Using the digits 1,2,5,7,9 and 0, form the following
the smallest 8-digit number repeating zero thrice
For each of the aboe numbers, place commas for easy reading, make the place value chart in both the systems. Indian and International, give number names in both the systems and write the expanded forms.

Answer

To solve the question step by step, we will follow these instructions:

### Step 1: Form the smallest 8-digit number using the digits 1, 2, 5, 7, 9, and 0, with 0 repeating thrice.
- The smallest 8-digit number must start with the smallest non-zero digit, which is 1.
- Since we need to include three zeros, we will place them next.
- After placing the zeros, we will arrange the remaining digits (2, 5, 7, 9) in ascending order.

**Smallest 8-digit number:** 10002579

### Step 2: Write the number with commas for easy reading.
- In the Indian system, we place commas after every two digits starting from the right after the first three digits.
- In the International system, we place commas after every three digits starting from the right.

**Indian System:** 1,00,02,579
**International System:** 100,025,79

### Step 3: Create the place value chart for both systems.

**Indian System:**
- Crore: 1
- Lakh: 0
- Thousand: 0
- Hundred: 2
- Ten: 5
- Unit: 7
- Zeroes: 0, 0, 0 (three zeros)

**International System:**
- Millions: 0
- Hundred Thousands: 1
- Ten Thousands: 0
- Thousands: 0
- Hundreds: 2
- Tens: 5
- Units: 7
- Zeroes: 0

### Step 4: Write the number names in both systems.

**Indian System:** One Crore Two Thousand Five Hundred Seventy-Nine
**International System:** One Hundred Thousand Twenty-Five Thousand Seven Hundred Seventy-Nine

### Step 5: Write the expanded form of the number.

**Expanded Form:**
- In the Indian system:
1 Crore + 0 Lakh + 0 Thousand + 2 Hundred + 5 Ten + 7 One + 0 + 0 + 0
= 1,00,00,000 + 0 + 0 + 200 + 50 + 7 + 0 + 0 + 0
= 1,00,00,000 + 200 + 50 + 7

- In the International system:
1 Hundred Thousand + 0 + 0 + 2 Hundred + 5 Ten + 7 One
= 1,00,000 + 0 + 0 + 200 + 50 + 7
= 1,00,000 + 200 + 50 + 7

### Final Answers:
- **Smallest 8-digit number:** 10002579
- **Indian System:** 1,00,02,579
- **International System:** 100,025,79
- **Number Names:** One Crore Two Thousand Five Hundred Seventy-Nine (Indian); One Hundred Thousand Twenty-Five Thousand Seven Hundred Seventy-Nine (International)
- **Expanded Form:** 1,00,00,000 + 200 + 50 + 7 (Indian); 1,00,000 + 200 + 50 + 7 (International)