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Given:
- \( a = 2.03647 \)
- \( b \) is obtained by rounding \( a \) to the nearest hundredth.

### Step 1: Round \( a \) to the nearest hundredth
The hundredth place is the second digit after the decimal point.

- The digit in the hundredth place of \( a \) is 3.
- The digit in the thousandth place (next digit) is 6, which is 5 or greater. So, we round up the hundredth digit from 3 to 4.

Thus, \( b = 2.04 \).

### Step 2: Calculate \( b - a \)
We need to find \( b - a \).

\[
b - a = 2.04 - 2.03647 = 0.00353
\]

So, the correct answer is \( \boxed{C} \) (0.00353).

Would you like further details or have any questions about the solution? Here are some related questions to consider:

1. How do you determine which place to round to when rounding to a specific decimal place?
2. What happens when the digit right after the rounding digit is exactly 5?
3. How would you round a number like \( 2.03642 \) to the nearest hundredth?
4. What if \( a \) was rounded to the nearest thousandth instead? What would be \( b \)?
5. How does the difference between the original number and its rounded value change as you round to different decimal places?

**Tip:** Always check the digit immediately after the place to which you are rounding to decide whether to round up or down.

Given: a = 2.03647 and b is obtained by rounding off a to the nearest hundredth. Then b - a = ?

Learn how to round the number 2.03647 to the nearest hundredth and subtract the original number from the rounded value. This problem focuses on rounding concepts and decimal subtraction, suitable for students in Grades 5-7.

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