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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:

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:

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

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 = _____ + _____ + _____

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 _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

 (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

(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

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