Compute the value of 25.7322 − 15.7322. What is the exact result of this subtraction?

Introduction:
This is a straightforward problem involving subtraction of decimal numbers. Such questions test your ability to align decimal points correctly and subtract without making place value mistakes, which is an essential arithmetic skill.

Given Data / Assumptions:

• We must evaluate: 25.7322 − 15.7322.
• Both numbers have four decimal places.
• We are asked for the exact result.

Concept / Approach:
When subtracting decimals, the key is to align the decimal points so that digits of the same place value (ones, tenths, hundredths, thousandths, ten-thousandths) line up vertically. Then, subtract column by column just as with whole numbers. Because the decimal parts in this problem are identical, the subtraction simplifies nicely.

Step-by-Step Solution:
Step 1: Write the numbers aligned by decimal point:25.732215.7322Step 2: Subtract the decimal parts. Since 0.7322 − 0.7322 = 0, the decimal portion cancels out entirely.Step 3: Now subtract the whole number parts: 25 − 15 = 10.Step 4: Combine the results. There is no remaining decimal part, so the final answer is exactly 10.0000, which we usually write as 10.

Verification / Alternative check:
We can also see that 25.7322 − 15.7322 = (15.7322 + 10) − 15.7322. The 15.7322 terms cancel, leaving 10, which confirms the earlier calculation. Another quick check is to think of the subtraction as removing the same fractional part from both numbers, leaving only the difference in whole numbers.

Why Other Options Are Wrong:
9.64, 11.64, 10.5, and 12 do not match the exact difference. Any decimal result would imply that the decimal parts were not identical. Since the digits after the decimal point are exactly the same in both numbers, the subtraction must result in a whole number. Only 10 satisfies this reasoning and matches the detailed calculation.

Common Pitfalls:
Common mistakes include misaligning the decimal points, subtracting the wrong digits, or incorrectly assuming a non zero decimal result because of the presence of decimal digits. Remember that if two numbers have identical decimal parts, subtracting them will cancel the decimal, leaving the difference of the whole number parts alone.

Final Answer:
The exact value of 25.7322 − 15.7322 is 10.