For the following numbers. Place commas at appropriate places. Make the place value chart. Give the number name and write the expanded form.
a. 674309 b. 3794012 c. 76067123 d. 403287615 e. 72354098

Answer

Let's solve the question step by step for each number:

### a. Number: 674309

**Step 1: Place Commas**
- Start from the right, place a comma after every three digits.
- The number becomes: **6,74,309**

**Step 2: Place Value Chart**
- 6 in the lakh place
- 7 in the ten thousand place
- 4 in the thousand place
- 3 in the hundred place
- 0 in the ten place
- 9 in the unit place

| Place Value | Crores | Lakhs | Ten Thousands | Thousands | Hundreds | Tens | Units |
|------------------|--------|-------|---------------|-----------|----------|------|-------|
| Value | 0 | 6 | 7 | 4 | 3 | 0 | 9 |

**Step 3: Number Name**
- The number name is: **Six Lakh Seventy-Four Thousand Three Hundred Nine**

**Step 4: Expanded Form**
- The expanded form is:
- \( 6 \times 100000 + 7 \times 10000 + 4 \times 1000 + 3 \times 100 + 0 \times 10 + 9 \times 1 \)
- Which simplifies to:
- \( 600000 + 70000 + 4000 + 300 + 0 + 9 \)

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### b. Number: 3794012

**Step 1: Place Commas**
- The number becomes: **37,94,012**

**Step 2: Place Value Chart**
| Place Value | Crores | Lakhs | Ten Thousands | Thousands | Hundreds | Tens | Units |
|------------------|--------|-------|---------------|-----------|----------|------|-------|
| Value | 0 | 3 | 7 | 9 | 4 | 0 | 12 |

**Step 3: Number Name**
- The number name is: **Thirty-Seven Lakh Ninety-Four Thousand Twelve**

**Step 4: Expanded Form**
- The expanded form is:
- \( 3 \times 1000000 + 7 \times 100000 + 9 \times 10000 + 4 \times 1000 + 0 \times 100 + 12 \)
- Which simplifies to:
- \( 3000000 + 700000 + 90000 + 4000 + 0 + 12 \)

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### c. Number: 76067123

**Step 1: Place Commas**
- The number becomes: **76,06,71,23**

**Step 2: Place Value Chart**
| Place Value | Crores | Lakhs | Ten Thousands | Thousands | Hundreds | Tens | Units |
|------------------|--------|-------|---------------|-----------|----------|------|-------|
| Value | 7 | 6 | 0 | 6 | 7 | 1 | 23 |

**Step 3: Number Name**
- The number name is: **Seventy-Six Crore Six Lakh Seventy-One Thousand Twenty-Three**

**Step 4: Expanded Form**
- The expanded form is:
- \( 7 \times 10000000 + 6 \times 1000000 + 0 \times 100000 + 6 \times 10000 + 7 \times 1000 + 1 \times 100 + 23 \)
- Which simplifies to:
- \( 70000000 + 6000000 + 0 + 60000 + 7000 + 100 + 23 \)

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### d. Number: 403287615

**Step 1: Place Commas**
- The number becomes: **40,32,87,615**

**Step 2: Place Value Chart**
| Place Value | Crores | Lakhs | Ten Thousands | Thousands | Hundreds | Tens | Units |
|------------------|--------|-------|---------------|-----------|----------|------|-------|
| Value | 4 | 0 | 3 | 2 | 8 | 7 | 615 |

**Step 3: Number Name**
- The number name is: **Forty Crore Thirty-Two Lakh Eighty-Seven Thousand Six Hundred Fifteen**

**Step 4: Expanded Form**
- The expanded form is:
- \( 4 \times 10000000 + 0 \times 1000000 + 3 \times 100000 + 2 \times 10000 + 8 \times 1000 + 7 \times 100 + 615 \)
- Which simplifies to:
- \( 40000000 + 0 + 300000 + 20000 + 8000 + 700 + 615 \)

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### e. Number: 72354098

**Step 1: Place Commas**
- The number becomes: **72,35,40,98**

**Step 2: Place Value Chart**
| Place Value | Crores | Lakhs | Ten Thousands | Thousands | Hundreds | Tens | Units |
|------------------|--------|-------|---------------|-----------|----------|------|-------|
| Value | 7 | 2 | 3 | 5 | 4 | 0 | 98 |

**Step 3: Number Name**
- The number name is: **Seventy-Two Crore Thirty-Five Lakh Forty Thousand Ninety-Eight**

**Step 4: Expanded Form**
- The expanded form is:
- \( 7 \times 10000000 + 2 \times 1000000 + 3 \times 100000 + 5 \times 10000 + 4 \times 1000 + 0 \times 100 + 98 \)
- Which simplifies to:
- \( 70000000 + 2000000 + 300000 + 50000 + 4000 + 0 + 98 \)

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