Expanded form of a Number

We know that the number written as sum of the place-values of its digits is called the expanded form of a number.

Standard Form

Expanded Form

20,37,81,405

=

20,00,00,000 + 0 + 30,00,000 + 7,00,000 + 80,000 + 1,000 + 400 + 0 + 5

In expanded form of a number, the number is shown according to the place values of its digits.

This is shown here:

In 2385, the place values of the digits are given below:

Standard Form and Expanded Form

Hence, 2385 = 2000 + 300 + 80 + 5

Thus, 2000 + 300 + 80 + 5 is the expanded form of 2385.


Again, 

2,55,109

=

2,00,000 + 50,000 + 5,000 + 100 + 0 + 9

Standard Form                          

Expanded Form


Expanded Notation

The digits of the numerals 394381, 163845, 583927 are entered in the place value chart as given below.

Lakhs

100000


Ten thousands 

10000


Thousands

1000


Hundreds

100


Tens

10


Ones

1


3

9

4

3

8

1

1

6

3

8

4

5

5

8

3

9

2

7

(i) What is the expanded form of the number 394381?

394381 = 3 lakhs + 9 ten thousands + 4 thousands + 3 hundreds +

               8 tens + 1 one

            = 3 × 100000 + 9 × 10000 + 4 × 1000 + 3 × 100 + 8 × 10 +

               1 × 1

            = 300000 + 90000 + 4000 + 300 + 80 + 1


(ii) What is the expanded form of the number 163845?

163845 = 1 lakhs + 6 ten thousands + 3 thousands + 8 hundreds +

               4 tens + 5 ones

            = 1 × 100000 + 6 × 10000 + 3 × 1000 + 8 × 100 + 4 × 10 +

            = 5 × 1

            = 100000 + 60000 + 3000 + 800 + 40 + 5


(iii) What is the place value of all the digits of number 583927?

Digit

Place Value

5

5 lakhs


5 × 100000 =      500000

8

8 ten thousands


8 × 10000   =      80000

3

3 thousands


3 × 1000     =      3000

9

9 hundreds


9 × 100       =      900

2

2 tens


2 × 10        =      20

7

7 ones 


7 × 1          =      7

Given the expanded form of a number, we can also write the numeral in the standard form.

500000 + 80000 + 3000 + 900 + 20 + 7

= 583927


Expanded form of a number to standard form.

(iv) 3000 + 200 + 40 + 8 = 3248

(v) 7 ten thousands + 4 thousands + 2 hundreds + 3 tens + 8 ones

   = 74238


Solved Examples on Expanded Form of a Number:

1. Write the expanded form for the number 70,39,41,295.

Solution:

Expanded Form of a Number

Therefore, the expanded form of the number 70,39,41,295 is 70,00,00,000 + 00000000 + 3000000+ 900000 + 40000 + 1000 + 200 + 90 + 5.


2. Find the expanded form of 453169.

Solution:

Place values of digits 453169

Find the Expanded Form of a Number

So, 453169 = 400000 + 50000 + 3000 + 100 + 60 + 9



3. Write the number in figures and then in words for the following expanded form:


(i) 80000 + 8000 + 500 + 50 + 7

Solution:

80000 + 8000 + 500 + 50 + 7

= 88557 (in figures)

Eighty eight thousand five hundred fifty seven (in words)

(ii) 100000 + 30000 + 2000 + 10 + 6

Solution:

100000 + 30000 + 2000 + 10 + 6 = 132016 (in figures)

One hundred thirty two thousand sixteen (in words)

We can write the expanded form of numbers in different ways.


4. Write in expanded form:

(i) 28369

Write as:

(a) 20000 + 8000 + 300 + 60 + 9

(b) 2 × 10000 + 8 × 1000 + 3 × 100 + 6 × 10 + 9 × 1

(c) 2 ten thousands + 8 thousands + 3 hundreds + 6 tens + 9 ones


(ii) 419,247

Write as:

(a) 400000 + 10000 + 9000 + 200 + 40 + 7

(b) 4 × 100000 + 1 × 10000 + 9 × 1000 + 2 × 100 + 4 × 10 + 7 × 1

(c) 4 hundred thousands + 1 ten thousands + 9 thousands + 2 hundreds + 4 tens + 7 ones


Writing a numeral as the sum of the place values of all its digits is called the expanded form of that numeral.


5. Write (i) 72,908; (ii) 5,01,492 in the expanded form.

Solution:

Write the given numbers in the place-value chart.

(i) 72,908

Expanded Form - Place Value Chart

Thus, 72, 90870,000 + 2,000 + 900 + 0 + 8


(ii)

Expanded Form and Place Value Chart

Thus, 5,01,492 = 5,00,000 + 0 + 1,000 + 400 + 90 + 2

                       = 5,00,000 + 1,000 + 400 + 90 + 2

Numbers Beyond One Lakh

1 lakh

=     105

=     100000

2 lakh

=     5 × 102

=     200000

3 lakh

=     5 × 103

=     300000

4 lakh

=     5 × 104

=     400000

5 lakh

=     5 × 105

=     500000

6 lakh

=     6 × 105

=     600000

7 lakh

=     7 × 105

=     700000

8 lakh

=     8 × 105

=     800000

9 lakh

=     9 × 105

=     900000

10 lakh

=     10 × 105

=     1000000


Note: There are 7 digits in ten lakhs.

         Therefore the seventh place is called ten lakhs place.


Questions and Answers on Expanded Form of a Number:

I. Write the given numbers in expanded form:

(i) 617 = _____ + _____ + _____

(ii) 319 = _____ + _____ + _____

(iii) 286 = _____ + _____ + _____

(iv) 939 = _____ + _____ + _____

(v) 677 = _____ + _____ + _____

(vi) 918 = _____ + _____ + _____

(vii) 328 = _____ + _____ + _____

(viii) 520 = _____ + _____ + _____

(ix) 647 = _____ + _____ + _____

(x) 474 = _____ + _____ + _____


Answer:

I. (i) 600 + 10 + 7

(ii) 300 + 10 + 9

(iii) 200 + 80 + 6

(iv) 900 + 30 + 9

(v) 600 + 70 + 7

(vi) 900 + 10 + 8

(vii) 300 + 20 + 8

(viii) 500 + 20 + 0

(ix) 600 + 40 + 7

(x) 400 + 70 + 4


II. Write the expanded form for the given numbers:

(i) 7,12,306

(ii) 8,07,392

(iii) 6,44,895

(iv) 3,73,737

(v) 9,22,005


Answers:

II. (i) 7,00,000 + 10,000 + 2,000 + 300 + 0 + 6

(ii) 8,00,000 + 0 + 7,000 + 300 + 90 + 2

(iii) 6,00,000 + 40,000 + 4,000 + 800 + 90 + 5

(iv) 3,00,000 + 70,000 + 3,000 + 700 + 30 + 7

(v) 9,00,000 + 20,000 + 2,000 + 0 + 0 + 5


III. Write the given number in standard form:

(i) 30,000 + 4,000 + 700 + 2

(ii) 2,00,000 + 80,000 + 4,000 + 800 + 50

(iii) 6,00,000 + 40,000 + 4,000 + 800 + 90 + 5

(iv) 8,00,000 + 10,000 + 6,000 + 200 + 50 + 7

(v) 1,00,000 + 20,000 + 1,000 + 200 + 10 + 2

(vi) 9,00,000 + 2


Answers:

III. (i) 34702

(ii) 2,84,850

(iii) 6,44,895

(iv) 8,16,257

(v) 1,21,212

(vi) 9,00,002


IV. Rearrange and write the number:

(i) 5 ones 6 tens 1 hundred

(ii) 7 hundreds 9 ones 1 ten

(iii) 3 tens 5 hundreds 6 ones

(iv) 8 ones 9 tens 2 hundreds

(v) 4 hundreds 6 ones 7 tens

(vi) 2 tens 3 hundreds 6 ones

_____ _____ _____

_____ _____ _____

_____ _____ _____

_____ _____ _____

_____ _____ _____

_____ _____ _____


Answer:

(i) 1 hundred 6 tens 5 ones

(ii) 7 hundreds 1 ten 9 ones 

(iii) 5 hundreds 3 tens 6 ones

(iv) 2 hundreds 9 tens 8 ones 

(v) 4 hundreds 7 tens 6 ones 

(vi) 3 hundreds 2 tens 6 ones

 =

 =

 =

 =

 =

 =

165

719

536

298

476

326


V. Circle the correct one

(i) 9 hundreds 2 tens 3 ones

(ii) 6 hundreds 0 tens 1 one

(iii) 3 hundreds 6 tens 3 ones

(iv) 2 hundreds 2 tens 1 one 

(v) 5 hundreds 8 tens 4 ones 

(vi) 9 hundreds 8 tens 0 ones







932     923     329

106     601     610

363     336     633

212     221     122

854     584     485

980     908     809


Answer:

(i) 923

(ii) 601

(iii) 363

(iv) 221

(v) 584

(vi) 980


VI. Write the following numbers in the expanded form in three different ways as shown in the examples.

(i) 61,052

61,052 -   6 ten thousands + 1 thousand + 0 hundreds + 5 tens + 2 ones

                 -   6 × 10000 + 1 × 1000 + 0 × 100 + 5 × 10 + 2× 1

                 -   60000 + 1000 + 0 + 50 + 2


(ii) 1, 99, 099

(iii) 2,80,476

(iv) 3,67,814

(v) 8,31, 879


VII. Write the correct numbers in the blanks:

(i) _____ + 800 + 30 = 5,00,832

(ii) 1,00,000 +_____ + 5 = 1,10,005

(iii) _____ lakh + 2 ten thousands + 3 thousands + 7 hundreds + 6 tens + 5 ones = 9,23,465

(iv) 60,000 + _____ + 500 + 70 + 2 = 62,572

(v) _____ + 900 + 40 + 9 = 8,949


Answer:

VII. (i) 5,00,000

(ii) 10,000

(iii) 9

(iv) 2,000

(v) 8,000

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