In the equation 54.?3 + 543 + 5.43 = 603.26, what digit should replace the question mark to make the decimal sum correct?

Introduction / Context:
This question focuses on decimal place value and basic arithmetic. You must determine the missing digit in a decimal number so that when all terms are added, the total matches a given value. Such problems check attention to detail and understanding of how digits contribute to the overall sum.

Given Data / Assumptions:

• Unknown number: 54.?3, where ? is a single digit from 0 to 9.
• Equation: 54.?3 + 543 + 5.43 = 603.26.
• We must find the digit that replaces the question mark.

Concept / Approach:
We treat 54.?3 as a decimal number with hundredths position unknown. Write it as 54.x3, where x is the unknown digit in the tenths place. We then form an equation for the total sum and solve for x so that the right hand side equals 603.26. The method uses simple addition and subtraction of decimals.

Step-by-Step Solution:
Step 1: Represent the unknown number as 54.x3 where x is the unknown digit. Step 2: The equation is 54.x3 + 543 + 5.43 = 603.26. Step 3: Combine the known terms first: 543 + 5.43 = 548.43. Step 4: Now the equation becomes 54.x3 + 548.43 = 603.26. Step 5: Subtract 548.43 from both sides to isolate 54.x3. Step 6: 603.26 − 548.43 = 54.83. Step 7: Therefore 54.x3 must equal 54.83. The digit in the tenths place is 8, and the hundredths place is 3, so x = 8.

Verification / Alternative check:
Substitute 8 for the question mark and recompute the total. The number becomes 54.83. Now calculate 54.83 + 543 + 5.43. First 54.83 + 543 = 597.83. Then 597.83 + 5.43 = 603.26, which matches the right hand side exactly. This confirms that the digit 8 makes the equation correct.

Why Other Options Are Wrong:
If the digit were 6, we would get 54.63, and the sum would be 54.63 + 548.43 = 603.06, which is too small.
If the digit were 1, we would get 54.13, giving 54.13 + 548.43 = 602.56, still not equal to 603.26.
If the digit were 9, we would get 54.93, giving 54.93 + 548.43 = 603.36, which is too large.

Common Pitfalls:
Some learners misalign decimal places when adding or subtracting, or they confuse the position of the tenths and hundredths digits. Others may try random guessing without verifying with proper addition. Always work symbolically, isolate the unknown term, and then calculate systematically to avoid such mistakes.

Final Answer:
The missing digit that makes the equation correct is 8.