Place Value — Indian and International System

Mathematics

Class 5 | CBSE, NCERT & ICSE

Learning Objectives

Understand the difference between place value and face value
Find the place value of any digit in 7–8 digit numbers
Use the Indian Place Value Chart (Ones to Crores)
Use the International Place Value Chart (Ones to Ten Millions)
Write numbers in expanded form using place values
Convert expanded form back to standard form
Understand the special role of zero as a placeholder
Compare how place values are described in both systems

Introduction — What Is Place Value?

Look at the number 555. All three digits are the same — they are all 5. But do they all have the same value? No! The 5 on the right means 5 ones, the middle 5 means 5 tens (50), and the 5 on the left means 5 hundreds (500). The value of a digit depends on its position (place) in the number. This is called place value.

In Class 5, we work with numbers up to 8 digits (crores). Understanding place value helps us read, write, compare, and perform operations on large numbers correctly. Without place value, we could never tell the difference between 50 and 5,00,000!

In this chapter, we will learn how to find the place value and face value of every digit in a number, and how the same number is described in the Indian and International systems.

Place Value vs Face Value

Every digit in a number has two values — its face value and its place value. These are different concepts and students often confuse them. Let us understand each clearly.

Definitions

Face Value: The face value of a digit is the digit itself, no matter where it is placed in the number. It never changes. The face value of 7 is always 7, whether it is in the ones place, thousands place, or crores place.
Place Value: The place value of a digit is the digit multiplied by the value of its position. It depends on WHERE the digit sits in the number. Place Value = Face Value × Value of the Position.

Example 1: Find the face value and place value of each digit in the number 4,83,625.

Digit	Position	Face Value	Place Value
4	Lakhs	4	4 × 1,00,000 = 4,00,000
8	Ten Thousands	8	8 × 10,000 = 80,000
3	Thousands	3	3 × 1,000 = 3,000
6	Hundreds	6	6 × 100 = 600
2	Tens	2	2 × 10 = 20
5	Ones	5	5 × 1 = 5

Example 2: In the number 7,56,03,841, find the place value and face value of the digit 5.

The digit 5 is in the Ten Lakhs place.
Face Value of 5 = 5
Place Value of 5 = 5 × 10,00,000 = 50,00,000 (Fifty lakh)

Image needed: A visual showing the same digit (e.g., 6) placed in different positions of a number, with arrows showing how its place value changes: 6 in ones = 6, 6 in tens = 60, 6 in hundreds = 600, 6 in thousands = 6000, etc. Use a staircase or ladder visual.
Style: Colourful staircase/ladder diagram, child-friendly, each step labelled with place name and value
Size: 700×450px

Think About It: The digit 3 appears twice in 3,00,03,000. But its place values are completely different! The first 3 (from left) is in the Crores place (value = 3,00,00,000), while the second 3 is in the Thousands place (value = 3,000). Same face value, very different place values!

Place Value Chart — Indian System

In the Indian Number System, the places from right to left are grouped as follows. Remember: the first group has 3 digits, and every group after that has 2 digits.

Crores (Cr)	Ten Lakhs (TL)	Lakhs (L)	Ten Thousands (TTh)	Thousands (Th)	Hundreds (H)	Tens (T)	Ones (O)
1,00,00,000	10,00,000	1,00,000	10,000	1,000	100	10	1
Crores Period		Lakhs Period		Thousands Period			Ones

Image needed: Indian Place Value Chart with all 8 columns (Cr, TL, L, TTh, Th, H, T, O). The number 3,72,45,689 is placed in the chart with each digit in its column. Periods (Crores, Lakhs, Thousands, Ones) are colour-coded. Each column header shows the place name and its value.
Style: Clean flat table-style illustration, bright colour-coded columns, child-friendly
Size: 800×400px

Worked Example — Finding Place Values (Indian System)

Example: Place the number 3,72,45,689 in the Indian place value chart and find the place value of each digit.

Cr	TL	L	TTh	Th	H	T	O
3	7	2	4	5	6	8	9

Place values:

3 is in Crores place → Place value = 3 × 1,00,00,000 = 3,00,00,000
7 is in Ten Lakhs place → Place value = 7 × 10,00,000 = 70,00,000
2 is in Lakhs place → Place value = 2 × 1,00,000 = 2,00,000
4 is in Ten Thousands place → Place value = 4 × 10,000 = 40,000
5 is in Thousands place → Place value = 5 × 1,000 = 5,000
6 is in Hundreds place → Place value = 6 × 100 = 600
8 is in Tens place → Place value = 8 × 10 = 80
9 is in Ones place → Place value = 9 × 1 = 9

Example: What is the place value of 7 in 3,72,45,689?

Step 1: Identify the position of 7 → 7 is in the Ten Lakhs place.
Step 2: Multiply the digit by the value of its position → 7 × 10,00,000 = 70,00,000

Answer: The place value of 7 in 3,72,45,689 is 70,00,000 (Seventy lakh).

Place Value Chart — International System

In the International Number System, digits are grouped in sets of 3 from the right. The places from right to left are:

Ten Millions (TM)	Millions (M)	Hundred Thousands (HTh)	Ten Thousands (TTh)	Thousands (Th)	Hundreds (H)	Tens (T)	Ones (O)
10,000,000	1,000,000	100,000	10,000	1,000	100	10	1
Millions Period		Thousands Period			Ones Period

Image needed: International Place Value Chart with all 8 columns (TM, M, HTh, TTh, Th, H, T, O). The number 37,245,689 is placed in the chart. Periods (Millions, Thousands, Ones) are colour-coded. Each column header shows place name and value.
Style: Clean flat table-style illustration, bright colour-coded columns, child-friendly
Size: 800×400px

Worked Example — Finding Place Values (International System)

Example: Place the number 37,245,689 in the International place value chart and find the place value of each digit.

TM	M	HTh	TTh	Th	H	T	O
3	7	2	4	5	6	8	9

Place values:

3 is in Ten Millions place → Place value = 3 × 10,000,000 = 30,000,000
7 is in Millions place → Place value = 7 × 1,000,000 = 7,000,000
2 is in Hundred Thousands place → Place value = 2 × 100,000 = 200,000
4 is in Ten Thousands place → Place value = 4 × 10,000 = 40,000
5 is in Thousands place → Place value = 5 × 1,000 = 5,000
6 is in Hundreds place → Place value = 6 × 100 = 600
8 is in Tens place → Place value = 8 × 10 = 80
9 is in Ones place → Place value = 9 × 1 = 9

Think About It: Notice that the number 3,72,45,689 (Indian) and 37,245,689 (International) are the same number! The digit 7 has the same actual value in both systems — but we describe it differently. In the Indian system, 7 is in "Ten Lakhs" place. In the International system, 7 is in "Millions" place. Both mean 70,00,000 = 7,000,000!

Finding the Place Value of a Digit — Step by Step

Follow these three simple steps to find the place value of any digit in a number:

Steps to Find Place Value

Step 1: Identify the digit whose place value you need to find.
Step 2: Count its position from the right (ones = 1st, tens = 2nd, hundreds = 3rd, etc.) or place the number in a place value chart.
Step 3: Multiply the digit by the value of its position.
Place Value = Digit × Position Value

Example 1: What is the place value of 4 in 5,04,23,716?

Step 1: The digit is 4.
Step 2: Counting from right: 5,04,23,716 → The digit 4 is in the Lakhs place.
Step 3: Place value = 4 × 1,00,000 = 4,00,000

Answer: The place value of 4 is 4,00,000 (Four lakh).

Example 2: What is the place value of 9 in 2,93,50,842?

Step 1: The digit is 9.
Step 2: 2,93,50,842 → The digit 9 is in the Ten Lakhs place.
Step 3: Place value = 9 × 10,00,000 = 90,00,000

Answer: The place value of 9 is 90,00,000 (Ninety lakh).

Example 3: What is the place value of 6 in 6,18,47,253?

Step 1: The digit is 6.
Step 2: 6,18,47,253 → The digit 6 is in the Crores place.
Step 3: Place value = 6 × 1,00,00,000 = 6,00,00,000

Answer: The place value of 6 is 6,00,00,000 (Six crore).

Example 4 (International): What is the place value of 5 in 45,321,608?

Step 1: The digit is 5.
Step 2: 45,321,608 → The digit 5 is in the Millions place.
Step 3: Place value = 5 × 1,000,000 = 5,000,000

Answer: The place value of 5 is 5,000,000 (Five million).

Example 5: In the number 8,07,60,452, the digit 0 appears twice. What is the place value of each 0?

First 0 (from left): 8,07,60,452 → 0 is in Ten Lakhs place → 0 × 10,00,000 = 0
Second 0 (from left): 8,07,60,452 → 0 is in Thousands place → 0 × 1,000 = 0

The place value of 0 is always 0, regardless of its position!

Place Value and Face Value — Comparison Table

Let us take the number 5,84,60,372 and compare the face value and place value of every digit:

Digit	Position (Indian)	Face Value	Place Value
5	Crores	5	5 × 1,00,00,000 = 5,00,00,000
8	Ten Lakhs	8	8 × 10,00,000 = 80,00,000
4	Lakhs	4	4 × 1,00,000 = 4,00,000
6	Ten Thousands	6	6 × 10,000 = 60,000
0	Thousands	0	0 × 1,000 = 0
3	Hundreds	3	3 × 100 = 300
7	Tens	7	7 × 10 = 70
2	Ones	2	2 × 1 = 2

Key Differences — Face Value vs Place Value

Face Value	Place Value
It is the digit itself	It is the digit × position value
It never changes	It changes based on position
Face value of 7 is always 7	Place value of 7 can be 7, 70, 700, 7000, etc.
Face value of 0 is 0	Place value of 0 is always 0
Does not depend on position	Completely depends on position

Expanded Form Using Place Values

The expanded form of a number shows it as the sum of the place values of all its digits. Each digit is multiplied by its position value, and all the products are added together.

How to Write Expanded Form

Write each digit × its place value
Connect them with + signs
You may skip digits that are 0 (since 0 × anything = 0)

Example 1: Write 6,35,42,871 in expanded form.

6,35,42,871 = 6 × 1,00,00,000 + 3 × 10,00,000 + 5 × 1,00,000 + 4 × 10,000 + 2 × 1,000 + 8 × 100 + 7 × 10 + 1 × 1

= 6,00,00,000 + 30,00,000 + 5,00,000 + 40,000 + 2,000 + 800 + 70 + 1

Example 2: Write 9,04,00,506 in expanded form.

9,04,00,506 = 9 × 1,00,00,000 + 0 × 10,00,000 + 4 × 1,00,000 + 0 × 10,000 + 0 × 1,000 + 5 × 100 + 0 × 10 + 6 × 1

= 9,00,00,000 + 4,00,000 + 500 + 6
(We skip the terms with 0 value when writing the simplified expanded form.)

Example 3 (International): Write 52,307,014 in expanded form.

52,307,014 = 5 × 10,000,000 + 2 × 1,000,000 + 3 × 100,000 + 0 × 10,000 + 7 × 1,000 + 0 × 100 + 1 × 10 + 4 × 1

= 50,000,000 + 2,000,000 + 300,000 + 7,000 + 10 + 4

Standard Form from Expanded Form

The reverse process — going from expanded form back to the regular number — is called writing in standard form. Add all the place values together.

Example 1: Write in standard form:
7 × 1,00,00,000 + 2 × 10,00,000 + 0 × 1,00,000 + 8 × 10,000 + 5 × 1,000 + 3 × 100 + 4 × 10 + 9 × 1

= 7,00,00,000 + 20,00,000 + 0 + 80,000 + 5,000 + 300 + 40 + 9
= 7,20,85,349

Example 2: Write in standard form:
4 × 1,00,00,000 + 6 × 1,00,000 + 1 × 1,000 + 8 × 1

= 4,00,00,000 + 6,00,000 + 1,000 + 8
= 4,06,01,008
(Notice: positions with no value get 0 — Ten Lakhs, Ten Thousands, Hundreds, and Tens are all 0.)

Example 3 (International): Write in standard form:
8 × 10,000,000 + 3 × 1,000,000 + 5 × 100,000 + 2 × 1,000 + 7 × 10

= 80,000,000 + 3,000,000 + 500,000 + 2,000 + 70
= 83,502,070

Think About It: When converting expanded form to standard form, if a place is "missing" from the sum, you must put 0 in that position. For example, if there is no "Ten Thousands" term, the Ten Thousands digit must be 0.

The Role of Zero — Zero as a Placeholder

Zero is a very special digit. It has a unique role in our number system:

Special Properties of Zero

The face value of 0 is 0.
The place value of 0 is always 0, no matter where it is placed.
Zero acts as a placeholder — it holds a position so that other digits stay in their correct places.
Without zero, numbers would lose their meaning. Removing a zero completely changes the number!

Example — Why Zero Matters:

Consider the number 5,07,02,030.
- If we remove the 0 from Ten Lakhs place: 57,02,030 → completely different number!
- If we remove the 0 from Thousands place: 5,07,2,030 → wrong structure!

Zero does not add any value, but it holds the place so the other digits are in the correct position.

In 5,07,02,030:
- 0 in Ten Lakhs place → place value = 0 × 10,00,000 = 0
- 0 in Thousands place → place value = 0 × 1,000 = 0
- 0 in Ones place → place value = 0 × 1 = 0

Even though all three 0s have place value = 0, they are essential for the number to be correct!

Image needed: Visual showing how removing zero changes a number. Show the number 3,05,000 on top. Below it, show what happens if zero is removed: the digits shift and the number becomes 35,000 (completely different!). Use crossed-out zero and sliding arrows to show digits moving.
Style: Before/after comparison, child-friendly, colourful digits with arrows
Size: 700×350px

Quick Check:
- Face value of 0 in 8,06,90,010 = 0
- Place value of 0 in 8,06,90,010 (in the Hundreds place) = 0
- Place value of 0 in 8,06,90,010 (in the Lakhs place) = 0
- Is 0 important in this number? Yes! Without it, the number would collapse.

Comparing Place Values in Both Systems

The same number can be described using either the Indian or International system. The digit has the same actual value but is named differently depending on the system. Let us see how:

Example: Take the number 4,56,78,923 (Indian) = 45,678,923 (International).
Let us compare how we describe the digit 4 in both systems:

Digit	Indian System — Position Name	Indian Place Value	International — Position Name	International Place Value
4	Crores	4 × 1,00,00,000 = 4,00,00,000	Ten Millions	4 × 10,000,000 = 40,000,000
5	Ten Lakhs	5 × 10,00,000 = 50,00,000	Millions	5 × 1,000,000 = 5,000,000
6	Lakhs	6 × 1,00,000 = 6,00,000	Hundred Thousands	6 × 100,000 = 600,000
7	Ten Thousands	7 × 10,000 = 70,000	Ten Thousands	7 × 10,000 = 70,000
8	Thousands	8 × 1,000 = 8,000	Thousands	8 × 1,000 = 8,000
9	Hundreds	9 × 100 = 900	Hundreds	9 × 100 = 900
2	Tens	2 × 10 = 20	Tens	2 × 10 = 20
3	Ones	3 × 1 = 3	Ones	3 × 1 = 3

Important Observations

The actual value (the number itself) is the SAME in both systems: 4,00,00,000 = 40,000,000.
Ones, Tens, Hundreds, Thousands, and Ten Thousands places have the same names in both systems.
The difference starts from the 6th position: Lakhs (Indian) = Hundred Thousands (International).
Ten Lakhs (Indian) = Millions (International).
Crores (Indian) = Ten Millions (International).

Key Words

Term	Meaning
Place Value	The value of a digit based on its position in the number (digit × position value)
Face Value	The digit itself, regardless of its position in the number
Placeholder	A zero that holds a position in a number without adding value
Expanded Form	A number written as the sum of the place values of all its digits
Standard Form	The normal way of writing a number (e.g., 4,56,78,923)
Period	A group of digits separated by commas (Ones, Thousands, Lakhs, Crores)
Indian System	Number system used in India — groups of 3, then 2, then 2 digits
International System	Number system used worldwide — groups of 3 digits each
Crore	1,00,00,000 — equal to Ten Million in International system
Lakh	1,00,000 — equal to Hundred Thousand in International system
Million	1,000,000 — equal to Ten Lakh in Indian system

Key Points to Remember

Place value = Face value × Value of the position. It tells you how much a digit is worth based on where it sits.
Face value = The digit itself. It never changes no matter where the digit is placed.
The place value of 0 is always 0, regardless of its position. But zero is crucial as a placeholder!
In the Indian system, places are: Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores.
In the International system, places are: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions.
Lakhs (Indian) = Hundred Thousands (International)
Ten Lakhs (Indian) = Millions (International)
Crores (Indian) = Ten Millions (International)
The expanded form of a number = sum of all place values of its digits.
When a digit repeats in a number (e.g., 5 in 5,05,50,500), each occurrence has a different place value based on its position.
Removing a zero from a number changes the number completely — zero holds the position of other digits.

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. In 6,84,37,215, which digit is in the ten-lakhs place?

Reading from the right in the Indian system: 6=crore, 8=ten lakh, 4=lakh…

2. What is the face value of 5 in 4,53,89,120?

Face value is always just the digit itself — 5.

3. The place value of 3 in 3,00,00,000 is:

3 is in the crores place, so its place value is 3 crore = 3,00,00,000.

4. In the International system, 8 in 58,436,000 is in which place?

58,436,000 → 5 = ten millions, 8 = millions.

5. What is the place value of 7 in 27,45,983? (digits only)

7 is in the lakhs place → place value = 7,00,000.

6. Write the expanded value of the digit 3 in 6,38,42,105 (digits only):

3 is in the ten-lakhs place → 30,00,000. (In 6,38,42,105: 6 crore, 3 ten-lakh…)

7. How many lakhs make 5 lakh? (a warm-up) — write the number of lakhs in 5,00,000:

5,00,000 = 5 lakh.

8. What is the place value of the digit 4 in 2,47,318? (digits only)

In 2,47,318 the 4 is in the ten-thousands place → place value = 40,000.

Practice Questions

A. Write the place value of the underlined digit:

1. 4,58,23,190 (digit 8)

2. 7,63,50,412 (digit 7)

3. 2,90,45,678 (digit 0)

4. 8,12,34,567 (digit 4)

5. 3,45,67,890 (digit 9)

6. 6,00,05,003 (digit 5)

B. Write the face value of the underlined digit:

1. 9,45,67,823

2. 5,38,20,741

3. 1,00,00,006

4. 2,78,91,345

C. Write in expanded form:

1. 7,23,45,681

2. 3,08,06,005

3. 9,50,00,420

4. 1,11,11,111

D. Write in standard form from expanded form:

1. 5 × 1,00,00,000 + 3 × 10,00,000 + 7 × 1,00,000 + 2 × 10,000 + 9 × 1,000 + 4 × 100 + 6 × 10 + 8 × 1

2. 2 × 1,00,00,000 + 4 × 1,00,000 + 3 × 100 + 1 × 1

3. 8 × 10,000,000 + 6 × 1,000,000 + 1 × 10,000 + 5 × 100 + 2 × 1

4. 4 × 1,00,00,000 + 4 × 10,00,000 + 4 × 1,00,000 + 4 × 10,000 + 4 × 1,000 + 4 × 100 + 4 × 10 + 4 × 1

E. Fill in the blanks:

1. The place value of a digit depends on its in the number.

2. The face value of 9 in 9,87,65,432 is .

3. The place value of 0 is always regardless of its position.

4. In the Indian system, the place after Ten Lakhs is .

5. In the International system, the place after Hundred Thousands is .

F. True or False:

1. The face value of a digit changes based on its position.

2. The place value of 5 in 5,00,000 is 5,00,000.

3. Zero has no role in a number since its place value is always 0.

4. 1 Crore in the Indian system = 10 Million in the International system.

5. The place value of a digit is always greater than its face value.

G. Choose the correct answer (MCQ):

1. The place value of 6 in 2,63,45,891 is:

a) 6 b) 6,000 c) 60,00,000 d) 6,00,000

2. Which digit has both face value and place value the same?

a) Tens place digit b) Ones place digit c) Hundreds place digit d) Thousands place digit

3. The face value of 8 in 8,08,08,808 is:

a) 8,00,00,000 b) 80,000 c) 800 d) 8

4. In 4,07,50,326, how many zeros are there and what is the sum of their place values?

a) 1 zero, sum = 0 b) 2 zeros, sum = 0 c) 2 zeros, sum = 10,00,000 d) 3 zeros, sum = 0

H. Word Problems:

1. Arjun's father has ₹5,34,28,760 in his bank account. What is the place value of 3 in this amount? Write it in words.

2. The population of Rajasthan is approximately 7,89,00,000. What is the place value of 7 in this number? What is the face value of 7?

3. ISRO's rocket fuel costs ₹2,05,40,000 per launch. Meena says the place value of 5 is 5. Sita says the place value of 5 is 5,00,000. Who is correct and why?

4. The distance from Delhi to Chennai by road is approximately 2,175 km. Ravi says "the place value of 2 is 2." His teacher says "the place value of 2 is 2,000." Who is correct? Explain the difference between face value and place value in this context.

Activity — Place Value Detective!

Play this game with a partner or family member:

Write any 7-digit or 8-digit number on a piece of paper.
Ask your partner to point to any digit in the number.
Your partner must tell both the face value and the place value of that digit within 10 seconds!
If they get it right, they earn 1 point. If they can also name the place in the International system, they get a bonus point!
Take turns. The player with the most points after 10 rounds wins!

Challenge Round: Include numbers with zeros! Finding the place value of a digit next to a zero is tricky because the zero can confuse the counting.

Round	Number	Digit Chosen	Face Value	Place Value	Points
1
2
3
4
5

Want to review the lesson again?

Mathematics

Place Value — Indian and International System

Class 5 | CBSE / NCERT / ICSE

Name: Class: Date:

Learning Objectives

Understand the difference between place value and face value
Find the place value of any digit in 7–8 digit numbers
Use Indian and International Place Value Charts
Write numbers in expanded form and convert back to standard form
Understand zero as a placeholder

Introduction — What Is Place Value?

In the number 555, all digits are 5, but their values are different: 500, 50, and 5. The value of a digit depends on its position in the number. This is called place value. Place value helps us read, write, and compare large numbers correctly.

Place Value vs Face Value

Face Value: The digit itself — never changes. Face value of 7 is always 7.
Place Value: Digit × Value of its position. Changes with position. Place Value of 7 in Lakhs = 7,00,000.

Example: In the number 4,83,625:
• Digit 4 in Lakhs → Face Value = 4, Place Value = 4,00,000
• Digit 8 in Ten Thousands → Face Value = 8, Place Value = 80,000
• Digit 3 in Thousands → Face Value = 3, Place Value = 3,000
• Digit 6 in Hundreds → Face Value = 6, Place Value = 600
• Digit 2 in Tens → Face Value = 2, Place Value = 20
• Digit 5 in Ones → Face Value = 5, Place Value = 5

[Image: Visual showing digit 6 at different positions — 6 in ones=6, tens=60, hundreds=600, thousands=6000 — staircase diagram]

Place Value Chart — Indian System

Cr	TL	L	TTh	Th	H	T	O
1,00,00,000	10,00,000	1,00,000	10,000	1,000	100	10	1

[Image: Indian Place Value Chart with number 3,72,45,689 placed in columns, colour-coded periods]

Place Value Chart — International System

TM	M	HTh	TTh	Th	H	T	O
10,000,000	1,000,000	100,000	10,000	1,000	100	10	1

[Image: International Place Value Chart with number 37,245,689 placed in columns, colour-coded periods]

Example: Place value of each digit in 37,245,689 (same number, International):
3 → Ten Millions = 30,000,000 | 7 → Millions = 7,000,000 | 2 → Hundred Thousands = 200,000
4 → Ten Thousands = 40,000 | 5 → Thousands = 5,000 | 6 → Hundreds = 600
8 → Tens = 80 | 9 → Ones = 9

Same number, different names: Lakhs = Hundred Thousands | Ten Lakhs = Millions | Crores = Ten Millions

Finding Place Value — Step by Step

Steps: 1. Identify the digit. 2. Find its position. 3. Multiply: Place Value = Digit × Position Value.

Example 1: Place value of 4 in 5,04,23,716 → 4 is in Lakhs place → 4 × 1,00,000 = 4,00,000
Example 2: Place value of 9 in 2,93,50,842 → 9 is in Ten Lakhs place → 9 × 10,00,000 = 90,00,000
Example 3: Place value of 6 in 6,18,47,253 → 6 is in Crores place → 6 × 1,00,00,000 = 6,00,00,000
Example 4 (Int'l): Place value of 5 in 45,321,608 → 5 is in Millions → 5 × 1,000,000 = 5,000,000

Place Value and Face Value — Comparison

For the number 5,84,60,372:

Digit	Position	Face Value	Place Value
5	Crores	5	5,00,00,000
8	Ten Lakhs	8	80,00,000
4	Lakhs	4	4,00,000
6	Ten Thousands	6	60,000
0	Thousands	0	0
3	Hundreds	3	300
7	Tens	7	70
2	Ones	2	2

Expanded Form Using Place Values

Rule: Write each digit × its place value. Add them all together. Skip zeros.

Example 1: 6,35,42,871 = 6×1,00,00,000 + 3×10,00,000 + 5×1,00,000 + 4×10,000 + 2×1,000 + 8×100 + 7×10 + 1×1
Example 2: 9,04,00,506 = 9×1,00,00,000 + 4×1,00,000 + 5×100 + 6×1 (zeros skipped)
Example 3 (Int'l): 52,307,014 = 5×10,000,000 + 2×1,000,000 + 3×100,000 + 7×1,000 + 1×10 + 4×1

Standard Form from Expanded Form

Example 1: 7×1,00,00,000 + 2×10,00,000 + 8×10,000 + 5×1,000 + 3×100 + 4×10 + 9×1 = 7,20,85,349
Example 2: 4×1,00,00,000 + 6×1,00,000 + 1×1,000 + 8×1 = 4,06,01,008 (missing places get 0)

The Role of Zero — Placeholder

Properties of Zero:
• Face value of 0 = 0 always | Place value of 0 = 0 always
• Zero holds a position so other digits stay correct
• Removing a 0 changes the number completely!

Example: In 5,07,02,030: Removing 0 from Ten Lakhs gives 57,02,030 — wrong number!
All three 0s have place value = 0, but they are essential as placeholders.

[Image: Visual showing how removing zero from 3,05,000 changes it to 35,000 — before/after with arrows]

Comparing Place Values in Both Systems

Digit in 4,56,78,923	Indian Position	International Position	Value (same!)
4	Crores	Ten Millions	4,00,00,000 = 40,000,000
5	Ten Lakhs	Millions	50,00,000 = 5,000,000
6	Lakhs	Hundred Thousands	6,00,000 = 600,000
7	Ten Thousands	Ten Thousands	70,000 = 70,000

Key Words

Term	Meaning
Place Value	Digit × value of its position
Face Value	The digit itself (never changes)
Placeholder	Zero that holds a position
Expanded Form	Sum of place values of all digits
Standard Form	Normal way of writing a number
Indian System	Groups: 3, 2, 2 (Cr, L, Th, Ones)
International System	Groups: 3, 3, 3 (M, Th, Ones)

Key Points:
• Place value = Face value × Position value
• Face value never changes; place value depends on position
• Place value of 0 = always 0, but zero is essential as placeholder
• Lakhs = Hundred Thousands | Ten Lakhs = Millions | Crores = Ten Millions
• Ones place digit has same face value and place value
• Expanded form = sum of all (digit × place value)

Practice Questions

A. Write the place value of the underlined digit:

1. 4,58,23,190 (digit 8)

2. 7,63,50,412 (digit 7)

3. 2,90,45,678 (digit 0)

4. 8,12,34,567 (digit 4)

5. 3,45,67,890 (digit 9)

6. 6,00,05,003 (digit 5)

B. Write the face value of the underlined digit:

1. 9,45,67,823

2. 5,38,20,741

3. 1,00,00,006

4. 2,78,91,345

C. Write in expanded form:

1. 7,23,45,681

2. 3,08,06,005

3. 9,50,00,420

4. 1,11,11,111

D. Write in standard form from expanded form:

1. 5×1,00,00,000 + 3×10,00,000 + 7×1,00,000 + 2×10,000 + 9×1,000 + 4×100 + 6×10 + 8×1

2. 2×1,00,00,000 + 4×1,00,000 + 3×100 + 1×1

3. 8×10,000,000 + 6×1,000,000 + 1×10,000 + 5×100 + 2×1

4. 4×1,00,00,000 + 4×10,00,000 + 4×1,00,000 + 4×10,000 + 4×1,000 + 4×100 + 4×10 + 4×1

E. Fill in the blanks:

1. The place value of a digit depends on its in the number.

2. The face value of 9 in 9,87,65,432 is .

3. The place value of 0 is always regardless of its position.

4. In the Indian system, the place after Ten Lakhs is .

5. In the International system, the place after Hundred Thousands is .

F. True or False:

1. The face value of a digit changes based on its position.

2. The place value of 5 in 5,00,000 is 5,00,000.

3. Zero has no role in a number since its place value is always 0.

4. 1 Crore in the Indian system = 10 Million in the International system.

5. The place value of a digit is always greater than its face value.

G. Choose the correct answer (MCQ):

1. The place value of 6 in 2,63,45,891 is:

a) 6 b) 6,000 c) 60,00,000 d) 6,00,000

2. Which digit has both face value and place value the same?

a) Tens place b) Ones place c) Hundreds place d) Thousands place

3. The face value of 8 in 8,08,08,808 is:

a) 8,00,00,000 b) 80,000 c) 800 d) 8

4. In 4,07,50,326, how many zeros are there and what is the sum of their place values?

a) 1 zero, sum=0 b) 2 zeros, sum=0 c) 2 zeros, sum=10,00,000 d) 3 zeros, sum=0

H. Word Problems:

1. Arjun's father has ₹5,34,28,760 in his bank account. What is the place value of 3 in this amount?

2. The population of Rajasthan is approximately 7,89,00,000. What is the place value of 7? What is the face value of 7?

3. ISRO's rocket fuel costs ₹2,05,40,000. Meena says the place value of 5 is 5. Sita says it is 5,00,000. Who is correct?

4. The distance from Delhi to Chennai is approximately 2,175 km. Ravi says "the place value of 2 is 2." His teacher says "it is 2,000." Who is correct?

Activity — Place Value Detective!

Play with a partner: Write a 7-8 digit number. Your partner picks any digit and tells its face value and place value within 10 seconds. Bonus point for naming the place in the International system!

Round	Number	Digit	Face Value	Place Value	Points
1
2
3
4
5

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