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:

$Standard Form and Expanded Form$

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

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

Questions and Answers 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

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