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HomeMathExpanded Type of a Quantity | Writing Numbers in Expanded Type

Expanded Type of a Quantity | Writing Numbers in Expanded Type


We all know that the quantity written as sum of the place-values of its digits is known as the expanded type of a quantity.

Customary Type

Expanded Type

20,37,81,405

=

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

In expanded type of a quantity, the quantity is proven in line with the place values of its digits.


That is proven right here:

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

Standard Form and Expanded Form

Therefore, 2385 = 2000 + 300 + 80 + 5

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

Once more, 

2,55,109

=

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

Customary Type                          

Expanded Type

Expanded
Notation

The digits of the numerals 394381, 163845, 583927 are
entered within the place worth chart as given under.

Lakhs

100000


Ten hundreds 

10000


Hundreds

1000


A whole lot

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’s the expanded type of the quantity 394381?

394381 =
3 lakhs + 9 ten hundreds + 4 hundreds + 3 a whole lot +

               8 tens + 1 one

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

               1 × 1

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

(ii) What’s the expanded type of the quantity 163845?

163845 =
1 lakhs + 6 ten hundreds + 3 hundreds + 8 a whole lot +

               4 tens + 5 ones

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

            = 5 × 1

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

(iii) What’s the place worth of all of the digits of quantity 583927?

Digit

Place Worth

5

5
lakhs

5 × 100000 =      500000

8

8
ten hundreds

8 × 10000   =      80000

3

3
hundreds

3 ×
1000     =      3000

9

9
a whole lot

9 ×
100       =      900

2

2
tens

2 ×
10        =      20

7

7
ones 

7 ×
1          =      7

Given the expanded type of a quantity, we are able to additionally write the
numeral in the usual type.

500000 + 80000 + 3000 + 900 + 20 + 7

= 583927

Expanded type of a quantity to plain type.

(iv) 3000 + 200 + 40 + 8 = 3248

(v) 7 ten hundreds + 4 hundreds + 2 a whole lot + 3 tens + 8 ones

   = 74238

Solved Examples on Expanded Type of a Quantity:

1. Write the expanded type for the quantity 70,39,41,295.

Resolution:

Expanded Form of a Number

Due to this fact, the expanded type of the quantity 70,39,41,295 is 70,00,00,000 + 00000000 + 3000000+ 900000 + 40000 + 1000 + 200 + 90 + 5.

2. Discover the expanded type of 453169.

Resolution:

Place values of digits 453169

Find the Expanded Form of a Number

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

3. Write the quantity in figures after which in phrases for the next expanded type:

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

Resolution:

80000 + 8000 + 500 + 50 + 7

= 88557 (in figures)

Eighty eight thousand 5 hundred fifty seven (in phrases)

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

Resolution:

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

100 thirty two thousand sixteen (in phrases)

We are able to write the expanded type of numbers in numerous methods.

4. Write in expanded type:

(i) 28369

Write as:

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

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

(c) 2 ten hundreds + 8 hundreds + 3 a whole lot + 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 hundreds + 1 ten hundreds + 9 hundreds + 2 a whole lot + 4 tens + 7 ones

Numbers Past One Lakh

1
lakh

2 lakhs

3 lakhs

4 lakhs

5 lakhs

6 lakhs

7 lakhs

8 lakhs

9 lakhs

10 lakhs

=     10(^{5})

=     2 × 10(^{5})

=     3 × 10(^{5})

=     4 × 10(^{5})

=     5 × 10(^{5})

=     6 × 10(^{5})

=     7 × 10(^{5})

=     8 × 10(^{5})

=     9 × 10(^{5})

=     10 × 10(^{5})

=     100000

=     200000

=     300000

=     400000

=     500000

=     600000

=     700000

=     800000

=     900000

=     1000000

Observe: There are 7 digits in ten lakhs.

         Due to this fact the seventh place is known as ten lakhs place.

Questions and Solutions on Expanded Type of a Quantity:

I. Write the given numbers in expanded type:

(i) 617 = _____ + _____ + _____

(ii) 319 = _____ + _____ + _____

(iii) 286 = _____ + _____ + _____

(iv) 939 = _____ + _____ + _____

(v) 677 = _____ + _____ + _____

(vi) 918 = _____ + _____ + _____

(vii) 328 = _____ + _____ + _____

(viii) 520 = _____ + _____ + _____

(ix) 647 = _____ + _____ + _____

(x) 474 = _____ + _____ + _____

Reply:

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 type for the given numbers:

(i) 7,12,306

(ii) 8,07,392

(iii) 6,44,895

(iv) 3,73,737

(v) 9,22,005

Solutions:

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 quantity in customary type:

(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

Solutions:

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 quantity:

(i) 5 ones 6 tens 1 hundred

(ii) 7 a whole lot 9 ones 1 ten

(iii) 3 tens 5 a whole lot 6 ones

(iv) 8 ones 9 tens 2 a whole lot

(v) 4 a whole lot 6 ones 7 tens

(vi) 2 tens 3 a whole lot 6 ones

_____ _____ _____

_____ _____ _____

_____ _____ _____

_____ _____ _____

_____ _____ _____

_____ _____ _____

Reply:

(i) 1 hundred 6 tens 5 ones

(ii) 7 a whole lot 1 ten 9 ones 

(iii) 5 a whole lot 3 tens 6 ones

(iv) 2 a whole lot 9 tens 8 ones 

(v) 4 a whole lot 7 tens 6 ones 

(vi) 3 a whole lot 2 tens 6 ones

 =

 =

 =

 =

 =

 =

165

719

536

298

476

326

V. Circle the proper one

(i) 9 a whole lot 2 tens 3 ones

(ii) 6 a whole lot 0 tens 1 one

(iii) 3 a whole lot 6 tens 3 ones

(iv) 2 a whole lot 2 tens 1 one 

(v) 5 a whole lot 8 tens 4 ones 

(vi) 9 a whole lot 8 tens 0 ones

932     923     329

106     601     610

363     336     633

212     221     122

854     584     485

980     908     809

Reply:

(i) 923

(ii) 601

(iii) 363

(iv) 221

(v) 584

(vi) 980

VI. Write the next numbers within the expanded type in three
other ways as proven within the examples.

(i) 61,052

61,052 –   6 ten hundreds + 1 thousand + 0
a whole lot + 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

Associated Idea 

4th Grade Math Actions

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