Number system — In the number 65231, determine the product of the place value and the face value of the digit 5. Show careful reasoning based on the decimal place positions.

Introduction / Context:
This problem checks understanding of face value and place value in the decimal number system. The face value of a digit is the digit itself, while the place value depends on its position in the number. Multiplying these correctly is a common aptitude skill used in digit and place-based questions.

Given Data / Assumptions:

• Number considered: 65231.
• Digit of interest: 5.
• Decimal place positions from right: ones, tens, hundreds, thousands, ten thousands.

Concept / Approach:
Face value = the digit itself. Place value = digit * positional weight. For thousands place, the positional weight is 1000. The product requested is (place value of the digit) * (face value of the digit).

Step-by-Step Solution:
Identify the position of 5 in 65231: it sits in the thousands place.Place value of 5 = 5 * 1000 = 5000.Face value of 5 = 5.Required product = 5000 * 5 = 25000.

Verification / Alternative check:
Rewrite 65231 as 6*10000 + 5*1000 + 2*100 + 3*10 + 1. The term involving 5 is 5000, confirming the place value. Multiplying by the face value 5 again yields 25000.

Why Other Options Are Wrong:

• 28000 / 27000 / 26000 / 20000: Each assumes an incorrect place (ten thousands or hundreds) or mis-multiplies the values.

Common Pitfalls:
Confusing face value with place value; assuming 5 is in ten thousands or hundreds by misreading the number; forgetting to multiply by 1000 for the thousands place.

Final Answer:
25000