answer:

The digits in the whole part are 571,the digits occupies three place values.

 i.e: Hundred(H), Tens( T) ,Ones(O).

The digits in the decimal part are 872,the digits occupies three place values.

i.e; Tenths(th),Hundredths( h),Thousandths(th).

Place value Chart :

Place Value	Hundreds    (H)	Tens   (T)	Ones  (O)	Tenths   (t)	Hundredths     (h)	Thousandths       (th)
Number	5	7	1	8	7	2
	Whole Part			Decimal Part

Place Value :

 

Expanded Form:

571.872 = 500 + 70 + 1 + 0.8 + 0.07 + 0.002.

3) 4.02

Answer:

The digit in the whole part  is 4, the digits occupies only one place vlaue. i.e; Ones(O)

The digits in the decimal part are 02, the digits occupies two place values.

i.e; Tenths(t), Hundredths(h).

Place value Chart :

Place value	Ones     ( O)	Tenths     (th)	Hundredths      (h)
Number	4	0	2
	Whole Part	Decimal Part

Place Value:

Expanded Form :

4.02 = 4 + 0.0 + 0.02

        = 4 + 0.02

Note: In writing the expanded form,we can leave out the digit zero in the number.

Decimal Place- Number Name

DECIMAL PLACE  NUMBER NAME (OR) WORD FORM:

In writing the number name for decimal number,the decimal point can be written in two ways.

In the number name the decimal point is replaced by “ POINT “ or  “ AND” .

Case(i)  POINT :

If the decimal point is replaced by “POINT”,in writing the numbers names.

We have to write number names of a particular decimal digit.

We should not write place value number names for the decimal digits.

Example:

Let the number be :231.946

Answer:

The number of digits in the number 231.946 after decimal point (decimal places) are : 3

The number of digits in Whole part of the number 231.946 are 3.

The digits in the whole part of the number 231.946  number names are written as

231= Two Hundred and thirty-one.

The digits in the decimal part of the number 231.946 are 9 ,4 , 6

Therfore, the number names are written as:

9 = nine

4 = four

6 = six.

So,the number name for the number 231.946 is written as:

231.946 = Two Hundred and thirty-one point nine four six.

 

Case(ii): “ AND “

If the decimal point is replaced by “AND” in writing the number name.We should write Place Value number names for the decimal digits.

Example:

Let the number be : 231.946.

In the number 231.946, the whole part is 231.

The decimal part is 946,after the decimal point there are 3 digits.Therfore, the decimal part comes under THOUSANDTHS(th) period.

The number name for the whole part in the number 231.946 is:

231 = Two Hundred and thirty-one.

The number name for the decimal part in the number231.946 is :

946 = Nine Hundred forty-six Thousandths

We have to write the number name for the decimal digits as in whole part and atlast have to write the corresponding PlaceValue of the decimal part.

The number name for the digit 231.946 is : “ Two Hundred thirty-one and nine hundred forty-six Thousandths”.

 

1. 103.4:

Answer:

 One Hundred and three Point four.

         (or)

One Hundred and three and four Tenth.

 

 

2.  47.095

Answer:

            Forty-seven Point zero nine five.

                       (or )

            Forty-seven And Ninety-five Thousandths.

 

3. 171.62

Answer:

             One Hundred and seventy-one Point six two.

                        (or)

            One Hundred and seventy-one And sixty-two Hundredths.

 

4. 300.8241

Answer:

             Three Hundred Point eight two four one.

                        (or)

             Three Hundred And Eight Thousand two hundred forty-one TenThousandths.

 

 Number Name - Number:

 1.  Four thousand three hundred twenty And seven hundred two Thousandths =                      4,320.702

                        (or)

     Four thousand three hundred twenty Point seven zero two = 4,320.702

2.   Eight And sixty-two Hundredth = 8.62

                        (or)

      Eight Point six two = 8.62

 3.   Nine Thousand four hundred twelve TenThousandths = 0.9412

                        (or)

      Point nine four one two =0.9412

4.   Sixty Point one three = 60.13

         (or)

    Sixty And thirteen Hundredth = 60.13

5.   One Tenth = 0.1

             

6.   Seventy-two And five Hundredths = 72.05

                 (or)

       Seventy-two Point zero five = 72.05