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