Writing Numbers Using Place Value Blocks – Class 2 & 3 Maths | CBSE & UP Board | GPN

Class 2 Class 3 CBSE UP Board

📘 What's inside:

1 What is a Place Value Chart
2 Reading Numbers from a Chart
3 Writing Numbers into a Chart
4 Place Value Blocks
5 Indian System — Lakhs & Crores
6 International System — Millions
7 Exam Questions

Concept 1 — What is a Place Value Chart?

Every digit in a number has two things: its face value (the digit itself) and its place value (what it is worth based on its position). A place value chart is a table that shows the position of each digit clearly.

Face Value vs Place Value — Let us observe:

In the number 347:
The digit 3 has face value 3, but place value = 300 (Hundreds).
The digit 4 has face value 4, but place value = 40 (Tens).
The digit 7 has face value 7, and place value = 7 (Ones). Same!

▶ How to Read a Place Value Chart

The chart has columns. Each column represents one place — Ones, Tens, Hundreds, etc.
Write one digit per column only. Never write two digits in one column.
If a place has no value, write 0 in that column.
Read the chart from left to right to get the full number.

Example: the number 4,572 in a place value chart

Thousands (Th)	Hundreds (H)	Tens (T)	Ones (O)
4	5	7	2

4000
Thousands

500
Hundreds

70
Tens

2
Ones

= 4,572

⚠ Common Mistake

Many students skip the zero when writing numbers like 305. They write only 3 and 5, missing the Tens column. Always write 0 for any empty place. 305 = 3 (Hundreds), 0 (Tens), 5 (Ones).

▶ Solved Example 1

Write the place value and face value of each digit in 6,038.

Th	H	T	O
6	0	3	8

1Digit 6 is in the Thousands place. Face value = 6. Place value = 6,000.
2Digit 0 is in the Hundreds place. Face value = 0. Place value = 0. (Zero has no value.)
3Digit 3 is in the Tens place. Face value = 3. Place value = 30.
4Digit 8 is in the Ones place. Face value = 8. Place value = 8.

6,038 = 6,000 + 0 + 30 + 8

▶ Solved Example 2

In the number 5,274, what is the place value of 2?

Th	H	T	O
5	2	7	4

1Write 5,274 in the chart: Th=5, H=2, T=7, O=4.
2The digit 2 is in the Hundreds column.
3Place value = 2 × 100 = 200.

Place value of 2 in 5,274 = 200 (Hundreds place)

✍ Practice — Concept 1

Q1 What is the place value of 7 in 3,715? ▼

Answer

Th	H	T	O
3	7	1	5

7 is in the Hundreds place.
Place value = 7 × 100 = 700

Q2 Write the face value and place value of each digit in 4,809. ▼

Answer

Th	H	T	O
4	8	0	9

4 → Thousands → Face value: 4, Place value: 4,000
8 → Hundreds → Face value: 8, Place value: 800
0 → Tens → Face value: 0, Place value: 0
9 → Ones → Face value: 9, Place value: 9

Q3 In 2,050, the digit 5 is in which place? What is its place value? ▼

Answer

Th	H	T	O
2	0	5	0

5 is in the Tens place.
Place value = 5 × 10 = 50

Q4 True or False: In 7,777, all four digits have the same face value but different place values. ▼

Answer

Th	H	T	O
7	7	7	7

True.
Face value of all 7s = 7 (same).
Place values: 7,000 | 700 | 70 | 7 (all different).

Concept 2 — Reading Numbers from a Place Value Chart

When digits are already placed in a chart, we read from left to right to form the number. We must include every digit — including zeros.

▶ Steps to Read from a Chart

Start from the leftmost column (highest place value).
Write down each digit in order from left to right.
Include all zeros — never skip them.
The digits written together form the number.

▶ Solved Example 3

Read the number from this chart and write it in figures and words:

Th	H	T	O
8	0	6	4

1Read left to right: Th=8, H=0, T=6, O=4.
2Do not skip the zero. Write: 8,064.
3In words: Eight thousand and sixty-four.

Number = 8,064 Eight thousand and sixty-four

▶ Solved Example 4

Two charts are shown. Which number is greater?

Chart A
Th	H	T	O
3	9	0	5

Chart B
Th	H	T	O
3	7	8	2

1Chart A = 3,905. Chart B = 3,782.
2Thousands digit: both have 3. Same → compare Hundreds.
3Hundreds: A has 9, B has 7. 9 > 7. So Chart A is greater.

Chart A (3,905) > Chart B (3,782)

✍ Practice — Concept 2

Q5 Read the number: Th=5, H=0, T=0, O=7. Write in figures and words. ▼

Answer

Th	H	T	O
5	0	0	7

Read left to right including zeros: 5,007
In words: Five thousand and seven

Q6 Compare: Chart A has Th=6, H=2, T=4, O=9. Chart B has Th=6, H=3, T=1, O=0. Which is greater? ▼

Answer Chart A = 6,249. Chart B = 6,310.
Thousands: both 6. Compare Hundreds: A=2, B=3. 3 > 2.
Chart B (6,310) is greater.

» Ever wondered how to write 4,872 in words? Head over to number names up to 9,999 and unlock the pattern, then put pen to paper with the free worksheet. Once you're comfortable, test your logical thinking with even and odd numbers and sort them out using the interactive practice sheet.

Concept 3 — Writing Numbers into a Place Value Chart

We can also work the other way — take a number and place each digit into the correct column of the chart.

▶ Steps to Write into a Chart

Start from the ones digit (rightmost digit) and place it in the Ones column.
Move left: next digit goes in Tens, then Hundreds, then Thousands.
If a place is empty, write 0 in that column.
Check: the digits read left to right must give back your original number.

▶ Solved Example 5

Write 7,306 in a place value chart.

1Start from the right. Ones digit = 6. Write 6 in O column.
2Next digit = 0. Write 0 in T column. Do not skip it.
3Next digit = 3. Write 3 in H column.
4Next digit = 7. Write 7 in Th column.

Th	H	T	O
7	3	0	6

7,306 placed correctly: Th=7, H=3, T=0, O=6

▶ Solved Example 6

Write 509 in a four-column place value chart.

1509 has only 3 digits. The Thousands column will be 0 (empty).
2From right: O=9, T=0, H=5, Th=0.

Th	H	T	O
0	5	0	9

509 in chart: Th=0, H=5, T=0, O=9

✍ Practice — Concept 3

Q7 Write 9,405 in a place value chart. State the place value of each digit. ▼

Answer

Th	H	T	O
9	4	0	5

9 → Th → place value 9,000
4 → H → place value 400
0 → T → place value 0
5 → O → place value 5

Q8 Write 600 in a four-column chart. How many zeros appear? ▼

Answer

Th	H	T	O
0	6	0	0

3 zeros appear (Th, T and O columns).
Only the Hundreds column has a non-zero digit.

Q9 A number has 3 in Thousands, 0 in Hundreds, 7 in Tens and 2 in Ones. Write the number. ▼

Answer

Th	H	T	O
3	0	7	2

Read left to right: 3,072

Concept 4 — Place Value Blocks

Place value blocks (also called Dienes blocks or base-ten blocks) are a visual way to understand how numbers are built. Each type of block represents a different place value.

▶ Types of Blocks

■ Unit cube — represents 1 (Ones).
■ Long rod (10 units) — represents 10 (Tens).
■ Flat square (100 units) — represents 100 (Hundreds).
■ Large cube (1000 units) — represents 1,000 (Thousands).

▶ Solved Example 7

The blocks show: 2 hundreds, 3 tens and 4 ones. What number do they represent?

Hundreds 2 × 100 = 200

Tens 3 × 10 = 30

Ones 4 × 1 = 4

12 hundreds = 200.
23 tens = 30.
34 ones = 4.
4Total = 200 + 30 + 4 = 234.

The blocks represent 234.

▶ Solved Example 8

How many tens blocks and ones blocks are needed to show 157?

1Write 157 in chart: H=1, T=5, O=7.
2We need 1 hundreds block, 5 tens blocks and 7 ones blocks.
3Check: 100 + 50 + 7 = 157.

1 hundred
= 100

5 tens
= 50

7 ones
= 7

= 157

1 hundreds block + 5 tens blocks + 7 ones blocks = 157

✍ Practice — Concept 4

Q10 Blocks show: 1 thousand, 2 hundreds, 0 tens, 8 ones. What is the number? ▼

Answer 1,000 + 200 + 0 + 8 = 1,208
In chart: Th=1, H=2, T=0, O=8.

Q11 How many hundreds, tens and ones blocks are needed for 346? ▼

Answer 346 → H=3, T=4, O=6.
3 hundreds blocks (= 300)
4 tens blocks (= 40)
6 ones blocks (= 6)
Total = 300 + 40 + 6 = 346.

Section Indian Place Value System — Lakhs & Crores

Concept 5 — Indian Place Value Chart (up to Crores)

In the Indian number system, we group digits differently from the international system. After the first three digits (ones period), we group in pairs of two from the right.

Crores Period		Lakhs Period		Thousands Period		Ones Period
Ten Crores (T.Cr)	Crores (Cr)	Ten Lakhs (T.L)	Lakhs (L)	Ten Thousands (T.Th)	Thousands (Th)	Hundreds (H)	Tens (T)	Ones (O)
10	1	10	1	10	1	100	10	1

Value represented by each column position

▶ Indian Comma Placement

First comma after 3 digits from the right: e.g. 4,572
Second comma after 2 more digits: e.g. 45,72,000
Third comma after 2 more digits: e.g. 4,57,20,000
Pattern: Cr, T.L L, T.Th Th, H T O

▶ Solved Example 9

Write 47,25,836 in the Indian place value chart and state the place value of each digit.

Lakhs Period		Thousands Period		Ones Period
T.L	L	T.Th	Th	H	T	O
4	7	2	5	8	3	6

14 is in Ten Lakhs place. Place value = 40,00,000.
27 is in Lakhs place. Place value = 7,00,000.
32 is in Ten Thousands place. Place value = 20,000.
45 is in Thousands place. Place value = 5,000.
58 → Hundreds = 800. 3 → Tens = 30. 6 → Ones = 6.

47,25,836 = 40,00,000 + 7,00,000 + 20,000 + 5,000 + 800 + 30 + 6

▶ Solved Example 10

A number has digits: T.L=3, L=0, T.Th=5, Th=2, H=0, T=9, O=4. Write the number in Indian format with commas.

T.L	L	T.Th	Th	H	T	O
3	0	5	2	0	9	4

1Read left to right: 3, 0, 5, 2, 0, 9, 4.
2Apply Indian commas: Lakhs period (T.L, L) | Thousands period (T.Th, Th) | Ones period (H, T, O).
3Number = 30,52,094.

Number = 30,52,094 (Thirty lakh fifty-two thousand and ninety-four)

✍ Practice — Indian System

Q12 Write 85,40,672 in the Indian place value chart. What is the place value of 5? ▼

Answer

T.L	L	T.Th	Th	H	T	O
8	5	4	0	6	7	2

5 is in the Lakhs place.
Place value of 5 = 5,00,000 (Five lakh)

Q13 Read and write the number: T.L=2, L=4, T.Th=0, Th=8, H=3, T=5, O=1. Write with Indian commas. ▼

Answer

T.L	L	T.Th	Th	H	T	O
2	4	0	8	3	5	1

24,08,351
Twenty-four lakh eight thousand three hundred and fifty-one.

Q14 In 1,05,47,230, what is the place value of 1? Which period does it belong to? ▼

Answer

Crores		Lakhs		Thousands		Ones
T.Cr	Cr	T.L	L	T.Th	Th	H	T	O
0	1	0	5	4	7	2	3	0

1 is in the Crores place.
Place value = 1,00,00,000 (One crore).
It belongs to the Crores period.

Let's talk about people, places and things! Explore proper and common nouns with clear examples and cement the concept using the free worksheet. Next, discover words for groups and feelings through collective and abstract nouns and reinforce with the accompanying practice sheet.
संज्ञा की गहराई में उतरें! जातिवाचक संज्ञा की पूरी व्याख्या पढ़ें और अभ्यास वर्कशीट से अभ्यास करें। फिर आगे बढ़ें द्रव्यवाचक संज्ञा पर और वर्कशीट के साथ अपनी समझ को जांचें।

Section International Place Value System — Millions & Billions

Concept 6 — International Place Value Chart (up to Billions)

In the International number system (used in most countries and in science), we always group digits in sets of three from the right, separated by commas.

Billions Period			Millions Period			Thousands Period			Ones Period
H.B	T.B	B	H.M	T.M	M	H.Th	T.Th	Th	H	T	O
100B	10B	1B	100M	10M	1M	100K	10K	1K	100	10	1

B = Billion | M = Million | K = Thousand

▶ International Comma Placement

Groups of three from the right, every time.
Pattern: B, M, Th, O — e.g. 1,234,567,890
1,000 = One thousand | 1,000,000 = One million | 1,000,000,000 = One billion

⚠ Indian vs International — Key Difference

Indian system: after first 3 digits, groups of 2. International system: always groups of 3. So the same number looks different: Indian = 47,25,836 International = 4,725,836 (Four million seven hundred twenty-five thousand eight hundred and thirty-six).

▶ Solved Example 11

Write 4,725,836 in the international place value chart. State the place value of 7.

Millions Period			Thousands Period			Ones Period
H.M	T.M	M	H.Th	T.Th	Th	H	T	O
0	0	4	7	2	5	8	3	6

14 is in the Millions place. Place value = 4,000,000.
27 is in the Hundred-Thousands place. Place value = 7 × 100,000 = 700,000.
3Remaining: 2 → 20,000. 5 → 5,000. 8 → 800. 3 → 30. 6 → 6.

Place value of 7 = 700,000 (Seven hundred thousand) | Hundred-Thousands place

▶ Solved Example 12

The same number is written in both systems. Match them:
Indian: 6,24,59,308 International: ?

1Remove Indian commas: digits are 6, 2, 4, 5, 9, 3, 0, 8 = 62459308.
2Apply international grouping (groups of 3 from right): 62,459,308.

Millions			Thousands			Ones
H.M	T.M	M	H.Th	T.Th	Th	H	T	O
0	6	2	4	5	9	3	0	8

Indian: 6,24,59,308 = International: 62,459,308 (Sixty-two million four hundred fifty-nine thousand three hundred and eight)

✍ Practice — International System

Q15 Write 9,045,200 in the international place value chart. State the place value of 9. ▼

Answer

Millions			Thousands			Ones
H.M	T.M	M	H.Th	T.Th	Th	H	T	O
0	0	9	0	4	5	2	0	0

9 is in the Millions place.
Place value = 9,000,000 (Nine million)

Q16 Convert Indian format to International: 3,54,72,819 ▼

Answer Remove Indian commas: 35472819
Group in 3s from right: 35,472,819
Thirty-five million four hundred seventy-two thousand eight hundred and nineteen.

Q17 Convert International to Indian: 12,500,750 ▼

Answer Remove international commas: 12500750
Apply Indian grouping (3, then 2, then 2 from right): 1,25,00,750
One crore twenty-five lakh seven hundred and fifty.

★ Key Points to Remember

Face value = the digit itself. Place value = digit × its position value.
Always write one digit per column. Empty places get a 0.
Place value blocks: ones (cyan), tens (gold), hundreds (green), thousands (orange).
Indian system: groups of 3, then 2, then 2 from right. Periods: Ones, Thousands, Lakhs, Crores.
International system: always groups of 3 from right. Periods: Ones, Thousands, Millions, Billions.
To convert between systems: remove all commas first, then regroup.

Exam Style — Full Topic

5 Questions on Place Value Charts & Blocks

Q1 In 8,407: (a) What is the place value of 4? (b) What is the face value of 0? (c) Write in expanded form. ▼

Answer

Th	H	T	O
8	4	0	7

(a) 4 is in Hundreds place. Place value = 400.
(b) Face value of 0 = 0 (face value is always the digit itself).
(c) 8,407 = 8,000 + 400 + 0 + 7

Q2 A chart shows: Th=0, H=3, T=9, O=2. Write the number. How many blocks of each type are needed? ▼

Answer

Th	H	T	O
0	3	9	2

Number = 392.
Blocks needed: 3 hundreds + 9 tens + 2 ones.
Check: 300 + 90 + 2 = 392.

Q3 Write 56,09,743 in the Indian place value chart and write the place value of each digit. ▼

Answer

T.L	L	T.Th	Th	H	T	O
5	6	0	9	7	4	3

5 → T.L → 50,00,000 6 → L → 6,00,000
0 → T.Th → 0 9 → Th → 9,000
7 → H → 700 4 → T → 40 3 → O → 3

Q4 Write the international number 3,204,810 in Indian format. Write it in words using both systems. ▼

Answer Digits: 3204810.
Indian format: 32,04,810
International words: Three million two hundred four thousand eight hundred and ten.
Indian words: Thirty-two lakh four thousand eight hundred and ten.

Q5 Two numbers: A = 4,28,650 and B = 4,29,350. Which is greater? Compare using place value charts. ▼

Answer

	T.L	L	T.Th	Th	H	T	O
A	4	2	8	6	5	0	0
B	4	2	9	3	5	0	0

T.L = 4, L = 2 → same for both. Compare T.Th: A=8, B=9. 9 > 8.
B (4,29,350) is greater than A (4,28,650).

📄 Free Worksheet

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