# 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.

 Lakhs100000 Ten thousands 10000 Thousands1000 Hundreds100 Tens10 Ones1 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.

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 = _____ + _____ + _____

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

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

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 _____ _____ __________ _____ __________ _____ __________ _____ __________ _____ __________ _____ _____

 (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 = = = = = = 165719536298476326

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     329106     601     610363     336     633212     221     122854     584     485980     908     809

(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

VII. (i) 5,00,000

(ii) 10,000

(iii) 9

(iv) 2,000

(v) 8,000

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