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.

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

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

You might like these

International Place-value Chart | International Place-value System
In International place-value system, there are three periods namely Ones, thousands and millions for the nine places from right to left. Ones period is made up of three place-values. Ones, tens, and hundreds. The next period thousands is made up of one, ten and hundred-thous
Comparison of Numbers | Compare Numbers Rules | Examples of Comparison
Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits from left most place until we come across unequal digits. To learn
Number of Days in a Year | Days Of The Year | Leap Year | Common Year
Here we will learn the rule of knuckle to understand the number of days in a month. All the knuckles show the months with 31 days. The others (except February) have 30 days.
Arranging Numbers | Ascending Order | Descending Order |Compare Digits
We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the smallest number then the numbers are arranged in descending order.
Dividing 3-Digit by 1-Digit Number | Long Division |Worksheet Answer
Dividing 3-Digit by 1-Digit Numbers are discussed here step-by-step. How to divide 3-digit numbers by single-digit numbers? Let us follow the examples to learn to divide 3-digit number by one-digit number. I: Dividing 3-digit Number by 1-Digit Number without Remainder:
Worksheet on Estimating Sums and Differences | Find the Estimated Sum
In 4th grade worksheet on estimating sums and differences, all grade students can practice the questions on estimations.This exercise sheet on estimating sums and differences can be practiced
Word Problems on Division | Examples on Word Problems on Division
Word problems on division for fourth grade students are solved here step by step. Consider the following examples on word problems involving division: 1. $5,876 are distributed equally among 26 men. How much money will each person get?
Adding 4-digit Numbers without Regrouping | 4-digit Addition |Addition
We will learn adding 4-digit numbers without regrouping. We first arrange the numbers one below the other in place value columns and then add the digits under each column as shown in the following examples. For example: 1. Add 1547 and 5231. Solution: Add the ones. 7 + 1 = 8
Worksheet on Subtraction | Practice the Questions | Free Answers
In worksheet on subtraction, all grade students can practice the questions on subtracting numbers with more than two digits. This exercise sheet on subtraction can be practiced by the students
How to Read a Large Number? | Place Value Chart | Reading Large Number
To read a large number easily, we split the number into groups. We separate the groups by using comma or a space between them. The grouping of places is done from the right. The first group is ones group it has 3 places from the right. The second and the third group

Related Concept

4th Grade Math Activities

From Expanded form of a Number to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Facebook X Pinterest WhatsApp Messenger

[?]Subscribe To This Site

$XML RSS$

Recent Articles

2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic
Nov 20, 24 01:00 PM
$2nd Grade Math Worksheet$
2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.
Read More
2nd Grade Measurement Worksheet | Measuring Length, Mass and Volume
Nov 20, 24 12:50 AM
In 2nd Grade Measurement Worksheet you will get different types of questions on measurement of length, measurement of weight (mass), measurement of capacity (volume), addition of length, addition of w…
Read More
2nd Grade Fractions Worksheet | Basic Concept of Fractions | Answers
Nov 20, 24 12:16 AM
$Divide the Collection into 4 Equal Parts$
In 2nd Grade Fractions Worksheet we will solve different types of problems on fractions, one-whole, one-half, one-third, one-fourth, three-fourth or s quarter. In a fraction, it is important that the…
Read More
2nd Grade Math Practice | Second Grade Math |2nd Grade Math Worksheets
Nov 18, 24 02:23 PM
In 2nd grade math practice you will get all types of examples on different topics along with the solutions. Second grade math games are arranged in such a way that students can learn math
Read More
Worksheet on Addition of Length | Word Problems on Addition of Length
Nov 17, 24 10:29 PM
Practice the third grade math worksheet on addition of length. This sheet provides different types of questions where you need to arrange the values of length under different columns to find their sum
Read More

E-mail Address

First Name

Then Don't worry — your e-mail address is totally secure. I promise to use it only to send you Math Only Math.