Arrange the following numbers in descending order :
199988, 1704382, 200175, 1702497, 201200, 1712040

Answer

To arrange the numbers 199988, 1704382, 200175, 1702497, 201200, and 1712040 in descending order, we will follow these steps:

### Step 1: Count the Number of Digits
First, we need to determine how many digits each number has:

- 199988 has 6 digits.
- 1704382 has 7 digits.
- 200175 has 6 digits.
- 1702497 has 7 digits.
- 201200 has 6 digits.
- 1712040 has 7 digits.

### Step 2: Compare the Number of Digits
Since the number with the most digits is the largest, we can see that the numbers with 7 digits are larger than those with 6 digits. The 7-digit numbers are:

- 1704382
- 1702497
- 1712040

### Step 3: Arrange the 7-Digit Numbers
Now, we will compare the 7-digit numbers:

1. **1704382**
2. **1702497**
3. **1712040**

To compare:
- The first digit is the same (1).
- The second digit is the same (7).
- The third digit is different (0 for 1704382 and 2 for 1702497). Since 2 is greater than 0, **1712040** is the largest.

So, the largest 7-digit number is **1712040**.

Next, we compare **1704382** and **1702497**:
- The first digit is the same (1).
- The second digit is the same (7).
- The third digit is the same (0).
- The fourth digit is different (4 for 1704382 and 2 for 1702497). Since 4 is greater than 2, **1704382** is larger than **1702497**.

Thus, the order of the 7-digit numbers from largest to smallest is:
1. **1712040**
2. **1704382**
3. **1702497**

### Step 4: Arrange the 6-Digit Numbers
Now, we will compare the 6-digit numbers:

1. **199988**
2. **200175**
3. **201200**

To compare:
- The first digit is different (1 for 199988, 2 for 200175, and 2 for 201200).
- The largest 6-digit number is **201200** (since 2 is greater than 1).

Next, we compare **200175** and **199988**:
- The first digit is different (2 for 200175 and 1 for 199988).
- Thus, **200175** is larger than **199988**.

So, the order of the 6-digit numbers from largest to smallest is:
1. **201200**
2. **200175**
3. **199988**

### Step 5: Combine All Numbers in Descending Order
Now we can combine both sets of numbers in descending order:

1. **1712040** (7 digits)
2. **1704382** (7 digits)
3. **1702497** (7 digits)
4. **201200** (6 digits)
5. **200175** (6 digits)
6. **199988** (6 digits)

### Final Answer
The numbers arranged in descending order are:
**1712040, 1704382, 1702497, 201200, 200175, 199988**

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