What is the value of 361 + 3.61 + 0.0361 (correct to four decimal places)?

Introduction / Context:
This question again focuses on decimal addition, but now with more digits after the decimal point. Being comfortable with four decimal places is useful in questions related to percentages, interest rates, and scientific style calculations where precision is important.

Given Data / Assumptions:

• We must evaluate 361 + 3.61 + 0.0361.
• The result must be expressed correct to four decimal places.
• All values are positive real numbers.

Concept / Approach:
The key idea is to line up decimal points and then add each column of digits from right to left. Writing each number with the same number of decimal places simplifies the process. Here, the smallest place value is ten thousandths, so we convert each number into a form with four decimal places before adding.

Step-by-Step Solution:
Step 1: Rewrite 361 as 361.0000, 3.61 as 3.6100, and 0.0361 remains 0.0361. Step 2: Add the ten thousandths place: 0 + 0 + 1 = 1. Step 3: Add the thousandths place: 0 + 0 + 6 = 6. Step 4: Add the hundredths place: 0 + 1 + 3 = 4. Step 5: Add the tenths place: 0 + 6 + 0 = 6. Step 6: Add the units place: 1 (from 361) + 3 (from 3.6100) + 0 = 4. Step 7: Add the tens and hundreds of the whole part: 6 tens and 3 hundreds simply give 60 and 300, so the total whole number part is 364. Step 8: Combining the whole and decimal parts, we obtain 364.6461.

Verification / Alternative check:
We can first add the whole numbers and then the decimals separately. Whole parts: 361 + 3 = 364. Decimal parts: 0.61 + 0.0361 = 0.6461. Adding these gives 364 + 0.6461 = 364.6461. This matches the earlier detailed calculation, confirming that the answer is consistent.

Why Other Options Are Wrong:
Option 364.6614 rearranges the decimal digits incorrectly and does not match proper column addition. Option 364.6416 also represents a misplacement of digits when summing the thousandths and ten thousandths places. Option 361.6461 comes from forgetting to add the 3 in 3.61 to the whole part. Option 374.6461 mistakenly increases the hundreds digit to 7 instead of 3 plus 0, leading to an inflated total.

Common Pitfalls:
Many learners rush through decimal addition and mix up the order of digits, especially when more than two decimal places are involved. Another common issue is treating 3.61 as 3.610 or 3.601 accidentally. Carefully rewriting all numbers with the same number of decimal digits before adding is a reliable way to avoid such mistakes.

Final Answer:
Hence, the value of 361 + 3.61 + 0.0361 is 364.6461 when written to four decimal places.