Using the digits 1,2,5,7,9 and 0, form the following
th smallest 6-digit number without repeating the digits
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 problem of forming the smallest 6-digit number using the digits 1, 2, 5, 7, 9, and 0 without repeating any digits, we will follow these steps:

### Step 1: Identify the digits
The available digits are 1, 2, 5, 7, 9, and 0.

### Step 2: Determine the smallest 6-digit number
To form the smallest 6-digit number, we need to arrange the digits in ascending order, keeping in mind that the first digit cannot be 0 (as it would not be a 6-digit number).

1. The smallest digit is 1. We will use 1 as the first digit.
2. The next smallest digit is 0, but we cannot place 0 in the first position. So we will choose the next smallest digit, which is 2.
3. After 1 and 2, the next smallest digits are 5, 7, and 9. We will arrange these in ascending order.

Thus, the smallest 6-digit number we can form is **1, 0, 2, 5, 7, 9**.

### Step 3: Write the number with commas for easy reading
The number can be written as **1, 0, 2, 5, 7, 9**.

### Step 4: Create the place value chart
#### Indian System:
| Place Value | Lakh | 10,000 | 1,000 | 100 | 10 | 1 |
|---------------|------|--------|-------|-----|----|---|
| Number | 1 | 0 | 2 | 5 | 7 | 9 |

#### International System:
| Place Value | Million | 100,000 | 10,000 | 1,000 | 100 | 10 | 1 |
|---------------|---------|---------|--------|-------|-----|----|---|
| Number | 0 | 1 | 0 | 2 | 5 | 7 | 9 |

### Step 5: Write the number names
- **Indian System:** One lakh, two thousand, five hundred seventy-nine.
- **International System:** One hundred two thousand five hundred seventy-nine.

### Step 6: Write the expanded form
The expanded form of the number 1, 0, 2, 5, 7, 9 is:
- **1, 0, 2, 5, 7, 9 = 1 × 100000 + 0 × 10000 + 2 × 1000 + 5 × 100 + 7 × 10 + 9 × 1**

### Summary of the solution:
The smallest 6-digit number formed is **1, 0, 2, 5, 7, 9**.

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