Which of the following is the correct ?

Options

A. `2.2 lt 2.02 lt 2.002 lt 2.222`
B. `2.002 lt 2.02 lt 2.2 lt 2.222`
C. `2.02 lt 2.22 lt 2.002 lt 2.222`
D. None of these

Answer

To determine which of the following statements is correct regarding the decimal numbers, we will compare the given numbers step by step.

### Step-by-Step Solution:

1. **Identify the Numbers**: The numbers we need to compare are:
- 2.2
- 2.02
- 2.002
- 2.222

2. **Align the Decimal Points**: To compare these numbers accurately, we can align them by their decimal points:
```
2.200
2.020
2.002
2.222
```

3. **Compare the Whole Numbers**: First, we look at the whole number part (the part before the decimal). All numbers have the same whole number part, which is 2.

4. **Compare the Tenths Place**: Next, we compare the tenths place (the first digit after the decimal):
- 2.200 has 2 in the tenths place.
- 2.020 has 0 in the tenths place.
- 2.002 has 0 in the tenths place.
- 2.222 has 2 in the tenths place.

Here, we can see that 2.020 and 2.002 are less than 2.200 and 2.222.

5. **Compare the Hundredths Place**: Now, we compare the hundredths place (the second digit after the decimal):
- 2.200 has 0 in the hundredths place.
- 2.020 has 2 in the hundredths place.
- 2.002 has 0 in the hundredths place.
- 2.222 has 2 in the hundredths place.

This shows that 2.020 is greater than 2.002 but less than 2.200 and 2.222.

6. **Compare the Thousandths Place**: Finally, we look at the thousandths place (the third digit after the decimal):
- 2.200 has 0 in the thousandths place.
- 2.020 has 0 in the thousandths place.
- 2.002 has 2 in the thousandths place.
- 2.222 has 2 in the thousandths place.

Here, we see that 2.002 is less than both 2.200 and 2.020.

7. **Order the Numbers**: Based on the comparisons:
- The smallest number is **2.002**.
- The next is **2.020**.
- Then comes **2.200**.
- The largest is **2.222**.

8. **Conclusion**: The correct statement is:
- **2.002 is less than 2.020**, which is true.
- **2.2 is not less than 2.02**, which is false.
- **2.222 is not less than 2.222**, which is also false.

Thus, the correct answer is that **2.002 is less than 2.020**.