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.
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?
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
You might like these
Adding 5-digit Numbers with Regrouping | 5-digit Addition |Addition
We will learn adding 5-digit numbers with regrouping. We have learnt the addition of 4-digit numbers with regrouping and now in the same way we will do addition of 5-digit numbers with regrouping. We arrange the numbers one below the other in place value columns and then we
Subtraction without Regrouping |4-Digit, 5-Digit & 6-Digit Subtraction
We will learn subtracting 4-digit, 5-digit and 6-digit numbers without regrouping. We first arrange the numbers one below the other in place value columns and then subtract the digits under each column as shown in the following examples. 1. Subtract 3248 from 6589.
Worksheet on Word Problems on Addition and Subtraction Together | Ans
In 4th grade worksheet on word problems on addition and subtraction, all grade students can practice the questions on word problems based on addition and subtraction. This exercise sheet on
Rounding off Numbers | Nearest Multiple of 10 | Nearest Whole Number
Rounding off numbers are discussed here, where we need to round a number. (i) If we purchase anything and its cost is $12 and 23¢, the cost is rounded up to it’s nearest $ 12 and 23¢ is left. (ii) If we purchase another thing and its cost is $15.78. The cost is rounded up
Division of Two-Digit by a One-Digit Numbers | Dividing Larger Numbers
In division of two-digit by a one-digit numbers are discussed here step by step. How to divide 2-digit numbers by single-digit numbers?
Find the Missing Digits | Missing Digits in Addition and Subtraction
How to find the missing digits in the blank spaces? Add the ONES: 5 + 9 = 14 Regroup as 1 Ten and 4 Ones Add the TENS: 2 + 1 carry over = 3 Write 2 in the box to make 3 + 2 = 5 Add the HUNDREDS: 4
Number Worksheets | Practice Different Questions on Numbers | Answers
In number worksheets, students can practice different questions on numbers from printable free worksheets for grade 4 math on numbers. Write the number which is 1 more than 9? Write the number which
Worksheet on Expanded form of a Number | Expanded Form of a Number
Worksheet on expanded form of a number for fourth grade math questions to practice the expanded form according to the place values of its digit. 1. Write the expanded form of the following numbers
Subtraction | How to Subtract 2-digit, 3-digit, 4-digit Numbers?|Steps
The answer of a subtraction sum is called DIFFERENCE. How to subtract 2-digit numbers? Steps are shown to subtract 2-digit numbers.
4th Grade Multiplication Worksheet | Math Multiplication Worksheets
In 4th grade multiplication worksheet we will solve multiplication of 4-digit numbers, properties of multiplication, estimate the product and word problems on multiplication. I. Complete the given multiplication pyramids. First one is done for you. II. Fill in the blanks:
Related Concept
- Formation of Numbers.
- Finding Out the Numbers
- Names of the Numbers.
- Numbers Showing on Spike Abacus.
- 1 Digit Number on Spike Abacus.
- 2 Digits Number on Spike Abacus.
- 3 Digits Number on Spike Abacus.
- 4 Digits Number on Spike Abacus.
- 5 Digits Number on Spike Abacus.
- Large Number.
- Place Value Chart.
- Place Value.
- Problems Related to Place Value.
- 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.
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.
Recent Articles
-
Worksheets on Comparison of Numbers | Find the Greatest Number
Oct 10, 24 05:15 PM
In worksheets on comparison of numbers students can practice the questions for fourth grade to compare numbers. This worksheet contains questions on numbers like to find the greatest number, arranging… -
Counting Before, After and Between Numbers up to 10 | Number Counting
Oct 10, 24 10:06 AM
Counting before, after and between numbers up to 10 improves the child’s counting skills. -
Expanded Form of a Number | Writing Numbers in Expanded Form | Values
Oct 10, 24 03:19 AM
We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its… -
Place Value | Place, Place Value and Face Value | Grouping the Digits
Oct 09, 24 05:16 PM
The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know th… -
3-digit Numbers on an Abacus | Learning Three Digit Numbers | Math
Oct 08, 24 10:53 AM
We already know about hundreds, tens and ones. Now let us learn how to represent 3-digit numbers on an abacus. We know, an abacus is a tool or a toy for counting. An abacus which has three rods.
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.