Expanded Form of a Number

Q: 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.

Q: 2. What is the short form of a number?

Answer: The number written in standard form is said to be in short form

Q: 3. What is the expanded form of 468?

Answer: The expanded form of the number 468 = 400 + 60 + 8

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

(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

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.

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?

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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