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:
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 place-value 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
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.
Expanded Form of Large Numbers
Expanded Form (In Indian system)
We already know how to express a number in the expanded form. We can also express the larger number written in the Indian system or International system in the expanded form.
For Example.
1. Write the expanded form of the number 34,78,35,334 in the Indian system.
Solution:
In the Indian system the number 34,78,35,334 can be written in the expanded form as:
30,00,00,000 + 4,00,00,000 + 70,00,000 + 8,00,000 + 30,000 + 5,000 + 300 + 30 + 4.
2. Write the expanded form of the number 748,301,413,119 in the International system.
Solution:
In the International system the number 748,301,413,119 can be written in the expanded form as:
700,000,000,000 + 40,000,000,000 + 8,000,000,000 + 300,000,000 + 1,000,000 + 400,000 + 10,000 + 3,000 + 100 + 10 + 9.
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 3-digit 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 3-digit 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
XI. Express in expanded form.
(i) 49,38,268
(ii) 29,17,25,219
(iii) 76,09,25,011
(iv) 524,698,432,381
(v) 94,308,409,002
(vi) 174,325,946,791
Answer:
XI. (i) 40,00,000 + 9,00,000 + 30,000 + 8,000 + 200 + 60 +8
(ii) 20,00,00,000 + 9,00,00,000 + 10,00,000 + 7,00,000 + 20,000 + 5,000 + 200 + 10 + 9
(iii) 70,00,00,000 + 6,00,00,000 + 9,00,000 + 20,000 + 5,000 + 10 + 1
(iv) 500,000,000,000 + 20,000,000,000 + 4,000,000,000 + 600,000,000 + 90,000,000 + 8,000,000 + 400,000 + 30,000 + 2,000 + 300 + 80 + 1
(v) 90,000,000,000 + 4,000,000,000 + 300,000,000 + 8,000,000 + 400,000 + 9,000 + 2
(vi) 100,000,000,000 + 70,000,000,000 + 4,000,000,000 + 300,000,000 + 20,000,000 + 5,000,000 + 900,000 + 40,000 + 6,000 + 700 + 90 + 1
1. What is the expanded form of a number?
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?
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?
3. What is the expanded form of 468?
Answer:
The expanded form of the number 468 = 400 + 60 + 8
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- Formation of Numbers.
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- 4 Digits Number on Spike Abacus.
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- Large Number.
- Place Value Chart.
- Place Value.
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- Expanded form of a Number.
- Standard Form.
- Comparison of Numbers.
- Example on Comparison of Numbers.
- Successor and Predecessor of a Whole Number.
- Arranging Numbers.
- Formation of Numbers with the Given Digits.
- Formation of Greatest and Smallest Numbers.
- Examples on the Formation of Greatest and the Smallest Number.
- Rounding off Numbers.
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