We know that the number written as sum of the placevalues 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:
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:
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
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 placevalue chart.
(i) 72,908
Thus, 72, 90870,000 + 2,000 + 900 + 0 + 8
(ii)
Thus, 5,01,492 = 5,00,000 + 0 + 1,000 + 400 + 90 + 2
= 5,00,000 + 1,000 + 400 + 90 + 2
1 lakh 
= 10^{5} 
= 100000 
2 lakh 
= 5 × 10^{2} 
= 200000 
3 lakh 
= 5 × 10^{3} 
= 300000 
4 lakh 
= 5 × 10^{4} 
= 400000 
5 lakh 
= 5 × 10^{5} 
= 500000 
6 lakh 
= 6 × 10^{5} 
= 600000 
7 lakh 
= 7 × 10^{5} 
= 700000 
8 lakh 
= 8 × 10^{5} 
= 800000 
9 lakh 
= 9 × 10^{5} 
= 900000 
10 lakh 
= 10 × 10^{5} 
= 1000000 
Note: There are 7 digits in ten lakhs.
Therefore the seventh place is called ten lakhs place.
Worksheet 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
VIII. Fill in the blanks. One has been done for you.
(i) 356 = __3__ hundreds __5__ tens and __6__ ones
(ii) 593 = _____ hundreds _____ tens and _____ ones
(iii) 639 = _____ hundreds _____ tens and _____ ones
(iv) 765 = _____ hundreds _____ tens and _____ ones
Answer:
VIII. (ii) 5 hundreds; 9 tens; 3 ones
(iii) 6 hundreds; 3 tens; 9 ones
(iv) 7 hundreds; 6 tens; 5 ones
IX. Write the expanded form of 3digit numbers. One has been done for you.
(i) 645 = _600_ + __40__ + __5__
(ii) 397 = _____ + _____ + _____
(iii) 702 = _____ + _____ + _____
(iv) 631 = _____ + _____ + _____
Answer:
IX. (ii) 300 + 90 + 7
(iii) 700 + 0 + 2
(iv) 600 + 30 + 1
X. Write the 3digit numbers in short form as shown.
(i) 100 + 20 + 6 = __126__
(ii) 900 + 20 + 9 = _____
(iii) 600 + 60 + 6 = _____
(iv) 400 + 0 + 3 = _____
(v) 300 + 40 + 5 = _____
(vi) 800 + 70 + 4 = _____
(vii) 700 + 70 + 8 = _____
(viii) 900 + 20 + 0 = _____
X. (ii) 929
(iii) 666
(iv) 403
(v) 345
(vi) 874
(vii) 778
(viii) 920
1. What is the expanded form of a number?
Answer:
A number written as the sum of the place values of its digits, is said to be in expanded form of a number.
2. What is the short form of a number?
Answer:
The number written in standard form is said to be in short form
3. What is the expanded form of 468?
Answer:
The expanded form of the number 468 = 400 + 60 + 8
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