What is the value of 729 + 72.9 + 7.29 (correct to two decimal places)?

Introduction / Context:
This question checks your skill with adding whole numbers and decimal numbers together. Such mixed sums are very common in data interpretation, profit and loss, and general arithmetic sections of aptitude tests, so it is important to keep track of place values accurately.

Given Data / Assumptions:

• We must compute the sum 729 + 72.9 + 7.29.
• All numbers are positive.
• The answer is required correct to two decimal places.

Concept / Approach:
When adding whole numbers and decimal numbers, it is best to align them by their decimal point. The whole number can be written with a decimal point and trailing zeros, like 729.00. Then we add column wise, starting from the smallest place value on the right. Finally, we round the result to the required number of decimal places if necessary.

Step-by-Step Solution:
Step 1: Write the numbers as 729.00, 72.90, and 7.29 to align the decimals. Step 2: Add the hundredths place: 0 + 0 + 9 = 9. Step 3: Add the tenths place: 0 + 9 + 2 = 11, write 1 in the tenths place and carry 1 to the units place. Step 4: Add the units place: 9 (from 729) + 2 (from 72) + 7 (from 7) + carried 1 = 19, write 9 in the units place and carry 1 to the tens place. Step 5: Add the tens place: 2 (from 729) + 7 (from 72) + carried 1 = 10, write 0 in tens and carry 1 to the hundreds place. Step 6: Add the hundreds place: 7 (from 729) + carried 1 = 8. Step 7: The final result is 809.19, which is already correct to two decimal places.

Verification / Alternative check:
We can group the terms in a simpler way: 729 + 72.9 = 801.9. Then 801.9 + 7.29 = 809.19. This quick mental verification confirms that our detailed column addition is correct. The consistency between both methods increases confidence in the final answer.

Why Other Options Are Wrong:
Option 809.29 arises from misadding the tenths or hundredths place. Option 802.19 suggests an error in adding the tens digit of 72.9. Option 729.19 ignores adding 72.9 and 7.29 properly. Option 809.09 results from mishandling the hundredths place when adding 0.90 and 0.29. Only 809.19 matches both systematic calculation and mental checking.

Common Pitfalls:
Typical mistakes include not aligning decimal points, forgetting to carry from the tenths to the units place, or dropping decimal digits when converting whole numbers like 729 into 729.00. Careful alignment and stepwise addition prevent these errors and are essential for speed and accuracy in competitive exams.

Final Answer:
Therefore, the value of 729 + 72.9 + 7.29 is 809.19 when written to two decimal places.