Assertion `:` The number 211.902 is expressed in expanded form as `2 xx 100 xx1 xx 10 xx 1 + 9 xx ( 1)/( 10) xx 2 xx ( 1)/( 100)`.
Reason `:` As we go from left to right, the multiplying factor becomes ` ( 1)/( 10)` of the previous factor.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the problem, we need to express the number 211.902 in its expanded form and analyze the assertion and reason provided.

### Step-by-Step Solution:

1. **Identify the Place Values**:
- The number 211.902 can be broken down into its place values:
- 2 is in the hundreds place (200)
- 1 is in the tens place (10)
- 1 is in the units place (1)
- 9 is in the tenths place (0.9 or 9/10)
- 0 is in the hundredths place (0/100)
- 2 is in the thousandths place (0.002 or 2/1000)

2. **Write the Expanded Form**:
- The expanded form of the number can be written as:
\[ 211.902 = 2 \times 100 + 1 \times 10 + 1 \times 1 + 9 \times \frac{1}{10} + 0 \times \frac{1}{100} + 2 \times \frac{1}{1000} \]
- Simplifying this gives:
\[ = 200 + 10 + 1 + 0.9 + 0 + 0.002 \]
- Therefore, the complete expanded form is:
\[ 211.902 = 200 + 10 + 1 + 0.9 + 0 + 0.002 \]

3. **Evaluate the Assertion**:
- The assertion states that the number 211.902 is expressed as:
\[ 2 \times 100 \times 1 \times 10 \times 1 + 9 \times \frac{1}{10} \times 2 \times \frac{1}{100} \]
- This is incorrect because the multiplication factors are not represented correctly in the expanded form. The correct form should involve addition of place values, not multiplication.

4. **Evaluate the Reason**:
- The reason states that as we go from left to right, the multiplying factor becomes \(\frac{1}{10}\) of the previous factor. This is true because each subsequent place value is indeed a factor of \(\frac{1}{10}\) of the previous one.

5. **Conclusion**:
- Since the assertion is false and the reason is true, we conclude that the correct answer is that the assertion is false but the reason is true.

### Final Answer:
- Assertion: False
- Reason: True